Abstract
We revisit optimization theory involving set functions which are defined on a family of measurable subsets in a measure space. In this paper, we focus on a minimax fractional programming problem with subdifferentiable set functions. Using nonparametric necessary optimality conditions, we introduce generalized $(\mathcal{F},\rho, \theta)$-convexity to establish several sufficient optimality conditions for a minimax programming problem, and construct a new dual model to unify the Wolfe type dual and the Mond-Weir type dual as special cases of this dual programming problem. Finally we establish a weak, strong, and strict converse duality theorem.
Citation
T.-Y. Huang. H.-C. Lai. S. Schaible. "OPTIMIZATION THEORY FOR SET FUNCTIONS IN NONDIFFERENTIABLE FRACTIONAL PROGRAMMING WITH MIXED TYPE DUALITY." Taiwanese J. Math. 12 (8) 2031 - 2044, 2008. https://doi.org/10.11650/twjm/1500405134
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