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Global optimization of multiple variables functions
Vláčil, Stanislav ; Janda, Marcel (referee) ; Kloc, Petr (advisor)
Master’s thesis deals with numerical finding the global minimum. A theoretical part of project presents a problem of global optimization, her basic division and shows basic examples the specific problems of global optimization. Further, the reader is familiar with the basics of some numerical methods and with description of their strengths and weaknesses. A practical part shows concrete algorithm of global optimization, its use on data of specified function. Data refer to the issue of radiative heat transfer.
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Generalization of convex functions
Bessisso, Samir ; Lachout, Petr (advisor) ; Hlubinka, Daniel (referee)
Convex functions have range of useful properties that can be well utilized in mathe- matical optimization. For instance, their local minima is also global minima, they have convex lower level sets and if differentiable, their stationary point is also the point of global minima. For differentiable convex functions gradient methods and Karush-Kuhn-Tucker conditions can be effectively applied. On the other hand, the assumption of convexity is rather restrictive and not necessary for some of their desired properties. Theme of this thesis are convex functions and their generalizations, namely quasiconvex and K-convex functions, invex functions are also marginally mentioned. This thesis gathers knowledge about convex, quasiconvex and K-convex functions that can be used in mathematical optimization and ilustrates it on examples. 1
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Global optimization of multiple variables functions
Vláčil, Stanislav ; Janda, Marcel (referee) ; Kloc, Petr (advisor)
Master’s thesis deals with numerical finding the global minimum. A theoretical part of project presents a problem of global optimization, her basic division and shows basic examples the specific problems of global optimization. Further, the reader is familiar with the basics of some numerical methods and with description of their strengths and weaknesses. A practical part shows concrete algorithm of global optimization, its use on data of specified function. Data refer to the issue of radiative heat transfer.
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