In this thesis, we consider the computational methods for linear parabolic optimal control problems. We wish to minimize the cost functional while fulfilling the parabolic partial differential equations (PDE) constraint. This type of problems arises in many fields of science and engineering. Since solving such parabolic PDE optimal control problems often lead to a demanding computational cost and time, an effective algorithm is desired. In this research, we focus on the distributed control problems. Three types of cost functional are considered: Target States problems, Tracking problems, and All-time problems. Our major contribution in this research is that we developed a preconditioner for each kind of problems, so our iterative method is accelerated. In chapter 1, we gave a brief introduction to our problems with a literature review. In chapter 2, we demonstrated how to derive the first-order optimality conditions from the parabolic optimal control problems. Afterwards, we showed how to use the shooting method along with the flexible generalized minimal residual to find the solution. In chapter 3, we offered three preconditioners to enhance our shooting method for the problems with symmetric differential operator. Next, in chapter 4, we proposed another three preconditioners to speed up our scheme for the problems with non-symmetric differential operator. Lastly, we have the conclusion and the future development in chapter 5.

This paper analyzes theperformance of five commercial real estate property types (office, retail, industrial, apartment, and hotel) between 2000 and 2012 to determine the U.S. housing crisis'simpact on Real Estate investing. Under the concept of Modern Portfolio Theory, the data was analyzed using investment analysis programs to determine correlation, risk/return characteristics, and trade-offs (Sharpe ratio) as well as the optimal allocation among the individual property types. In light of the results, each property type plays a different role in investment strategies in various economic cycles. Some assets are attractive solely based onpotential return, or risk for return tradeoffs; however, through diversification, other property types play valuable roles in hedging risk on investors' target returns.

Thesis (Ph. D.)--OGI School of Science & Engineering at OHSU, 2002. / Includes bibliographical references.

Thesis (M.S.)--Ohio University, March, 2004. / Title from PDF t.p. Includes bibliographical references (leaves 80-81).

Thesis (Ph. D.)--University of Texas at Austin, 2008. / Vita. Includes bibliographical references.

Thesis (Ph.D.)--University of Adelaide, Dept. of Electrical and Electronic Engineering, 2003. / "January 2003" Includes bibliographical references (leaves 120-129).

This master's thesis deals with mathematical model building for routing problems and ways to solve them. There are discussed and implemented deterministic and heuristic approaches that are suitable to be utilized. A big effort is put into building of the mathematical model describing a real world problem from the field of waste management. Appropriate algorithms are developed and modified to solve a particular problem effectively. An original graphical environment is created to illustrate acquired results and perform testing computations.

V této práci je prezentována studie fragmentačního procesu zvolené molekuly a jeho vztah ke složení fragmentačních produktů. Práce je zaměřená na výpočet fragmentační energie molekuly pomocí ab initio kvantově chemických metod, metodou „density functional theory (DFT)“ a také srovnáním s experimentem. Je prezentován vliv výpočetní metody, bázového setu, a geometrie molekuly na simulaci. Byla porovnána fragmentace methylfenylsilanu (MPS), dimethylfenylsilanu (DMPS), a trimetylfenylsilanu (TMPS). Fragmentace byla iniciována monochromatickým elektronovým svazkem (EII). Hmotnostní spektrometrie byla využita ke studiu složení fragmentačních produktů MPS a TMPS. Fragmentační produkty MPS a TMPS měřené v rámci této práce byly doplněny o experimentální studii DMPS, která byla prezentována v literatuře. Takto byla získána řada molekul, které jsou strukturně podobné, ale mají výrazně rozdílné chování během fragmentace. Pomocí měření účinného průřezu byly měřeny disociační energie vazeb a tyto disociační energie byly vypočteny pomocí metody DFT. Kombinací teoretického výpočtu metodou DFT a experimentálního měření jsme poukázali na společné rysy a na rozdíly ve fragmentačním schématu všech tří molekul. Navrhli jsme odštěpení dvou vodíkových atomů během plazmově indukovaného fragmentačního procesu. Vodíky mohou být odštěpeny pomocí dvou mechanismů: i. odštěpení dvou vodíků jeden po druhém a ii. odštěpení molekuly H2 v jednom kroku. Z profilů energie dokážeme určit, který mechanismus bude v tom konkrétním případě pravděpodobnější. Předpokládaný mechanismus je v korelaci s experimentálními výsledky fragmentace zjištěnými z hmotnostních spekter.

[pt] A dificuldade de se prever movimento de ativos financeiros é objeto de estudo de diversos autores. A fim de se obter ganhos, se faz necessário estimar a direção (subida ou descida) e a magnitude do retorno do ativo no qual pretende-se comprar ou vender. A proposta desse trabalho consiste em desenvolver um modelo de otimização matemática com variáveis binárias capaz de prever movimentos de subidas e descidas de ativos financeiros e utilizar um modelo de otimização de portfólio para avaliar os resultados obtidos. O modelo de previsão será baseado no Support Vector Machine (SVM), no qual faremos modificações na regularização do modelo tradicional. Para o gerenciamento de portfólio será utilizada otimização robusta. As técnicas de otimização estão sendo cada vez mais aplicadas no gerenciamento de portfólio, pois são capazes de lidar com os problemas das incertezas introduzidas na estimativa dos parâmetros. Vale ressaltar que o modelo desenvolvido é data-driven, i.e, as previsões são feitas utilizando sinais não-lineares baseados em dados de retorno/preço histórico passado sem ter nenhum tipo de intervenção humana. Como os preços dependem de muitos fatores é de se esperar que um conjunto de parâmetros só consiga descrever a dinâmica dos preços dos ativos financeiros por um pequeno intervalo de dias. Para capturar de forma mais precisa essa mudança na dinâmica, a estimação dos parâmetros dos modelos é feita em janela móvel. Para testar a acurácia dos modelos e os ganhos obtidos foi feito um estudo de caso utilizando 6 ativos financeiros das classes de moedas, renda fixa, renda variável e commodities. Os dados abrangem o período de 01/01/2004 até 30/05/2018 totalizando um total de 3623 cotações diárias. Considerando os custos de transações e os resultados out-of-sample obtidos no período analisado percebe-se que a carteira de investimentos desenvolvida neste trabalho exibe resultados superiores aos dos índices tradicionais com risco limitado. / [en] The difficulty of predicting the movement of financial assets is the subject of study by several authors. In order to obtain gains, it is necessary to estimate the direction (rise or fall) and the magnitude of the return on the asset in which it is intended to be bought or sold. The purpose of this work is to develop a mathematical optimization model with binary variables capable of predicting up and down movements of financial assets and using a portfolio optimization model to evaluate the results obtained. The prediction model will be based on the textit Support Vector Machine (SVM), in which we will make modifications in the regularization of the traditional model. For the portfolio management will be used robust optimization. The robust optimization techniques are being increasingly applied in portfolio management, since they are able to deal with the problems of the uncertainties introduced in the estimation of the parameters. It is noteworthy that the developed model is data-driven, i.e., the predictions are made using nonlinear signals based on past historical price / return data without any human intervention. As prices depend on many factors it is to be expected that a set of parameters can only describe the dynamics of the prices of financial assets for a small interval of days. In order to more accurately capture this change in dynamics, the estimation of model parameters is done in a moving window To test the accuracy of the models and the gains obtained, a case study was made using 6 financial assets of the currencies, fixed income, variable income and commodities classes. The data cover the period from 01/01/2004 until 05/30/2018 totaling a total of 3623 daily quotations. Considering the transaction costs and out-of-sample results obtained in the analyzed period, it can be seen that the investment portfolio developed in this work shows higher results than the traditional indexes with limited risk.