<p>U doktorskoj disertaciji je prikazan postupak optimizacije podzemne mreže<br />za potrebe izgradnje beogradskog metroa. U postupku optimizacije kori&scaron;ćen<br />je metod prethodne ocene tačnosti. Na osnovu građevinskih standarda<br />izvr&scaron;en je proračun zahtevane tačnosti proboja tunela, kao osnovnog<br />kriterijuma tačnosti za razvijanje podzemne tunelske mreže. U postupku<br />optimizacije analizirani su različiti planovi opažanja, kao i dobijeni rezultati<br />prethodne analize za svaki plan pojedinačno. Na osnovu zadatog kriterijuma<br />maksimalne poprečene gre&scaron;ke proboja tunela usvojen je konačan plan<br />opažanja.</p> / <p>The docotoral thesis presents an optimization method of the underground<br />network for the construction of the Belgrade metro. In the process of<br />optimization, method of preanalysis has been used. Based on the<br />construction standards, the calculation of the required breakthrough<br />accuracy, as the fundamental criteria of accuracy for the development of the<br />underground tunnel network, has been made. In the process of optimization<br />different plans of observations have been analyzed, as well as the results<br />obtained from the preanalysis for each plan individually. Based on the<br />required criteria of maximal transverse error of the tunnel breakthrough, the<br />final plan of observations has been adopted.</p>

<p>U okviru doktorske disertacije ispitana je mogućnost proizvodnje<br />fermentisanog mlečnog napitka uz primenu različitih vrsta i koncentracija<br />nekonvencionalnog startera čajne gljive: a) nativnog inokuluma-I<br />(10% i 15%) b) koncentrovanog mikrofiltracijom - MFI (10% i 15%) i c)<br />koncentrovanog uparavanjem - UPI (1,5%, 3,0%, 10% i 15%). Varijante<br />fermentisanog mlečnog napitka dobijene su kori&scaron;ćenjem mleka sa 0,9%<br />i 2,2% mlečne masti. Za pobolj&scaron;anje fizičko-hemijskih i teksturalnih<br />karakteristika proizvoda u mleko pre inokulacije dodato je 0,02% enzima<br />transglutaminaze (aktiviran na 40&deg;C, a posle 2 sata je inaktiviran na<br />80&deg;C, 1 minut). Fermentacija mleka (pri temperaturi 42&deg;C) uz kori&scaron;ćenje<br />inokuluma čajne gljive praćena je do postizanja pH vrednosti 4,5.<br />Nakon proizvodnje analizirana je nutritivna vrednost fermentisanih<br />mlečnih napitaka: sadržaj masti, proteina, laktoze, galaktoze, glukoze,<br />fruktoze, mlečne i sirćetne kiseline, etanola, vitamina (B1, B2, B6 i<br />C), minerala (Ca, Mg, K, Na, Pb, Cd, Cu, Zn) i masnih kiselina. Sadržaj<br />odabranih komponenata u napicima praćen je tokom 10 dana skladi&scaron;tenja.<br />Fizičko-hemijske osobine (kiselost, sinerezis i sposobnost vezivanja<br />vode), teksturalne karakteristike (čvrstoća, konzistencija, kohezivnost i<br />indeks viskoziteta) i viskozitet uzoraka praćeni su nakon proizvodnje i<br />posle 10 dana skladi&scaron;tenja. Ukupan broj bakterija sirćetne kiseline (BSK)<br />i kvasaca u fermentisanim napicima analiziran je nakon proizvodnje i<br />tokom skladi&scaron;tenja. Varijante fermentisanih mlečnih napitaka senzorno<br />su ocenjene nakon proizvodnje.<br />Na osnovu rezultata ispitivanja utvrđeno je da fermentacija mleka<br />uz primenu nekonvencionalnog startera čajne gljive predstavlja složen<br />biohemijski proces pri čemu fermentacija traje od 9 do 12 sati i prosečno<br />je dva puta duža od fermentacije mleka u proizvodnji probiotskog i<br />tradicionalnog jogurta. Sadržaj laktoze tokom fermentacije mleka manji<br />je prosečno za 19,6% u odnosu na sadržaj laktoze u mleku. Uzorci<br />proizvedeni sa nativnim inokulumom uz primenu transglutaminaze i<br />koncentrata proteina surutke imaju za 15% niži sadržaj laktoze, a uzorak<br />15% I za 2% niži sadržaj u odnosu na uzorak 10% I. Uzorci proizvedeni<br />sa 10% MFI i 15% MFI imaju za 11%, odnosno 21% niži sadržaj laktoze<br />nakon proizvodnje u poređenju sa odgovarajućim uzorcima proizvedenim<br />uz primenu nativnog inokuluma. Sniženje sadržaja laktoze je<br />praćeno povećanjem sadržaja galaktoze i L-mlečne kiseline u svim uzorcima.<br />D-mlečna kiselina, sirćetna kiselina i etanol zastupljeni su u veoma<br />malim koncentracijama.<br />Imajući u vidu značaj vitamina C u ishrani i količinu detektovanu<br />u fermentisanom mlečnom napitku, konzumiranjem 500 g napitka<br />dobijenog primenom čajne gljive mogu da se zadovolje dnevne potrebe<br />za vitaminom C.