Abstract
In this paper, a class of nondifferentiable DC programming with DC inequality and DC equality constraints are considered. Firstly, in terms of this special nondifferentiable DC constraint system, an appropriate relaxed constant rank constraint qualification is proposed and used to deduce one necessary optimality condition. Then, by adopting the convexification technique, another necessary optimality condition is obtained. Further, combined with the conjugate theory, the zero duality gap properties between the pairs of Wolfe and Mond-Weir type primal-dual problems are characterized, respectively.
Highlights
DC programming has been one of the most active areas in nonconvex optimization
We mainly investigate a class of nondifferentiable DC programming with DC inequality and DC equality constraints
For the purpose of constructing Wolfe and Mond-Weir dual problems, if we directly use the first necessary optimality condition as constraint and give the objective function according to the traditional way, we find that even the weak duality is not satisfied
Summary
DC (difference of two convex functions) programming has been one of the most active areas in nonconvex optimization. Optimality and Duality for DC Programming with DC Inequality and DC Equality Constraints. There are few papers on the study of Wolfe and Mond-Weir type dual problems for DC programming with DC inequality and DC equality constraints since neither the objective nor the constrained functions enjoy the convexity.
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