Minimax Theory and its Applications 09 (2024), No. 2, 407--420
Copyright Heldermann Verlag 2024
Optimality Conditions for Quasiconvex Programming in Terms of Quasiconjugate Functions
Satoshi Suzuki
Department of Mathematical Sciences, Shimane University, Japan
suzuki@riko.shimane-u.ac.jp
We study optimality conditions for quasiconvex programming in terms of quasiconjugate functions. By using the Q-conjugate, we show a necessary and sufficient optimality condition for quasiconvex programming. Additionally, by using the H-quasiconjugate, the O-quasiconjugate, and the R-quasiconjugate, we introduce optimality conditions for some kind of evenly quasiconvex objective functions. We investigate evenly convex sets and evenly quasiconvex functions, and continuity of quasiconvex functions.
Keywords: Quasiconvex programming, optimality condition, quasiconjugate function, subdifferential.
MSC: 90C46, 90C26, 26B25.
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