<br />Tokom proizvodnje fermentisanih napitaka sadržaj vitamina B1<br />poraste za 5,09%, vitamina B2 za 2,65% i B6 za 2,03% u odnosu na<br />mleko. U fermentisanom mlečnom napitku iz mleka sa 2,2% masti<br />sadržaj vitamina B6 je povećan 24,76% u odnosu na sadržaj u polaznom<br />mleku. Fermentisani mlečni napici proizvedeni primenom čajne<br />gljive iz mleka sa 0,9% i 2,2% masti sa dodatkom 10% inokuluma<br />čajne gljive sadrže najvi&scaron;e vitamina B2 koji iznosi 108 (&mu;g/100g), odnosno<br />136 (&mu;g/100g). Mikrobiolo&scaron;ki sastav napitaka se razlikuje u zavisnosti<br />od vrste i sastava kori&scaron;ćenog inokuluma. Najveći broj BSK<br />(4,5 &middot; 104ćelija/mL) i kvasaca (9 &middot; 104 ćelija/mL) je u uzorku 10% MFI,<br />dok je manji u napitku 10% I (BSK: kvasci= 4,05 &middot; 104: 4,5 &middot; 104).<br />Dodatkom transglutaminaze u minimalnoj koncentraciji od<br />0,02% postižu se znatno bolje fizičko-hemijske i reolo&scaron;ke karakteristike<br />fermentisanih mlečnih napitaka dobijenih iz mleka sa 0,9% masti.<br />Generalno posmatrano, kori&scaron;ćenjem 10% nativnog inokuluma za<br />proizvodnju napitaka iz mleka sa 0,9% i 2,2% masti dobijaju se proizvodi<br />optimalnih hemijskih, mikrobiolo&scaron;kih i senzornih karakteristika.<br />Funkcionalni fermentisani mlečni napici proizvedeni uz primenu različitih<br />vrsta i koncentracija čajne gljive su proizvodi visoke nutritivne<br />vrednosti namenjeni različitim kategorijama potro&scaron;ača.</p> / <p> The possibility of fermented milk beverages manufacture<br /> by applying non-convenctional starter culture - tea fungus<br /> inoculum: a) natural inoculum (10% and 15%); b) concentrated<br /> by microfiltration (10% i 15%); c) concentrated by evaporation<br /> (1.5% and 3.0%) have been investigated. All fermented milk samples<br /> were produced from milk of 0.9% and 2.2 % fat content.<br /> Improvement of rheological properties of low fat fermented milk<br /> products by addition of enzyme transglutaminase (TG) was<br /> achieved. Transglutaminase (Activa MP, Ajinomoto Co. Inc.,<br /> Hamburg, Germany) was activated in milk at 40&deg;C for 2 hours,<br /> then it was inactivated by high temperature (80&deg;C for 1 minute)<br /> prior to fermentation. After cooling to optimal temperature<br /> (42&deg;C), chosen starter culture was added in milk. In all cases<br /> fermentation stopped when the pH=4.5 was reached.<br /> Nutritive characteristics of samples: content of proteins,<br /> lactose, galactose, glucose, fructose, lactic and acetic acid, ethanol,<br /> vitamins (B1, B2, B6 and C), minerals (Ca, Mg, K, Na, Pb,<br /> Cd, Cu, Zn) and total fatty acids content were analysed after<br /> production. Selected components were determined after 10 days<br /> of storage. Physico-chemical characteristics (acidity, syneresis,<br /> water-holding capacity), textural characteristics (firmness,<br /> consistency, cohessivnes, and index of viscosity) and viscosity<br /> were measured at 5&deg;C after production and during 10 days of<br /> storage.<br /> On the basis of the obtained results it can be concluded<br /> that milk fermentation lasted from 9 to 12 hours and is two times<br /> longer compared to fermentation during probiotic and traditional<br /> yoghurt production. Lactose content decreased during fermentation<br /> for 19.6% compared to milk. Higher transformation of lactose<br /> was determined in samples produced by using microfiltration<br /> inoculum. Decreasing of lactose content affected the increased<br /> galactose and L-lactic acid content. Content of D-lactic acid,<br /> acetic acid and ethanol were detected in low concentrations. High<br /> concentration of ascorbic acid in beverage contributed that 500 g<br /> fermented milk beverage could fullfill recommended daily intake<br /> for vitamin C. Sample produced from milk of 2.2% fat content<br /> using 10% natural inoculum contained the highest concentration<br /> of vitamin B2 &ndash; 136 (&mu;g/100g).<br /> The highest total cell count of acetic acid bacteria was<br /> 4.5 &middot; 104 cfu/ml and yeasts 9 &middot; 104 cfu/ml in samples produced by<br /> using 10% microfiltrated inoculum. Sample produced from milk<br /> of 0.9% fat content by applying 10% natural inoculum had also<br /> high number of acetic acid bacteria and yeasts in ratio 4.05 &middot; 104 :<br /> 4.5 &middot; 104.<br /> The sample having tea fungus concentrated inoculum<br /> and transglutaminase had the best textural characteristics. Fermented<br /> dairy beverages produced by 0.02% TG application had<br /> much better textural characteristics than those without TG.<br /> Generaly, fermented dairy drinks produced from milk of<br /> 0.9 and 2.2% fat content with addition of natural inoculum in<br /> concentration of 10% showed optimal sensory, nutritive and rheological<br /> characteristics.<br /> Therefore, fermented dairy drinks produced with tea<br /> fungus inoculum could be classified as high valuable functional<br /> food intended for all consumer categories.</p>

