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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 2011; 48(1): 13-21

Printed January 1, 2011

https://doi.org/10.4134/JKMS.2011.48.1.13

Copyright © The Korean Mathematical Society.

Nondifferentiable second-order minimax mixed integer symmetric duality

Tilak Raj Gulati and Shiv Kumar Gupta

Indian Institute of Technology Roorkee, Indian Institute of Technology Patna

Abstract

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In this paper, a pair of Wolfe type nondifferentiable second order symmetric minimax mixed integer dual problems is formulated. Symmetric and self-duality theorems are established under $\eta_1$-bonvexity/$\eta_2$-boncavity assumptions. Several known results are obtained as special cases. Examples of such primal and dual problems are also given.

Keywords: nonlinear programming, symmetric duality, minimax programming, self-duality, $\eta$-bonvexity

MSC numbers: 90C47, 90C11, 90C30, 90C25

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