Optimality Conditions for a Class of Major Constraints Nonsmooth Multi-objective Programming Problems
The optimality conditions of major constraints nonsmooth programming with multi-objectives are studied. The objective function of this class of multi-objective programming is the sum of a convex vector function and a differentiable vector function. The constraint condition is major cone constraint in Euclid space. By using of the structure representation of major cone constraint of the given problem, the Fritz John condition of Pareto weakly effective solution is obtained by Gordan theorem. Meanwhile, the Kuhn-Tucker condition for Pareto weakly effective solution under Slater constraint qualification is given. The results are very useful to design its numerical methods.
KeywordsNonsmooth multiobjective programming Gordan theorem Fritz John condition Slater constraint qualification Kuhn-Tucker condition
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