<p>U disertaciji su analizirani armiranobetonski ravanski nosači<br />primenom metode pritisnutih štapova i zatega. Optimizacija nosača<br />urađena je diskretnom topološkom otimizacijom kojom se pun nosač<br />zamenjuje ekvivalentnim rešetkastim. Dat je predlog algoritamskog<br />dobijanja Strut-and-Tie modela koji je implementiran u program sopstvene<br />izrade pod nazivom &bdquo;ST method&ldquo;. Provera pouzdanosti predloženog<br />algoritma utvrđena je primerima iz referentne literature, sopstvenim<br />eksperimentalnim ispitivanjem i numeričkom analizom u komercijalnim<br />programima. Rezulatati analiza su pokazali da se predloženi algoritam u<br />programu &bdquo;ST method&ldquo; može koristiti za dobijanje Strut-and-Tie modela i<br />njihovo dimenzionisanje i da se pri odabiru nekih modela mora koristiti<br />inženjersko iskustvo.</p> / <p>In dissertation thesis, reinforced concrete plane members have been analyzed by<br />the Strut-and-Tie method. Optimizing of the members is made by discrete<br />topological otimization which replaces full member with equivalent truss system.<br />Algorithmic manner of Strut-and-Tie model obtaining has been suggested, which<br />is implemented in the program of an own creation called &quot;ST method&quot;. The<br />reliability of the proposed algorithm is determined by the examples from reference<br />literature, an own experimental test and numerical analysis in commercial<br />programs. The results of the analysis showed that the proposed algorithm in the<br />&quot;ST method&quot; can be used to obtain Strut-and-tie models and their dimensioning<br />and that in certain models, the engineering experience must be used.</p>

<p>The problem under consideration is an unconstrained optimization&nbsp;problem with the objective function in the form of mathematical ex-pectation. The expectation is with respect to the random variable that represents the uncertainty. Therefore, the objective &nbsp;function is in fact deterministic. However, nding the analytical form of that objective function can be very dicult or even impossible. This is the reason why the sample average approximation is often used. In order to obtain reasonable good approximation of the objective function, we have to use relatively large sample size. We assume that the sample is generated at the beginning of the optimization process and therefore we can consider this sample average objective function as the deterministic one. However, applying some deterministic method on that sample average function from the start can be very costly. The number of evaluations of the function under expectation is a common way of measuring the cost of an algorithm. Therefore, methods that vary the sample size throughout the optimization process are developed. Most of them are trying to determine the optimal dynamics of increasing the sample size.</p><p>The main goal of this thesis is to develop the clas of methods that&nbsp;can decrease the cost of an algorithm by decreasing the number of&nbsp;function evaluations. The idea is to decrease the sample size whenever&nbsp;it seems to be reasonable - roughly speaking, we do not want to impose&nbsp;a large precision, i.e. a large sample size when we are far away from the&nbsp;solution we search for. The detailed description of the new methods&nbsp;<br />is presented in Chapter 4 together with the convergence analysis. It&nbsp;is shown that the approximate solution is of the same quality as the&nbsp;one obtained by dealing with the full sample from the start.</p><p>Another important characteristic of the methods that are proposed&nbsp;here is the line search technique which is used for obtaining the sub-sequent iterates. The idea is to nd a suitable direction and to search&nbsp;along it until we obtain a sucient decrease in the &nbsp;function value. The&nbsp;sucient decrease is determined throughout the line search rule. In&nbsp;Chapter 4, that rule is supposed to be monotone, i.e. we are imposing&nbsp;strict decrease of the function value. In order to decrease the cost of&nbsp;the algorithm even more and to enlarge the set of suitable search directions, we use nonmonotone line search rules in Chapter 5. Within that chapter, these rules are modied to t the variable sample size framework. Moreover, the conditions for the global convergence and the R-linear rate are presented.