Subdifferential calculus for a quasiconvex function with generator
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Recently, we discussed optimality conditions for quasiconvex programming by introducing 'Q-subdifferential', which is a notion of differential of quasiconvex functions. In this paper, we investigate basic and fundamental properties of the Q-subdifferential. Especially, we show results of a chain rule for composition with non-decreasing functions, monotonicity of the Qsubdifferential, mean-value theorem, a sufficient condition for a global minimizer for quasiconvex programming, and the calculus of the Q-subdifferential of the supremum of quasiconvex functions.
- Journal of Mathematical Analysis and Applications
Journal of Mathematical Analysis and Applications 384(2), 677-682, 2011-12-15