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Application of the Infinitely Many Times Repeated BNS Update and Conjugate Directions to Limited-Memory Optimization Methods
Vlček, Jan ; Lukšan, Ladislav
To improve the performance of the L-BFGS method for large scale unconstrained optimization, repeating of some BFGS updates was proposed. Since this can be time consuming, the extra updates need to be selected carefully. We show that groups of these updates can be repeated infinitely many times under some conditions, without a noticeable increase of the computational time. The limit update is a block BFGS update. It can be obtained by solving of some Lyapunov matrix equation whose order can be decreased by application of vector corrections for conjugacy. Global convergence of the proposed algorithm is established for convex and sufficiently smooth functions. Numerical results indicate the efficiency of the new method.
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Mountain hotel
Vlček, Jan ; Pilný, Ondřej (referee) ; Berková, Petra (advisor)
The aim of this diploma thesis is to design a mountain hotel in the village Rokytnice nad Jizernou. The object is placed on a sloping plot located in an attractive touristic and skiing area of mountain range Krkonoše. The mountain hotel has 4 floors and a basement. In the First floor there is a restaurant with a terrace, kitchen and administrative facilities of hotel. In the second and third floor we can find guest rooms and room for the hotel staff. In the basement there is wellness, technical facilities and garage compound. Construction of building is made of the reinforced concrete monolithic transverse frames with beam filling of ceramic block.
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