Browsing by Author "J.K. Maurya"

Now showing 1 - 8 of 8

Approximate stationary conditions for multiobjective mathematical programs with equilibrium constraints
(International Publications, 2020) J.K. Maurya; Kunwar V. K. Singh; S.K. Mishra
In this paper, we establish approximate proper efficient stationary conditions for multiobjective mathematical programs with equilibrium constraints and propose some constraint qualifications under which approximate proper efficient stationary conditions coincide on already existed traditional stationary conditions for multiobjective mathematical programs with equilibrium constraints. © 2020, International Publications. All rights reserved.
Duality in Multiobjective Mathematical Programs with Equilibrium Constraints
(Springer, 2021) Kunwar V. K. Singh; J.K. Maurya; S.K. Mishra
In present article, we study a special class of nonlinear programming problems known as multiobjective mathematical programs with equilibrium constraints. We propose Wolfe type and Mond-Weir type dual models for multiobjective mathematical program with equilibrium constraints and establish fundamental duality results. Furthermore, we construct some examples to favor our established results. © 2021, The Author(s), under exclusive licence to Springer Nature India Private Limited.
Duality results for interval-valued semiinfinite optimization problems with equilibrium constraints using convexificators
(Institute for Ionics, 2022) K.K. Lai; S.K. Mishra; Mohd Hassan; Jaya Bisht; J.K. Maurya
This paper deals with the study of interval-valued semiinfinite optimization problems with equilibrium constraints (ISOPEC) using convexificators. First, we formulate Wolfe-type dual problem for (ISOPEC) and establish duality results between the (ISOPEC) and the corresponding Wolfe-type dual under the assumption of ∂∗-convexity. Second, we formulate Mond–Weir-type dual problem and propose duality results between the (ISOPEC) and the corresponding Mond–Weir-type dual under the assumption of ∂∗-convexity, ∂∗-pseudoconvexity, and ∂∗-quasiconvexity. © 2022, The Author(s).
Lagrange duality and saddle point optimality conditions for semi-infinite mathematical programming problems with equilibrium constraints
(Faculty of Organizational Sciences, Belgrade, 2019) Kunwar V.K. Singh; J.K. Maurya; S.K. Mishra
In this paper, we consider a special class of optimization problems which contains infinitely many inequality constraints and finitely many complementarity constraints known as the semi-infinite mathematical programming problem with equilibrium constraints (SIMPEC). We propose Lagrange type dual model for the SIMPEC and obtain their duality results using convexity assumptions. Further, we discuss the saddle point optimality conditions for the SIMPEC. Some examples are given to illustrate the obtained results. © 2019 Faculty of Organizational Sciences, Belgrade. All rights reserved.
Multiobjective approximate gradient projection method for constrained vector optimization: Sequential optimality conditions without constraint qualifications
(Elsevier B.V., 2022) Kin Keung Lai; J.K. Maurya; S.K. Mishra
In this paper, we establish multiobjective approximate gradient projection (MAGP) and linear multiobjective approximate gradient projection (LMAGP) sequential optimality conditions without constraint qualification for multiobjective constrained optimization problems. Further, we introduce constraint qualifications under which a point that satisfies established optimality conditions also satisfies Karush–Kuhn–Tucker optimality conditions. Such constraint qualifications are called strict constraint qualifications. We discuss the relationship between introduced constraint qualifications and validate it by suitable examples. © 2022 Elsevier B.V.
Nonsmooth approximate Karush-Kuhn-Tucker conditions for multiobjective optimization problems using convexificator
(International Publications, 2019) J.K. Maurya; Kunwar V. K. Singh; S.K. Mishra
In this paper, a multiobjective optimization problem in which feasible region defined by equality and inequality constraints is considered, where the objective and constraint functions are locally Lipschitz. Here, we investigate the necessary and sufficient opti- mality conditions of Giorgi et al: (J Optim Theory Appl 171:70-89, 2016) without any constraint qualification using convexificator. Furthermore, we show that under some suitable additional conditions the approximate Karush-Kuhn-Tucker (AKKT) optimality conditions coincide with KKT optimality conditions. © 2019, International Publications. All rights reserved.
On constraint qualifications in multiobjective optimization problems with vanishing constraints: Semidifferentiable case
(International Publications, 2020) Kunwar V. K. Singh; J.K. Maurya; S.K. Mishra
In this paper, we consider a multiobjective optimization problem with vanishing constraints. We discuss some constraint qualifications for multiobjective optimization problems with vanishing constraints involving semidifferentiable functions and establish relationships among them. Also, we derive Karush-Kuhn-Tucker type necessary optimality conditions for multiobjective optimization problems with vanishing constraints involving semidifferentiable functions under generalized convexity assumptions. © 2020, International Publications. All rights reserved.
On M-Stationary Conditions and Duality for Multiobjective Mathematical Programs with Vanishing Constraints
(Springer, 2022) Mohd Hassan; J.K. Maurya; S.K. Mishra
Mathematical programs with vanishing constraints are the optimization problems that do not satisfy most of the constraint qualifications due to nonconvex feasible region. Hence, some weaker first-order conditions like M-stationary come into existence. In this paper, we establish necessary and sufficient M-stationary conditions for multiobjective mathematical problems with vanishing constraints. We formulate Wolfe and Mond–Weir type dual models for the treated problem and propose weak, strong and strict converse duality results for Wolfe and Mond–Wier dual models. Further, we provide some examples in the support of our theory. © 2022, The Author(s), under exclusive licence to Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia.