On Semi-infinite Mathematical Programming Problems with Equilibrium Constraints Using Generalized Convexity

doi:10.1007/s40305-019-00263-y

Journal of the Operations Research Society of China ›› 2020, Vol. 8 ›› Issue (4): 619-636.doi: 10.1007/s40305-019-00263-y

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On Semi-infinite Mathematical Programming Problems with Equilibrium Constraints Using Generalized Convexity

Bhuwan Chandra Joshi¹, Shashi Kant Mishra², Pankaj Kumar³

1 Centre for Interdisciplinary Mathematical Sciences, Department of Science&Technology, Institute of Science, Banaras Hindu University, Varanasi 221005, India;
2 Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221005, India;
3 Mahila Maha Vidyalaya, Banaras Hindu University, Varanasi 221005, India

Received:2018-09-23 Revised:2019-07-20 Online:2020-12-30 Published:2020-12-29
Contact: Bhuwan Chandra Joshi, Shashi Kant Mishra, Pankaj Kumar E-mail:bhuwanjoshi007@gmail.com;bhu.skmishra@gmail.com;pankaj22iitr@gmail.com

Abstract

Abstract: In this paper, we consider semi-infinite mathematical programming problems with equilibrium constraints (SIMPPEC). By using the notion of convexificators, we establish sufficient optimality conditions for the SIMPPEC. We formulate Wolfe and Mond–Weir-type dual models for the SIMPPEC under the invexity and generalized invexity assumptions. Weak and strong duality theorems are established to relate the SIMPPEC and two dual programs in the framework of convexificators.

Key words: Duality, Convexificators, Generalized invexity, Constraint qualification

CLC Number:

Bhuwan Chandra Joshi, Shashi Kant Mishra, Pankaj Kumar. On Semi-infinite Mathematical Programming Problems with Equilibrium Constraints Using Generalized Convexity[J]. Journal of the Operations Research Society of China, 2020, 8(4): 619-636.

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On Semi-infinite Mathematical Programming Problems with Equilibrium Constraints Using Generalized Convexity

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