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- Title
ON OPTIMALITY CONDITIONS AND DUALITY FOR NON-DIFFERENTIABLE INTERVAL-VALUED PROGRAMMING PROBLEMS WITH THE GENERALIZED (F, ρ)-CONVEXITY.
- Authors
Chen, Xiuhong; Li, Zhihua
- Abstract
Because interval-valued programming problem is used to tackle interval uncertainty that appears in many mathematical or computer models of some deterministic real-world phenomena, this paper considers a nondifferentiable interval-valued optimization problem in which objective and all constraint functions are interval-valued functions, and the involved endpoint functions in interval-valued functions are locally Lipschitz and Clarke subdifferentiable. A necessary optimality condition is first established. Some sufficient optimality conditions of the considered problem are derived for a feasible solution to be an efficient solution under the G -- (F, ρ) convexity assumption. Weak, strong, and converse duality theorems for Wolfe and Mond--Weir type duals are also obtained in order to relate the efficient solution of primal and dual inter-valued programs.
- Subjects
NONDIFFERENTIABLE functions; MATHEMATICAL models of uncertainty; COMPUTER simulation; COMPUTER programming; MATHEMATICAL optimization
- Publication
Journal of Industrial & Management Optimization, 2018, Vol 14, Issue 3, p895
- ISSN
1547-5816
- Publication type
Article
- DOI
10.3934/jimo.2017081