&nbsp;</p><p>In Chapter 6, numerical results are presented. The test problems&nbsp;are various - some of them are academic and some of them are real&nbsp;world problems. The academic problems are here to give us more&nbsp;insight into the behavior of the algorithms. On the other hand, data&nbsp;that comes from the real world problems are here to test the real&nbsp;applicability of the proposed algorithms. In the rst part of that&nbsp;chapter, the focus is on the variable sample size techniques. Different&nbsp;implementations of the proposed algorithm are compared to each other&nbsp;and to the other sample schemes as well. The second part is mostly&nbsp;devoted to the comparison of the various line search rules combined&nbsp;with dierent search directions in the variable sample size framework.&nbsp;The overall numerical results show that using the variable sample size&nbsp;can improve the performance of the algorithms signicantly, especially&nbsp;when the nonmonotone line search rules are used.</p><p>The rst chapter of this thesis provides the background material&nbsp;for the subsequent chapters. In Chapter 2, basics of the nonlinear&nbsp;optimization are presented and the focus is on the line search, while&nbsp;Chapter 3 deals with the stochastic framework. These chapters are&nbsp;here to provide the review of the relevant known results, while the&nbsp;rest of the thesis represents the original contribution.&nbsp;</p> / <p>U okviru ove teze posmatra se problem optimizacije bez ograničenja pri čcemu je funkcija cilja u formi matematičkog očekivanja. Očekivanje se odnosi na slučajnu promenljivu koja predstavlja neizvesnost. Zbog toga je funkcija cilja, u stvari, deterministička veličina. Ipak, odredjivanje analitičkog oblika te funkcije cilja može biti vrlo komplikovano pa čak i nemoguće. Zbog toga se za aproksimaciju često koristi uzoračko očcekivanje. Da bi se postigla dobra aproksimacija, obično je neophodan obiman uzorak. Ako pretpostavimo da se uzorak realizuje pre početka procesa optimizacije, možemo posmatrati uzoračko očekivanje kao determinističku funkciju. Medjutim, primena nekog od determinističkih metoda direktno na tu funkciju&nbsp; moze biti veoma skupa jer evaluacija funkcije pod ocekivanjem često predstavlja veliki tro&scaron;ak i uobičajeno je da se ukupan tro&scaron;ak optimizacije meri po broju izračcunavanja funkcije pod očekivanjem. Zbog toga su razvijeni metodi sa promenljivom veličinom uzorka. Većcina njih je bazirana na odredjivanju optimalne dinamike uvećanja uzorka.</p><p>Glavni cilj ove teze je razvoj algoritma koji, kroz smanjenje broja izračcunavanja funkcije, smanjuje ukupne tro&scaron;skove optimizacije. Ideja je da se veličina uzorka smanji kad god je to moguće. Grubo rečeno, izbegava se koriscenje velike preciznosti&nbsp; (velikog uzorka) kada smo daleko od re&scaron;senja. U čcetvrtom poglavlju ove teze opisana je nova klasa metoda i predstavljena je analiza konvergencije. Dokazano je da je aproksimacija re&scaron;enja koju dobijamo bar toliko dobra koliko i za metod koji radi sa celim uzorkom sve vreme.</p><p>Jo&scaron; jedna bitna karakteristika metoda koji su ovde razmatrani je primena linijskog pretražzivanja u cilju odredjivanja naredne iteracije. Osnovna ideja je da se nadje odgovarajući pravac i da se duž njega vr&scaron;si pretraga za dužzinom koraka koja će dovoljno smanjiti vrednost funkcije. Dovoljno smanjenje je odredjeno pravilom linijskog pretraživanja. U čcetvrtom poglavlju to pravilo je monotono &scaron;to znači da zahtevamo striktno smanjenje vrednosti funkcije. U cilju jos većeg smanjenja tro&scaron;kova optimizacije kao i pro&scaron;irenja skupa pogodnih pravaca, u petom poglavlju koristimo nemonotona pravila linijskog pretraživanja koja su modifikovana zbog promenljive velicine uzorka. Takodje, razmatrani su uslovi za globalnu konvergenciju i R-linearnu brzinu konvergencije.</p><p>Numerički rezultati su predstavljeni u &scaron;estom poglavlju. Test problemi su razliciti - neki od njih su akademski, a neki su realni. Akademski problemi su tu da nam daju bolji uvid u pona&scaron;anje algoritama. Sa druge strane, podaci koji poticu od stvarnih problema služe kao pravi test za primenljivost pomenutih algoritama. U prvom delu tog poglavlja akcenat je na načinu ažuriranja veličine uzorka. Različite varijante metoda koji su ovde predloženi porede se medjusobno kao i sa drugim &scaron;emama za ažuriranje veličine uzorka. Drugi deo poglavlja pretežno je posvećen poredjenju različitih pravila linijskog pretraživanja sa različitim pravcima pretraživanja u okviru promenljive veličine uzorka. Uzimajuci sve postignute rezultate u obzir dolazi se do zaključcka da variranje veličine uzorka može značajno popraviti učinak algoritma, posebno ako se koriste nemonotone metode linijskog pretraživanja.</p><p>U prvom poglavlju ove teze opisana je motivacija kao i osnovni pojmovi potrebni za praćenje preostalih poglavlja. U drugom poglavlju je iznet pregled osnova nelinearne optimizacije sa akcentom na metode linijskog pretraživanja, dok su u trećem poglavlju predstavljene osnove stohastičke optimizacije. Pomenuta poglavlja su tu radi pregleda dosada&scaron;njih relevantnih rezultata dok je originalni doprinos ove teze predstavljen u poglavljima 4-6.</p>

