New dualities for mathematical programs with vanishing constraints

• Published in: Annals of operations research Vol. 287; no. 1; pp. 233 - 255
• Main Authors: Hu, Qingjie, Wang, Jiguang, Chen, Yu
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.04.2020; Springer; Springer Nature B.V
• Subjects: Algorithms; Business and Management; Combinatorics; Constraint modelling; Duality theory (Mathematics); Mathematical analysis; Mathematical optimization; Mathematical programming; Mathematical research; Nonlinear programming; Operations research; Operations Research/Decision Theory; Original Research; Theory of Computation; China; Mond–Weir dual; Mathematical programs with vanishing constraints; 49J52; 90C33; Wolfe dual
• ISSN: 0254-5330; 1572-9338
• DOI: 10.1007/s10479-019-03409-6

Recently, Mishra et al. (Ann Oper Res 243(1):249–272, 2016) formulate and study the Wolfe and the Mond–Weir type dual models for the mathematical programs with vanishing constraints. They establish the weak, strong, converse, restricted converse and strict converse duality results between the primal mathematical programs with vanishing constraints and the corresponding dual model under some assumptions. However, their models contain the calculation of the index sets, this makes it difficult to solve them from algorithm point of view. In this paper, we propose the new Wolfe and Mond–Weir type dual models for the mathematical programs with vanishing constraints, which do not involve the calculation of the index set. We show that the weak, strong, converse and restricted converse duality results hold between the primal mathematical programs with vanishing constraints and the corresponding new dual models under the same assumptions as the ones of Mishra et al.