In this paper,we present a central cutting plane algorithm for solving convex min-max semi-infinite programming problems.Because the objective function here is non-differentiable,we apply a smoothing technique to the ...In this paper,we present a central cutting plane algorithm for solving convex min-max semi-infinite programming problems.Because the objective function here is non-differentiable,we apply a smoothing technique to the considered problem and develop an algorithm based on the entropy function.It is shown that the global convergence of the proposed algorithm can be obtained under weaker conditions.Some numerical results are presented to show the potential of the proposed algorithm.展开更多
This paper introduces some new generalizations of the concept of （~, p）-invexity for non- differentiable locally Lipschitz functions using the tools of Clarke subdifferential. These functions are used to derive the ...This paper introduces some new generalizations of the concept of （~, p）-invexity for non- differentiable locally Lipschitz functions using the tools of Clarke subdifferential. These functions are used to derive the necessary and sufficient optimality conditions for a class of nonsmooth semi-infinite minmax programming problems, where set of restrictions are indexed in a compact set. Utilizing the sufficient optimality conditions, the authors formulate three types of dual models and establish weak and strong duality results. The results of the paper extend and unify naturally some earlier results from the literature.展开更多
基金supported by National Natural Science Foundation of China(Grant No.11271221)
文摘In this paper,we present a central cutting plane algorithm for solving convex min-max semi-infinite programming problems.Because the objective function here is non-differentiable,we apply a smoothing technique to the considered problem and develop an algorithm based on the entropy function.It is shown that the global convergence of the proposed algorithm can be obtained under weaker conditions.Some numerical results are presented to show the potential of the proposed algorithm.
基金supported by the National Board of Higher Mathematics(NBHM)Department of Atomic Energy,India,under Grant No.2/40(12)/2014/R&D-II/10054
文摘This paper introduces some new generalizations of the concept of （~, p）-invexity for non- differentiable locally Lipschitz functions using the tools of Clarke subdifferential. These functions are used to derive the necessary and sufficient optimality conditions for a class of nonsmooth semi-infinite minmax programming problems, where set of restrictions are indexed in a compact set. Utilizing the sufficient optimality conditions, the authors formulate three types of dual models and establish weak and strong duality results. The results of the paper extend and unify naturally some earlier results from the literature.