<p>Posmatra se problem optimizacije bez ograničenja. Za re&scaron;avanje<br />problema&nbsp; optimizacije bez ograničenja postoji mno&scaron;tvo raznovrsnih<br />metoda. Istraživanje ovde motivisano je potrebom za metodama koje<br />će brzo konvergirati.<br />Cilj je sistematizacija poznatih rezultata, kao i teorijska i numerička<br />analiza mogućnosti uvođenja parametra u gradijentne metode.<br />Najpre se razmatra problem minimizacije konveksne funkcije vi&scaron;e<br />promenljivih.<br />Problem minimizacije konveksne funkcije vi&scaron;e promenljivih ovde se<br />re&scaron;ava bez izračunavanja matrice hesijana, &scaron;to je naročito aktuelno za<br />sisteme velikih dimenzija, kao i za probleme optimizacije kod kojih<br />ne raspolažemo ni tačnom vredno&scaron;ću funkcije cilja, ni tačnom<br />vredno&scaron;ću gradijenta. Deo motivacije za istraživanjem ovde leži i u<br />postojanju problema kod kojih je funkcija cilja rezultat simulacija.<br />Numerički rezultati, predstavljeni u Glavi 6, pokazuju da uvođenje<br />izvesnog parametra može biti korisno, odnosno, dovodi do ubrzanja<br />određenog metoda optimizacije.<br />Takođe se predstavlja jedan novi hibridni metod konjugovanog<br />gradijenta, kod koga je parametar konjugovanog gradijenta<br />konveksna kombinacija dva poznata parametra konjugovanog<br />gradijenta.<br />U prvoj glavi opisuje se motivacija kao i osnovni pojmovi potrebni za<br />praćenje preostalih glava.<br />U drugoj glavi daje se pregled nekih gradijentnih metoda prvog i<br />drugog reda.<br />Četvrta glava sadrži pregled osnovnih pojmova i nekih rezultata<br />vezanih za metode konjugovanih gradijenata.<br />Pomenute glave su tu radi pregleda nekih poznatih rezultata, dok se<br />originalni doprinos predstavlja u trećoj, petoj i &scaron;estoj glavi.<br />U trećoj glavi se opisuje izvesna modifikacija određenog metoda u<br />kome se koristi multiplikativni parametar, izabran na slučajan način.<br />Dokazuje se linearna konvergencija tako formiranog novog metoda.<br />Peta glava sadrži originalne rezultate koji se odnose na metode<br />konjugovanih gradijenata. Naime, u ovoj glavi predstavlja se novi<br />hibridni metod konjugovanih gradijenata, koji je konveksna<br />kombinacija dva poznata metoda konjugovanih gradijenata.<br />U &scaron;estoj glavi se daju rezultati numeričkih eksperimenata, izvr&scaron;enih<br />na&nbsp; izvesnom skupu test funkcija, koji se odnose na metode iz treće i<br />pete glave. Implementacija svih razmatranih algoritama rađena je u<br />paketu MATHEMATICA. Kriterijum upoređivanja je vreme rada<br />centralne procesorske jedinice.6</p> / <p>The problem under consideration is an unconstrained optimization<br />problem. There are many different methods made in aim to solve the<br />optimization problems.&nbsp; The investigation made here is motivated by<br />the fact that the methods which converge fast are necessary.<br />The main goal is the systematization of some known results and also<br />theoretical and numerical analysis of the possibilities to int roduce<br />some parameters within gradient methods.<br />Firstly, the minimization problem is considered, where the objective<br />function is a convex, multivar iable function. This problem is solved<br />here without the calculation of Hessian, and such solution is very<br />important, for example, when the&nbsp; big dimension systems are solved,<br />and also for solving optimization problems with unknown values of<br />the objective function and its gradient. Partially, this investigation is<br />motivated by the existence of problems where the objective function<br />is the result of simulations.<br />Numerical results, presented in&nbsp; Chapter&nbsp; 6, show that the introduction<br />of a parameter is useful, i.e., such introduction results by the<br />acceleration of the known optimization method.<br />Further, one new hybrid conjugate gradient method is presented, in<br />which the conjugate gradient parameter is a convex combination of<br />two known conjugate gradient parameters.<br />In the first chapter, there is motivation and also the basic co ncepts<br />which are necessary for the other chapters.<br />The second chapter contains the survey of some first order and<br />second order gradient methods.<br />The fourth chapter contains the survey of some basic concepts and<br />results corresponding to conjugate gradient methods.