New second-order optimality conditions in multiobjective optimization problems: Differentiable case
نویسندگان
چکیده
To get positive Lagrange multipliers associated with each of the objective function, Maeda [Constraint qualification in multiobjective optimization problems: Differentiable case, J. Optimization Theory Appl., 80, 483–500 (1994)], gave some special sets and derived some generalized regularity conditions for first-order Karush–Kuhn– Tucker (KKT)-type necessary conditions of multiobjective optimization problems. Basing on Maeda’s set, Bigi and Castellani [Second order optimality conditions for differentiable multiobjective problems, RAIRO, Op. Res., 34, 411–426 (2000)], tried to get the same result for second-order optimality conditions but their treatment was not convincing. In this paper, we have generalized these regularity conditions for second-order optimality conditions under different sets and obtained positive Lagrange multipliers for the objective function.
منابع مشابه
New optimality conditions for multiobjective fuzzy programming problems
In this paper we study fuzzy multiobjective optimization problems defined for $n$ variables. Based on a new $p$-dimensional fuzzy stationary-point definition, necessary efficiency conditions are obtained. And we prove that these conditions are also sufficient under new fuzzy generalized convexity notions. Furthermore, the results are obtained under general differentiability hypothesis.
متن کاملRegularity Conditions for Non-Differentiable Infinite Programming Problems using Michel-Penot Subdifferential
In this paper we study optimization problems with infinite many inequality constraints on a Banach space where the objective function and the binding constraints are locally Lipschitz. Necessary optimality conditions and regularity conditions are given. Our approach are based on the Michel-Penot subdifferential.
متن کاملSufficiency and Duality in Multiobjective Programming under Generalized Type I Functions
In this paper, new classes of generalized (F,α,ρ, d)-V -type I functions are introduced for differentiable multiobjective programming problems. Based upon these generalized convex functions, sufficient optimality conditions are established. Weak, strong and strict converse duality theorems are also derived for Wolfe and Mond-Weir type multiobjective dual programs.
متن کاملOptimality Conditions for Approximate Solutions in Multiobjective Optimization Problems
We study firstand second-order necessary and sufficient optimality conditions for approximate weakly, properly efficient solutions of multiobjective optimization problems. Here, tangent cone, -normal cone, cones of feasible directions, second-order tangent set, asymptotic second-order cone, and Hadamard upper lower directional derivatives are used in the characterizations. The results are first...
متن کاملSufficient Second Order Optimality Conditions for C Multiobjective Optimization Problems
In this work, we use the notion of Approximate Hessian introduced by Jeyakumar and Luc [19], and a special scalarization to establish sufficient optimality conditions for constrained multiobjective optimization problems. Throughout this paper, the data are assumed to be of class C, but not necessarily of class C.
متن کامل