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Στην παρούσα διατριβή μελετάμε το πρόβλημα της βελτιστοποίησης μη γραμμικών συναρτήσεων πολλών μεταβλητών, όπου η αντικειμενική συνάρτηση είναι συνεχώς διαφορίσιμη σε ένα ανοιχτό υποσύνολο του Rn. Αναπτύσσουμε μαθηματικές μεθόδους βελτιστοποίησης αποσκοπώντας στην επίλυση προβλημάτων μεγάλης κλίμακας, δηλαδή προβλημάτων των οποίων οι μεταβλητές είναι πολλές χιλιάδες, ακόμα και εκατομμύρια. Η βασική ιδέα των μεθόδων που αναπτύσσουμε έγκειται στη θεωρητική μελέτη των χαρακτηριστικών μεγεθών των Quasi-Newton ενημερώσεων ελάχιστης και μικρής μνήμης. Διατυπώνουμε θεωρήματα αναφορικά με το χαρακτηριστικό πολυώνυμο, τον αριθμό των διακριτών ιδιοτιμών και των αντίστοιχων ιδιοδιανυσμάτων. Εξάγουμε κλειστούς τύπους για τον υπολογισμό των ανωτέρω ποσοτήτων, αποφεύγοντας τόσο την αποθήκευση όσο και την παραγοντοποίηση πινάκων. Τα νέα θεωρητικά απoτελέσματα εφαρμόζονται αφενός μεν στην επίλυση μεγάλης κλίμακας υποπροβλημάτων περιοχής εμπιστοσύνης, χρησιμοποιώντας τη μέθοδο της σχεδόν ακριβούς λύσης, αφετέρου δε, στην καμπυλόγραμμη αναζήτηση, η οποία χρησιμοποιεί ένα ζεύγος κατευθύνσεων μείωσης, την Quasi-Newton κατεύθυνση και την κατεύθυνση αρνητικής καμπυλότητας. Η νέα μέθοδος μειώνει δραστικά τη χωρική πολυπλοκότητα των γνωστών αλγορίθμων του μη γραμμικού προγραμματισμού, διατηρώντας παράλληλα τις καλές ιδιότητες σύγκλισής τους. Ως αποτέλεσμα, οι προκύπτοντες νέοι αλγόριθμοι έχουν χωρική πολυπλοκότητα Θ(n). Τα αριθμητικά αποτελέσματα δείχνουν ότι οι νέοι αλγόριθμοι είναι αποδοτικοί, γρήγοροι και πολύ αποτελεσματικοί όταν χρησιμοποιούνται στην επίλυση προβλημάτων με πολλές μεταβλητές. / In this thesis we study the problem of minimizing nonlinear functions of several variables, where the objective function is continuously differentiable on an open subset of Rn. We develop mathematical optimization methods for solving large scale problems, i.e., problems whose variables are many thousands, even millions. The proposed method is based on the theoretical study of the properties of minimal and low memory Quasi-Newton updates. We establish theorems concerning the characteristic polynomial, the number of distinct eigenvalues and corresponding eigenvectors. We derive closed formulas for calculating these quantities, avoiding both the storage and factorization of matrices. The new theoretical results are applied in the large scale trust region subproblem for calculating nearly exact solutions as well as in a curvilinear search that uses a Quasi-Newton and a negative curvature direction. The new method is drastically reducing the spatial complexity of known algorithms of nonlinear programming. As a result, the new algorithms have spatial complexity Θ(n), while they are maintaining good convergence properties. The numerical results show that the proposed algorithms are efficient, fast and very effective when used in solving large scale problems.

This diploma thesis is focused on nearly zero energy buildings, which are a mandatory part of construction of the buildings in Czech republic after 2020. It also deals with HVAC and its design as part of these buildings. The theoretical part deals with legal and technical regulations and possible savings in HVAC systems. The computational part is focused on two solution of HVAC systems in given object. The project part is about the given object, which is otevřená zahrada Brno. This building was founded by Nadace Partnerství s.r.o.. This third part of diploma thesis deals with the quality of indoor microclimate and evaluation of the heat recovery system effiency, which is applied in local HVAC unit.

This theoretical diploma thesis deals with „nearly zero energy buildings“. The aim of the thesis is to evaluate building constructions based on their impact on thermal requirements fulfilment and apply results of the evaluation on a design of a nearly zero energy building. The thesis describes individual factors impacting energy consumption of a nearly zero house building, evaluates individual types of insulations systems for roof constructions, analyses window details, foundation details and connection of roof and external wall or the floor structure and external wall. The basic criteria for the evaluation is the fulfilment of the thermal requirements as well as the costs of the construction itself and energy consumption for the individual construction or detail. The specialized part of the thesis deals with design and comparison of 2 types of timber roof truss systems, the purlin roof and the collar roof. The suitability of the roof systems for nearly zero energy building is evaluated as well. The result of he thesis is the proposal of solutions for the nearly zero energy building. The proposal consists of layout solutions, design of suitable construction system, load-bearing system including drawings. The output is also Energy Performance Certificate.

