Keywords
non-Lipschitz vector problem
inclusion constraint
approximation
regularity
optimality condition
inclusion constraint
approximation
regularity
optimality condition
How to Cite
1.
Tinh PN. Optimality conditions for non-Lipschitz vector problems with inclusion constraints. hueuni-jns [Internet]. 2019Nov.11 [cited 2024Nov.19];128(1D):5-15. Available from: https://jos.hueuni.edu.vn/index.php/hujos-ns/article/view/5276
Abstract
We use the concept of approximation introduced by D.T. Luc et al. [1] as a generalized derivative for non-Lipschitz vector functions to consider vector problems with non-Lipschitz data under inclusion constraints. Some calculus of approximations are presented. A necessary optimality condition, a type of KKT condition, for local efficient solutions of the problems is established under an assumption on regularity. Applications and numerical examples are also given.References
- Dhara A, Luc DT, Tinh PN. On Second-Order Conditions for Nonsmooth Problems with Constraints. Vietnam Journal of Mathematics. 2012;40(2&3).
- Dien PH. On the regularity condition for the extremal problem under locally Lipschitz inclusion constraints. Applied Mathematics and Optimization. 1985;13(1):151-61.
- Khanh P, Nguyen Dinh T. Optimality Conditions Using Approximations for Nonsmooth Vector Optimization Problems under General Inequality Constraints. Journal of Convex Analysis. 2009;16.
- Tuan ND. First and second-order optimality conditions for nonsmooth vector optimization using set-valued directional derivatives. Applied Mathematics and Computation. 2015;251:300-317.
- Taa A. Second-order conditions for nonsmooth multiobjective optimization problems with inclusion constraints. Journal of Global Optimization. 2010;50(2):271-291.
- Jourani A, Thibault L. Approximations and Metric Regularity in Mathematical Programming in Banach Space. Mathematics of Operations Research. 1993 05;18(2):390-401.
- Allali K, Amahroq T. Second order approximations and dual necessary optimality conditions. Optimization. 1997;40(3):229-246.
- Khanh PQ, Tuan ND. First and Second Order Optimality Conditions Using Approximations for Nonsmooth Vector Optimization in Banach Spaces. Journal of Optimization Theory and Applications. 2006;130(2):289-308.
- Clarke FH. A New Approach to Lagrange Multipliers. Mathematics of Operations Research. 1976;1(2):165-74.
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