排序方式: 共有27条查询结果,搜索用时 37 毫秒
1.
本文主要研究在某些较弱条件下求解带线性互补约束的数学规划问题(MPLCC)正则方法的收敛性.若衡约束规划线性独立约束规范条件(MPEC-LICQ)在由正则方法产生的点列的聚点处成立,且迭代点列满足二阶必要条件,同时,若比在文[7]中渐近弱非退化条件Ⅰ更弱的渐近弱非退化条件Ⅱ在聚点处也成立,那么所有这些聚点都是B-稳定点.此外,在弱MPEC-LICQ,二阶必要条件及渐近弱退化条件Ⅱ下,我们仍能证明通过正则方法所得的聚点都是B-稳定点. 相似文献
2.
This article considers the Dirichlet problem of homogeneous and inhomogeneous second-order ordinary differential systems. A nondegeneracy result is proven for positive solutions of homogeneous systems. Sufficient and necessary conditions for the existence of multiple positive solutions for inhomogeneous systems are obtained by making use of the nondegeneracy and uniqueness results of homogeneous systems. 相似文献
3.
In this paper, we present a new relaxation method for mathematical programs with complementarity constraints. Based on the fact that a variational inequality problem defined on a simplex can be represented by a finite number of inequalities, we use an expansive simplex instead of the nonnegative orthant involved in the complementarity constraints. We then remove some inequalities and obtain a standard nonlinear program. We show that the linear independence constraint qualification or the Mangasarian–Fromovitz constraint qualification holds for the relaxed problem under some mild conditions. We consider also a limiting behavior of the relaxed problem. We prove that any accumulation point of stationary points of the relaxed problems is a weakly stationary point of the original problem and that, if the function involved in the complementarity constraints does not vanish at this point, it is C-stationary. We obtain also some sufficient conditions of B-stationarity for a feasible point of the original problem. In particular, some conditions described by the eigenvalues of the Hessian matrices of the Lagrangian functions of the relaxed problems are new and can be verified easily. Our limited numerical experience indicates that the proposed approach is promising. 相似文献
4.
We consider a mathematical program with complementarity constraints (MPCC). Our purpose is to develop methods that enable
us to compute a solution or a point with some kind of stationarity to MPCC by solving a finite number of nonlinear programs.
We apply an active set identification technique to a smoothing continuation method (Ref. 1) and propose a hybrid algorithm
for solving MPCC. We develop also two modifications: one makes use of an index addition strategy; the other adopts an index
subtraction strategy. We show that, under reasonable assumptions, all the proposed algorithms possess a finite termination
property. Further discussions and numerical experience are given as well
This work was supported in part by the Scientific Research Grant-in-Aid from the Ministry of Education, Science, Sports, and
Culture of Japan. The authors are grateful to Professor Paul Tseng for helpful suggestions on an earlier version of the paper. 相似文献
5.
In this paper, we propose an infeasible-interior-point algorithm for linear programning based on the affine scaling algorithm by Dikin. The search direction of the algorithm is composed of two directions, one for satisfying feasibility and the other for aiming at optimality. Both directions are affine scaling directions of certain linear programming problems. Global convergence of the algorithm is proved under a reasonable nondegeneracy assumption. A summary of analogous global convergence results without any nondegeneracy assumption obtained in [17] is also given. 相似文献
6.
A Modified Relaxation Scheme for Mathematical Programs with Complementarity Constraints 总被引:3,自引:0,他引:3
In this paper, we consider a mathematical program with complementarity constraints. We present a modified relaxed program
for this problem, which involves less constraints than the relaxation scheme studied by Scholtes (2000). We show that the
linear independence constraint qualification holds for the new relaxed problem under some mild conditions. We also consider
a limiting behavior of the relaxed problem. We prove that any accumulation point of stationary points of the relaxed problems
is C-stationary to the original problem under the MPEC linear independence constraint qualification and, if the Hessian matrices
of the Lagrangian functions of the relaxed problems are uniformly bounded below on the corresponding tangent space, it is
M-stationary. We also obtain some sufficient conditions of B-stationarity for a feasible point of the original problem. In
particular, some conditions described by the eigenvalues of the Hessian matrices mentioned above are new and can be verified
easily.
This work was supported in part by the Scientific Research Grant-in-Aid from the Ministry of Education, Science, Sports, and
Culture of Japan. The authors are grateful to an anonymous referee for critical comments. 相似文献
7.
8.
We prove that many complete, noncompact, constant mean curvature (CMC) surfaces
are nondegenerate; that is, the Jacobi operator Δf + | Af |2 has no L2 kernel. In fact, if ∑ has genus zero with k ends, and if f (∑) is embedded (or Alexandrov immersed) in a half-space, then we find an explicit upper bound for the dimension of the L2 kernel in terms of the number of non-cylindrical ends. Our main tool is a conjugation operation on Jacobi fields which linearizes
the conjugate cousin construction. Consequences include partial regularity for CMC moduli space, a larger class of CMC surfaces
to use in gluing constructions, and a surprising characterization of CMC surfaces via spinning spheres.
R.K. partially supported by NSF grants DMS-0076085 at GANG/UMass and DMS-9810361 at MSRI, and by a FUNCAP grant in Fortaleza,
Brazil. J.R. partially supported by an NSF VIGRE grant at Utah.
Received: January 2005; Accepted: June 2005 相似文献
9.
We prove that strict complementarity, primal and dual nondegeneracy of optimal solutions of convex optimization problems in
conic form are generic properties. In this paper, we say generic to mean that the set of data possessing the desired property
(or properties) has strictly larger Hausdorff dimension than the set of data that does not. Our proof is elementary and it
employs an important result due to Larman [7] on the boundary structure of convex bodies.
Received: September 1997 / Accepted: May 2000?Published online November 17, 2000 相似文献
10.
In this paper, we study the local uniqueness of the solutions to the extended linear complementarity problem (XLCP, Ref. 1) by means of a concept which is an extension of the nondegenerate matrix in the standard LCP. Then, we give some special characterizations for the local uniqueness of the solutions to the horizontal linear complementarity problem (HLCP). 相似文献