Convexity and generalized convexity play important roles in optimization theory. With the development of programming problem, there has been a growing interest in the higher-order dual problem and a lot of related gen...Convexity and generalized convexity play important roles in optimization theory. With the development of programming problem, there has been a growing interest in the higher-order dual problem and a lot of related generalized convexities are given. In this paper, we give the convexity of (F, α ,p ,d ,b , φ )β vector-pseudo- quasi-Type I and formulate a higher-order duality for minimax fractional type programming involving symmetric matrices, and give the weak, strong and strict converse duality theorems under the condition of higher-order (F, α ,p ,d ,b , φ )β vector-pseudoquasi-Type I.展开更多
In this paper, we establish some new generalized KKM-type theorems based on weakly generalized KKM mapping without any convexity structure in topological spaces. As applications, some minimax inequalities and an exist...In this paper, we establish some new generalized KKM-type theorems based on weakly generalized KKM mapping without any convexity structure in topological spaces. As applications, some minimax inequalities and an existence theorem of equilibrium points for an abstract generalized vector equilibrium problem are proved in topological spaces. The results presented in this paper unify and generalize some known results in recent literature.展开更多
We focus on the convergence analysis of the extended linearized alternating direction method of multipliers(L-ADMM)for solving convex minimization problems with three or more separable blocks in the objective function...We focus on the convergence analysis of the extended linearized alternating direction method of multipliers(L-ADMM)for solving convex minimization problems with three or more separable blocks in the objective functions.Previous convergence analysis of the L-ADMM needs to reduce the multi-block convex minimization problems to two blocks by grouping the variables.Moreover,there has been no rate of convergence analysis for the L-ADMM.In this paper,we construct a counter example to show the failure of convergence of the extended L-ADMM.We prove the convergence and establish the sublinear convergence rate of the extended L-ADMM under the assumptions that the proximal gradient step sizes are smaller than certain values,and any two coefficient matrices in linear constraints are orthogonal.展开更多
文摘Convexity and generalized convexity play important roles in optimization theory. With the development of programming problem, there has been a growing interest in the higher-order dual problem and a lot of related generalized convexities are given. In this paper, we give the convexity of (F, α ,p ,d ,b , φ )β vector-pseudo- quasi-Type I and formulate a higher-order duality for minimax fractional type programming involving symmetric matrices, and give the weak, strong and strict converse duality theorems under the condition of higher-order (F, α ,p ,d ,b , φ )β vector-pseudoquasi-Type I.
基金Supported by the National Natural Science Foundation of China (No. 10771058)the Hunan Provincial Natural Science Foundation (No. 09JJ6013)
文摘In this paper, we establish some new generalized KKM-type theorems based on weakly generalized KKM mapping without any convexity structure in topological spaces. As applications, some minimax inequalities and an existence theorem of equilibrium points for an abstract generalized vector equilibrium problem are proved in topological spaces. The results presented in this paper unify and generalize some known results in recent literature.
基金supported by the National Natural Science Foundation of China(No.61179033).
文摘We focus on the convergence analysis of the extended linearized alternating direction method of multipliers(L-ADMM)for solving convex minimization problems with three or more separable blocks in the objective functions.Previous convergence analysis of the L-ADMM needs to reduce the multi-block convex minimization problems to two blocks by grouping the variables.Moreover,there has been no rate of convergence analysis for the L-ADMM.In this paper,we construct a counter example to show the failure of convergence of the extended L-ADMM.We prove the convergence and establish the sublinear convergence rate of the extended L-ADMM under the assumptions that the proximal gradient step sizes are smaller than certain values,and any two coefficient matrices in linear constraints are orthogonal.
