The proximal-based decomposition method was originally proposed by Chen and Teboulle （Math. Programming, 1994, 64：81-101 for solving corrvex minimization problems. This paper extends it to solving monotone variation...The proximal-based decomposition method was originally proposed by Chen and Teboulle （Math. Programming, 1994, 64：81-101 for solving corrvex minimization problems. This paper extends it to solving monotone variational inequalities associated with separable structures with the improvements that the restrictive assumptions on the involved parameters are much relaxed, and thus makes it practical to solve the subproblems easily. Without additional assumptions, global convergence of the new method is proved under the same mild assumptions on the problem＇s data as the original method.展开更多
The monotone variational inequalities VI（Ω, F） have vast applications, including optimal controls and convex programming. In this paper we focus on the VI problems that have a particular splitting structure and in ...The monotone variational inequalities VI（Ω, F） have vast applications, including optimal controls and convex programming. In this paper we focus on the VI problems that have a particular splitting structure and in which the mapping F does not have an explicit form, therefore only its function values can be employed in the numerical methods for solving such problems. We study a set of numerical methods that are easily implementable. Each iteration of the proposed methods consists of two procedures. The first （prediction） procedure utilizes alternating projections to produce a predictor. The second （correction） procedure generates the new iterate via some minor computations. Convergence of the proposed methods is proved under mild conditions. Preliminary numerical experiments for some traffic equilibrium problems illustrate the effectiveness of the proposed methods.展开更多
The centroafhine Minkowski problem is studied, which is the critical case of the L_p-Minkowski problem. It admits a variational structure that plays an important role in studying the existence of solutions.In this pap...The centroafhine Minkowski problem is studied, which is the critical case of the L_p-Minkowski problem. It admits a variational structure that plays an important role in studying the existence of solutions.In this paper, we find that there is generally no maximizer of the corresponding functional for the centroaffine Minkowski problem.展开更多
基金the National Natural Science Foundation of China(No.70671024)the Na-tional High-Tech Research and Development Program of China(863 Program)(No.2006AA11Z209)
文摘The proximal-based decomposition method was originally proposed by Chen and Teboulle （Math. Programming, 1994, 64：81-101 for solving corrvex minimization problems. This paper extends it to solving monotone variational inequalities associated with separable structures with the improvements that the restrictive assumptions on the involved parameters are much relaxed, and thus makes it practical to solve the subproblems easily. Without additional assumptions, global convergence of the new method is proved under the same mild assumptions on the problem＇s data as the original method.
文摘The monotone variational inequalities VI（Ω, F） have vast applications, including optimal controls and convex programming. In this paper we focus on the VI problems that have a particular splitting structure and in which the mapping F does not have an explicit form, therefore only its function values can be employed in the numerical methods for solving such problems. We study a set of numerical methods that are easily implementable. Each iteration of the proposed methods consists of two procedures. The first （prediction） procedure utilizes alternating projections to produce a predictor. The second （correction） procedure generates the new iterate via some minor computations. Convergence of the proposed methods is proved under mild conditions. Preliminary numerical experiments for some traffic equilibrium problems illustrate the effectiveness of the proposed methods.
基金supported by National Natural Science Foundation of China (Grant No 11401527)
文摘The centroafhine Minkowski problem is studied, which is the critical case of the L_p-Minkowski problem. It admits a variational structure that plays an important role in studying the existence of solutions.In this paper, we find that there is generally no maximizer of the corresponding functional for the centroaffine Minkowski problem.
