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Diem Huynh Thi Hong (Department of Mathematics, College of Cantho, Cantho, Vietnam), Khanh Phan Quoc (Department of Mathematics, International University, Vietnam National University Hochiminh City; Linh Trung, Thu Duc, Hochiminh City, Vietnam)
Optimality Conditions for a Class of Relaxed Quasiconvex Minimax Problems
Control and Cybernetics, 2014, vol. 43, nr 2, s. 249-260, bibliogr. s. 280
Słowa kluczowe
Teoria wspomagania decyzji, Teoria optymalizacji, Modele optymalizacyjne
Theory of decision support, Optimization theory, Optimizing models
A class of minimax problems is considered. We approach it with the techniques of quasiconvex optimization, which includes most important nonsmooth and relaxed convex problems and has been intensively developed. Observing that there have been many contributions to various themes of minimax problems, but surprisingly very few on optimality conditions, the most traditional and developed topic in optimization, we establish both necessary and sufficient conditions for solutions and unique solutions. A main feature of this work is that the involved functions are relaxed quasi- convex in the sense that the sublevel sets need to be convex only at the considered point. We use star subdifferentials, which are slightly bigger than other subdifferentials applied in many existing results for minimization problems, but may be empty or too small in various situations. Hence, when applied to the special case of minimization problems, our results may be more suitable. Many examples are provided to illustrate the applications of the results and also to discuss the imposed assumptions. (original abstract)
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Biblioteka Główna Uniwersytetu Ekonomicznego w Krakowie
Biblioteka Szkoły Głównej Handlowej w Warszawie
Pełny tekst
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