Abstract
Fritz John and Karush–Kuhn–Tucker necessary conditions for local LU-optimal solutions of the constrained interval-valued optimization problems involving inequality, equality and set constraints in Banach spaces in terms of convexificators are established. Under suitable assumptions on the generalized convexity of objective and constraint functions, sufficient conditions for LU-optimal solutions are given. The dual problems of Mond–Weir and Wolfe types are studied together with weak and strong duality theorems for them.
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The author is grateful to the referees for their valuable comments and suggestions which improve the paper.
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This study was funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant No. 101.01-2017.301.
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Van Luu, D., Mai, T.T. Optimality and duality in constrained interval-valued optimization. 4OR-Q J Oper Res 16, 311–337 (2018). https://doi.org/10.1007/s10288-017-0369-8
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DOI: https://doi.org/10.1007/s10288-017-0369-8
Keywords
- Interval-valued optimization problems
- Local LU-optimal solutions
- Fritz John and Karush–Kuhn–Tucker optimality conditions
- Convexificators
- Asymptotic pseudoconvexity
- Asymptotic quasiconvexity
- Duality