The thesis deals with the issue will be nearly zero energy. The theoretical part is divided into several chapters. Describes the requirements of applicable legislation of the Czech Republic and the EU and the application of renewable energy in these buildings. The third and last part serves as a basis for part of the experiment. Calculation section applies theoretical knowledge into practice. The subject has become a new residential building in which they are designed to ensure the technical equipment required internal environment. The proposal concerns the heating, ventilation, cooling, domestic hot water and lighting. At the end are attached graphic of energy performance certificates (PENB) and evaluated the economic and ecological point of view. The experiment deals with the measurement of the internal microclimate administrative building type in Brno, with regard to the requirements of current legislation of the Czech Republic.

The aim of this project is to design a kindergarten with nearly zero energy consumption in Veřovice. The building is purposefully divided into three parts, where one part consists of locker rooms, an office, a food service and facilities for employees. The second part consists of 2 separate playrooms with a capacity for 40 children and the third part consists of the building services of the building. The project consists of three parts. The first part deals with the design of a building solution. It is a single-storey non-basement building, where the vertical load-bearing structures are made of Porotherm ceramic blocks and the horizontal load-bearing structures are designed from hollow prestressed Spiroll panels. The roof of the building is designed as a flat, warm, extensive green roof. The second part deals with the design of individual technical equipment. A ground / water heat pump is designed as a source of heat and cold. The building also uses mechanical ventilation, with heat recovery and the possibility of cooling selected rooms in the summer months. The third part consists of a detailed design of the heating system and contains a calculation of heat losses and a design of floor heating.

The theoretical part deals at the beginning with wooden buildings and suitable materials. Then information about low energy houses, passive houses and requirements for new buildings is introduced. The theoretical part of the work also summarizes the selection of the technological solution. Important part is about individual life cycle stages of the building, wear and tear of the buildings and whole life costs of the building that the investor is interested in. Practical part of the thesis consists of a case study of the wooden family house where the whole life costs of the building life cycle are solved.

The aim of master‘s thesis is to renovate old agricultural building and design it as nzeb building. The thesis contains three parts: 1st – design of the building, 2nd – design of building services, and 3rd – assessment of the impact of different operations in building on energy consumption. The results are then evaluated for economic and environmental savings. The renovated building in village Rozkoš will be used for many purposes. It will be divided into 3 parts – a multifunctional hall, a pub, and a club room. Multifunctional hall will be used for various activities for village itself or public. In the pub will be only cold kitchen with small dishes and beverages. Club room can be used for elderly people, workout or young people. The building is low rise and structural system is combined. The vertical load-bearing walls and columns are built of bricks. Horizontal load-bearing structures are cross vaults made also of bricks. Saddle roof is made of timber roof truss. The building site contains also an outdoor car park and a garden. The project was carried out in the Revit.

The aim of this master project is to design a nearly zero-energy building of kindergarten. The kindergarten is designed as one storey building with capacity of 40 children split into two playrooms. Playrooms are separated and each of them has own sanitary facilities and locker room. Playrooms have large windows with external blinds on the south to provide solar gains. There is horizontal sun breaker above the windows which prevent overheating in summer. Load bearing walls are made of sand lime blocks. Walls are insulated with mineral wool board. Roof ceiling is made of prestressed concrete slabs. The building has a flat extensive green roof. The second task of the project includes design of lighting, rainwater harvesting, HVAC, source of heat and photovoltaic system. The third part is theoretical and includes searching for an ideal source of energy for the building. There are two types of heating compared such as gas boiler and a groundwater heating pump. The main software used for the project is Revit.

The subject of my diploma thesis is a design of new kindergarten and elaboration of documentation for the construction. The building is situated in the southwestern suburb of Brno, in the district Brno-Starý Lískovec district. The building is set in a slightly sloping terrain. The building has two floors and and basement, created by partial basement of the building. The building is characterized with two wings designed at right angles and a decent coloured facade. The building contains two kindergarten classrooms with a capacity of 48 children with operational facilities, a rentable part for public, the administrative of the school and a technical facilities of the building. The first floor contains two separate kindergarten classes, each with 24 children, teacher's cabinet, toy storage room and a kitchen. The kitchen is designed without food preparation, with a food delivery company. Each kindergarten class has its own entrance. On the second floor is a rentable space containing a classroom, workshop, lounge and terrace. There are also an isolation room, a gym for children and a head master's office. The building is designed to a low energy standard, definated by near zero heat energy building (nzeb) standarts. There is established a wheelchair access to the building, A lift is proposed in the building. The structural design is proposed as a ceramic block wall with contact insulation system. The vertical strucutres are made of reinforced concrete cast-in-place ceiling. The building is based on concrete foundation and is covered by a single-skin, flat roof with a layer of extensive flora.