An ε-subgradient projection algorithm for solving a convex feasibility problem is presented.Based on the iterative projection methods and the notion of ε-subgradient,a series of special projection hyperplanes is est...An ε-subgradient projection algorithm for solving a convex feasibility problem is presented.Based on the iterative projection methods and the notion of ε-subgradient,a series of special projection hyperplanes is established.Moreover,compared with the existing projection hyperplanes methods with subgradient,the proposed hyperplanes are interactive with ε,and their ranges are more larger.The convergence of the proposed algorithm is given under some mild conditions,and the validity of the algorithm is proved by the numerical test.展开更多
In this paper we present some algorithms for minimization of DC function (difference of two convex functions). They are descent methods of the proximal-type which use the convex properties of the two convex functions ...In this paper we present some algorithms for minimization of DC function (difference of two convex functions). They are descent methods of the proximal-type which use the convex properties of the two convex functions separately. We also consider an approximate proximal point algorithm. Some properties of the ε-subdifferential and the ε-directional derivative are discussed. The convergence properties of the algorithms are established in both exact and approximate forms. Finally, we give some applications to the concave programming and maximum eigenvalue problems.展开更多
This paper gives the definitions and some properties of E-directional derivate and ε-subgradientsof cone-convex function. mom them, the optimality conditions of local and global optimal point of unconstrained cone-d....This paper gives the definitions and some properties of E-directional derivate and ε-subgradientsof cone-convex function. mom them, the optimality conditions of local and global optimal point of unconstrained cone-d.c. programming are gained. At last, the duality theorems of this programming are presented.展开更多
基金supported by the National Natural Science Foundation of China (10671126)Shanghai Leading Academic Discipline Project(S30501)
文摘An ε-subgradient projection algorithm for solving a convex feasibility problem is presented.Based on the iterative projection methods and the notion of ε-subgradient,a series of special projection hyperplanes is established.Moreover,compared with the existing projection hyperplanes methods with subgradient,the proposed hyperplanes are interactive with ε,and their ranges are more larger.The convergence of the proposed algorithm is given under some mild conditions,and the validity of the algorithm is proved by the numerical test.
基金This work was supported by the National Natural Science Foundation of China,the Oversea ExchangeFund of Nanjing Normal University,and CNPq of Brazil
文摘In this paper we present some algorithms for minimization of DC function (difference of two convex functions). They are descent methods of the proximal-type which use the convex properties of the two convex functions separately. We also consider an approximate proximal point algorithm. Some properties of the ε-subdifferential and the ε-directional derivative are discussed. The convergence properties of the algorithms are established in both exact and approximate forms. Finally, we give some applications to the concave programming and maximum eigenvalue problems.
基金Project supported by the National Natural Science Foundation of China
文摘This paper gives the definitions and some properties of E-directional derivate and ε-subgradientsof cone-convex function. mom them, the optimality conditions of local and global optimal point of unconstrained cone-d.c. programming are gained. At last, the duality theorems of this programming are presented.