<br />The first, the second and the fourth&nbsp; chapters are here to help in<br />considering of some known results, and the original results are<br />presented in the chapters 3,5 and 6.<br />In the third chapter, a modification of one unco nstrained optimization<br />method is presented, in which the randomly chosen multiplicative<br />parameter is used. Also, the linear convergence of such modification<br />is proved.<br />The fifth chapter contains the original results, corresponding to<br />conjugate gradient methods. Namely, one new hybrid conjugate<br />gradient method is presented, and this&nbsp; method is the convex<br />combination of two known conjugate gradient methods.<br />The sixth chapter consists of the numerical results, performed on a set<br />of test functions, corresponding to methods in the chapters 3 and 5.<br />Implementation of all considered algorithms is made in Mathematica.<br />The comparison criterion is CPU time.</p> / <p>The problem under consideration is an unconstrained optimization<br />problem. There are many different methods made in aim to solve the<br />optimization problems.&nbsp; The investigation made here is motivated by<br />the fact that the methods which converge fast are necessary.<br />The main goal is the systematization of some known results and also<br />theoretical and numerical analysis of the possibilities to int roduce<br />some parameters within gradient methods.<br />Firstly, the minimization problem is considered, where the objective<br />function is a convex, multivar iable function. This problem is solved<br />here without the calculation of Hessian, and such solution is very<br />important, for example, when the&nbsp; big dimension systems are solved,<br />and also for solving optimization problems with unknown values of<br />the objective function and its gradient. Partially, this investigation is<br />motivated by the existence of problems where the objective function<br />is the result of simulations.<br />Numerical results, presented in&nbsp; Chapter&nbsp; 6, show that the introduction<br />of a parameter is useful, i.e., such introduction results by the<br />acceleration of the known optimization method.<br />Further, one new hybrid conjugate gradient method is presented, in<br />which the conjugate gradient parameter is a convex combination of<br />two known conjugate gradient parameters.<br />In the first chapter, there is motivation and also the basic co ncepts<br />which are necessary for the other chapters.<br />Key&nbsp; Words Documentation&nbsp; 97<br />The second chapter contains the survey of some first order and<br />second order gradient methods.<br />The fourth chapter contains the survey of some basic concepts and<br />results corresponding to conjugate gradient methods.<br />The first, the second and the fourth&nbsp; chapters are here to help in<br />considering of some known results, and the original results are<br />presented in the chapters 3,5 and 6.<br />In the third chapter, a modification of one unco nstrained optimization<br />method is presented, in which the randomly chosen multiplicative<br />parameter is used. Also, the linear convergence of such modification<br />is proved.<br />The fifth chapter contains the original results, corresponding to<br />conjugate gradient methods. Namely, one new hybrid conjugate<br />gradient method is presented, and this&nbsp; method is the convex<br />combination of two known conjugate gradient methods.<br />The sixth chapter consists of the numerical results, performed on a set<br />of test functions, corresponding to methods in the chapters 3 and 5.<br />Implementation of all considered algorithms is made in Mathematica.<br />The comparison criterion is CPU time</p>

<p>У докторској дисертацијиприказан је развој стохастичког модела оптимизације времена трајања циклуса производње у малим и средњим предузећима. Модел ће омогућити ефикасно праћење и анализу елемената врема циклуса производње у малим и средњим предузећима, у циљу оптимизације серијске производње и побољшања конкурентности у савременом пословању. Циљ је боље управљање производњом у малим и средљим предузећима као носиоцима привредног раста и развоја. Модел је примењен и експериментално доказан у три предузећа где је истраживање спроведено у периоду 2011-2014 године.</p> / <p>U doktorskoj disertacijiprikazan je razvoj stohastičkog modela optimizacije vremena trajanja ciklusa proizvodnje u malim i srednjim preduzećima. Model će omogućiti efikasno praćenje i analizu elemenata vrema ciklusa proizvodnje u malim i srednjim preduzećima, u cilju optimizacije serijske proizvodnje i poboljšanja konkurentnosti u savremenom poslovanju. Cilj je bolje upravljanje proizvodnjom u malim i sredljim preduzećima kao nosiocima privrednog rasta i razvoja. Model je primenjen i eksperimentalno dokazan u tri preduzeća gde je istraživanje sprovedeno u periodu 2011-2014 godine.