## Taiwanese Journal of Mathematics

### OPTIMIZATION THEORY FOR SET FUNCTIONS IN NONDIFFERENTIABLE FRACTIONAL PROGRAMMING WITH MIXED TYPE DUALITY

#### 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.

#### Article information

Source
Taiwanese J. Math., Volume 12, Number 8 (2008), 2031-2044.

Dates
First available in Project Euclid: 18 July 2017

https://projecteuclid.org/euclid.twjm/1500405134

Digital Object Identifier
doi:10.11650/twjm/1500405134

Mathematical Reviews number (MathSciNet)
MR2449961

Zentralblatt MATH identifier
1173.90008

Subjects
Primary: 26A51: Convexity, generalizations 49A50 90c25

#### Citation

Huang, T.-Y.; Lai, H.-C.; Schaible, S. OPTIMIZATION THEORY FOR SET FUNCTIONS IN NONDIFFERENTIABLE FRACTIONAL PROGRAMMING WITH MIXED TYPE DUALITY. Taiwanese J. Math. 12 (2008), no. 8, 2031--2044. doi:10.11650/twjm/1500405134. https://projecteuclid.org/euclid.twjm/1500405134

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