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- Title
OPTIMALITY CONDITIONS FOR NONCONVEX MATHEMATICAL PROGRAMMING PROBLEMS USING WEAK SUBDIFFERENTIALS AND AUGMENTED NORMAL CONES.
- Authors
TRAN VAN SU; CHU VAN TIEP
- Abstract
In this paper, we study some characterizations of the class of weakly subdifferentiable functions and formulate optimality conditions for nonconvex mathematical programming problems described by the class of weakly subdifferentiable functions in real normed spaces. The necessary and sufficient optimality conditions for a nonconvex scalar function with a global minimum/or a global maximum at a given vector via the weak subdifferentials and augmented normal cones are established. Additionally, the necessary and sufficient optimality conditions for a nonconvex vector function with a weakly efficient solution/or an efficient solution at a given vector via the augmented weak subdifferentials and normal cones are presented too. Finally, our optimality conditions are used to derive the necessary optimality conditions for nonsmooth nonconvex mathematical programming problems with set, inequality, and equality constraints.
- Subjects
NONCONVEX programming; SUBDIFFERENTIALS; CONVEX functions; MATHEMATICAL programming; VECTOR algebra
- Publication
Applied Set-Valued Analysis & Optimization, 2024, Vol 6, Issue 2, p245
- ISSN
2562-7775
- Publication type
Article
- DOI
10.23952/asvao.6.2024.2.08