</p> / <p>The Doctoral Dissertation presents the development of stochastic optimization model of production cycle time in small and medium size enterprises.The model will enable efficient tracking and analysis of production cycle time elements in small and medium size enterprises in order to optimize assenibly line production and to improve competitiveness in modern business.The aim is better production contol in small and medium size enterprisesas industial growth and development holders. The model was applied and proved experimentally in three enerprises where the research was caried out from 2011 to 2014.</p>

<p>У дисертацији је дат концепт микро мрежа и описане постојеће методе у управљању и оптимизацији рада микро мрежа. Предложен је нови централизовани контролер микро мрежe заснован на технологији више-агентног система, који омогућава координацију три режима рада (повезани, острвски и хаваријски) и обезбеђује једноставну конфигурацију и комбинацију оптимизационих критеријума, уз уважавање широког скупа ограничења. Предложени модел примењен је на релевантни тест систем и резултати су приказани уз одговарајућу анализу резултата.</p> / <p>U disertaciji je dat koncept mikro mreža i opisane postojeće metode u upravljanju i optimizaciji rada mikro mreža. Predložen je novi centralizovani kontroler mikro mreže zasnovan na tehnologiji više-agentnog sistema, koji omogućava koordinaciju tri režima rada (povezani, ostrvski i havarijski) i obezbeđuje jednostavnu konfiguraciju i kombinaciju optimizacionih kriterijuma, uz uvažavanje širokog skupa ograničenja. Predloženi model primenjen je na relevantni test sistem i rezultati su prikazani uz odgovarajuću analizu rezultata.</p> / <p>Dissertation provides the microgrids concept and describes existing methods for control and optimization of microgrid operation. This paper proposes a novel, centralized, multi-agent-based, microgrid controller architecture, which provides the coordination of all three operation modes (grid-connected, island and emergency) and enables the easy configuration/combination of optimization goals that are subject to a given set of operational constraints.<br />The simulation results are presented for a typical microgrid test example.</p>

<p>Klaster analiza ima dugu istoriju i mada se<br />primenjuje u mnogim oblastima i dalje ostaju<br />značajni izazovi. U disertaciji je prikazan uvod<br />u neglatki optimizacioni pristup u<br />klasterovanju, sa osvrtom na problem<br />klasterovanja velikih skupova podataka.<br />Međutim, ovi optimizacioni algoritmi bolje<br />funkcioni&scaron;u u radu sa neprekidnim podacima.<br />Jedan od glavnih izazova u klaster analizi je<br />rad sa velikim skupovima podataka sa<br />kategorijalnim i kombinovanim (numerički i<br />kategorijalni) tipovima promenljivih. Rad sa<br />velikim brojem instanci (objekata) i velikim<br />brojem dimenzija (promenljivih), može<br />predstavljati problem u klaster analizi, zbog<br />vremenske složenosti. Jedan od načina<br />re&scaron;avanja ovog problema je redukovanje broja<br />instanci, bez gubitka informacija.<br />Prvi cilj disertacije je bio upoređivanje<br />rezultata klasterovanja na celom skupu i<br />prostim slučajnim uzorcima sa kategorijalnim i<br />kombinovanim podacima, za različite veličine<br />uzorka i različit broj klastera. Nije utvrđena<br />značajna razlika (p&gt;0.05) u rezultatima<br />klasterovanja na uzorcima obima<br />0.03m,0.05m,0.1m,0.3m (gde je m obim<br />posmatranog skupa) i celom skupu.<br />Drugi cilj disertacije je bio konstrukcija<br />efikasnog postupka klasterovanja velikih<br />skupova podataka sa kategorijalnim i<br />kombinovanim tipovima promenljivih.<br />Predloženi postupak se sastoji iz sledećih<br />koraka: 1. klasterovanje na prostim slučajnim<br />uzorcima određene kardinalnosti; 2.<br />određivanje najboljeg klasterskog re&scaron;enja na<br />uzorku, primenom odgovarajućeg kriterijuma<br />validnosti; 3. dobijeni centri klastera iz ovog<br />uzorka služe za klasterovanje ostatka skupa.<br />Treći cilj disertacije predstavlja primenu<br />klaster analize u definisanju klastera<br />bihejvioralnih faktora rizika u populaciji<br />odraslog stanovni&scaron;tva Srbije, kao i analizu<br />sociodemografskih karakteristika dobijenih<br />klastera. Klaster analiza je primenjena na<br />velikom reprezentativnom uzorku odraslog<br />stanovni&scaron;tva Srbije, starosti 20 i vi&scaron;e godina.<br />Izdvojeno je pet jasno odvojenih klastera sa<br />karakterističnim kombinacijama bihejvioralnih<br />faktora rizika: Bez rizičnih faktora, &Scaron;tetna<br />upotreba alkohola i druge rizične navike,<br />Nepravilna ishrana i druge rizične navike,<br />Nedovoljna fizička aktivnost, Pu&scaron;enje. Rezultati<br />multinomnog logističkog regresionog modela<br />ukazuju da ispitanici koji nisu u braku, lo&scaron;ijeg<br />su materijalnog stanja, nižeg obrazovanja i žive<br />u Vojvodini imaju veću &scaron;ansu za prisustvo<br />vi&scaron;estrukih bihejvioralnih faktora rizika.</p> / <p>The cluster analysis has a long history and a<br />large number of clustering techniques have<br />been developed in many areas, however,<br />significant challenges still remain. In this<br />thesis we have provided a introduction to<br />nonsmooth optimization approach to clustering<br />with reference to clustering large datasets.<br />Nevertheless, these optimization clustering<br />algorithms work much better when a dataset<br />contains only vectors with continuous features.<br />One of the main challenges is clustering of large<br />datasets with categorical and mixed (numerical<br />and categorical) data. Clustering deals with a<br />large number of instances (objects) and a large<br />number of dimensions (variables) can be<br />problematic because of time complexity. One of<br />the ways to solve this problem is by reducing<br />the number of instances, without the loss of<br />information.<br />The first aim of this thesis was to compare<br />the results of cluster algorithms on the whole<br />dataset and on simple random samples with<br />categorical and mixed data, in terms of validity,<br />for different number of clusters and for<br />different sample sizes. There were no<br />significant differences (p&gt;0.05) between the<br />obtained results on the samples of the size of<br />0.03m,0.05m,0.1m,0.3m (where m is the size of<br />the dataset) and the whole dataset.<br />The second aim of this thesis was to<br />develop an efficient clustering procedure for<br />large datasets with categorical and mixed<br />(numeric and categorical) values. The proposed<br />procedure consists of the following steps: 1.<br />clustering on simple random samples of a given<br />cardinality; 2. finding the best cluster solution<br />on a sample (by appropriate validity measure);<br />3. using cluster centers from this sample for<br />clustering of the remaining data.<br />The third aim of this thesis was to<br />examine clustering of four lifestyle risk factors<br />and to examine the variation across different<br />socio-demographic groups in a Serbian adult<br />population. Cluster analysis was carried out on<br />a large representative sample of Serbian adults<br />aged 20 and over. We identified five<br />homogenous health behaviour clusters with<br />specific combination of risk factors: &#39;No Risk<br />Behaviours&#39;, &#39;Drinkers with Risk Behaviours&#39;,<br />&#39;Unhealthy diet with Risk Behaviours&#39;,<br />&#39;Smoking&#39;. Results of multinomial logistic<br />regression indicated that single adults, less<br />educated, with low socio-economic status and<br />living in the region of Vojvodina are most likely<br />to be a part of the clusters with a high-risk<br />profile.</p>

One of the main problems in neurosurgery is knowledge about human brain. It's very important to see the whole brain with its critical neurostructures in virtual reality. This document is about three dimensional human brain visualization strategies. Review most recently used three dimensional objects building strategies from two dimensional medical MRI images. This task was split into 4 significant problems: image segmentation, point-sets correspondence, image registration and its frequently used transformation functions with image matching measurements. All these problems were addressed reader to show most recently used algorithms with advantages and disadvantages. Atlas types, patterns and maps survey was introduced with widely popular brain model coordinate systems. In order to find a better correspondence between two point sets it was modeled a new robust and accurate Overhauser spline points location optimization algorithm. Instead of deletion outlier points from overloaded point set, this algorithm generates more points in other set at optimized points locations. Determination of an accurate point location and choosing the correct transformation function are the key steps in registration process. Whereas registration is vital task in precise human brain visualization for neurosurgeries at preoperative and intraoperative process.