共查询到20条相似文献,搜索用时 15 毫秒
1.
M. M. Kostreva 《Journal of Optimization Theory and Applications》1989,62(1):63-76
Murty's algorithm for the linear complementarity problem is generalized to solve the optimality conditions for linear and convex quadratic programming problems with both equality and inequality constraints. An implementation is suggested which provides both efficiency and tight error control. Numerical experiments as well as field tests in various applications show favorable results.The author thanks K. G. Murty for his encouragement and helpful comments. 相似文献
2.
3.
A projection and contraction method for a class of linear complementarity problems and its application in convex quadratic programming 总被引:3,自引:0,他引:3
Bingsheng He 《Applied Mathematics and Optimization》1992,25(3):247-262
In this paper we propose a new iterative method for solving a class of linear complementarity problems:u 0,Mu + q 0, uT(Mu + q)=0, where M is a givenl ×l positive semidefinite matrix (not necessarily symmetric) andq is a givenl-vector. The method makes two matrix-vector multiplications and a trivial projection onto the nonnegative orthant at each iteration, and the Euclidean distance of the iterates to the solution set monotonously converges to zero. The main advantages of the method presented are its simplicity, robustness, and ability to handle large problems with any start point. It is pointed out that the method may be used to solve general convex quadratic programming problems. Preliminary numerical experiments indicate that this method may be very efficient for large sparse problems.On leave from the Department of Mathematics, University of Nanjing, Nanjing, People's Republic of China. 相似文献
4.
5.
Local minima of quadratic forms on convex cones 总被引:1,自引:0,他引:1
We study the local minima and the critical values of a quadratic form on the trace of a convex cone. This variational problem
leads to the development of a spectral theory that combines matrix algebra and facial analysis of convex cones.
相似文献
6.
A technique for the resolution of degeneracy in an Active Set Method for Quadratic Programming is described. The approach generalises Fletcher's method [2] which applies to the LP case. The method is described in terms of an LCP tableau, which is seen to provide useful insights. It is shown that the degeneracy procedure only needs to operate when the degenerate constraints are linearly dependent on those in the active set. No significant overheads are incurred by the degeneracy procedure. It is readily implemented in a null space format, and no complications in the matrix algebra are introduced.The guarantees of termination provided by [2], extending in particular to the case where round-off error is present, are preserved in the QP case. It is argued that the technique gives stronger guarantees than are available with other popular methods such as Wolfe's method [11] or the method of Goldfarb and Idnani [7].Presented at the 14th International Symposium on Mathematical Programming, Amsterdam, August 5–9, 1991. 相似文献
7.
We present an optimal piecewise-linear approximation method for the objective function of separable convex quadratic programs. The method provides guidelines on how many grid points to use and how to position them for a piecewise-linear approximation if the error induced by the approximation is to be bounded a priori.Corresponding author. 相似文献
8.
In this note, we discuss some properties of a quadratic formulation for linear complementarity problems. Projected SOR methods proposed by Mangasarian apply to symmetric matrices only. The quadratic formulation discussed here makes it possible to use these SOR methods for solving nonsymmetric LCPs. SOR schemes based on this formulation preserve sparsity. For proper choice of a free parameter, this quadratic formulation also preserves convexity. The value of the quadratic function for the solution of original LCP is also known. 相似文献
9.
Marie-Christine Plateau 《4OR: A Quarterly Journal of Operations Research》2008,6(2):187-190
This is a summary of the author’s PhD thesis supervised by A. Billionnet and S. Elloumi and defended on November 2006 at the
CNAM, Paris (Conservatoire National des Arts et Métiers). The thesis is written in French and is available from http://www.cedric.cnam.fr/PUBLIS/RC1115.
This work deals with exact solution methods based on reformulations for quadratic 0–1 programs under linear constraints. These
problems are generally not convex; more precisely, the associated continuous relaxation is not a convex problem. We developed
approaches with the aim of making the initial problem convex and of obtaining a good lower bound by continuous relaxation.
The main contribution is a general method (called QCR) that we implemented and applied to classical combinatorial optimization
problems.
相似文献
10.
In this paper we consider the consistent partition problem in reverse convex and convex mixed-integer programming. In particular we will show that for the considered classes of convex functions, both integer and relaxed systems can be partitioned into two disjoint subsystems, each of which is consistent and defines an unbounded region. The polynomial time algorithm to generate the partition will be proposed and the algorithm for a maximal partition will also be provided. 相似文献
11.
S. -C. Fang 《Mathematical Methods of Operations Research》1992,36(2):149-161
The major interest of this paper is to show that, at least in theory, a pair of primal and dual -optimal solutions to a general linear program in Karmarkar's standard form can be obtained by solving an unconstrained convex program. Hence unconstrained convex optimization methods are suggested to be carefully reviewed for this purpose. 相似文献
12.
Yinyu Ye 《Mathematical Programming》1992,57(1-3):325-335
It has been shown [8] that numerous interior-point algorithms for linear programming (LP) generate solution sequences that converge to strict complementarity solutions, or interior solutions on the optimal face. In this note we further establish a theoretical base for Gay's test (Gay, 1989) to identify the optimal face, and develop a new termination procedure to obtain an exact solution on the optimal face. We also report some numerical results for solving a set of LP test problems, each of which has a highly degenerate and unbounded optimal face.Research supported in part by NSF Grant DDM-8922636, The Iowa Business School Summer Grant, and the Interdisciplinary Research Grant of the University of Iowa Center for Advanced Studies. 相似文献
13.
Consider a linear programming problem in Karmarkar's standard form. By perturbing its linear objective function with an entropic barrier function and applying generalized geometric programming theory to it, Fang recently proposed an unconstrained convex programming approach to finding an epsilon-optimal solution. In this paper, we show that Fang's derivation of an unconstrained convex dual program can be greatly simplified by using only one simple geometric inequality. In addition, a system of nonlinear equations, which leads to a pair of primal and dual epsilon-optimal solutions, is proposed for further investigation.This work was partially supported by the North Carolina Supercomputing Center and a 1990 Cray Research Grant. The authors are indebted to Professors E. L. Peterson and R. Saigal for stimulating discussions. 相似文献
14.
We describe a new convex quadratic programming bound for the quadratic assignment problem (QAP). The construction of the bound
uses a semidefinite programming representation of a basic eigenvalue bound for QAP. The new bound dominates the well-known
projected eigenvalue bound, and appears to be competitive with existing bounds in the trade-off between bound quality and
computational effort.
Received: February 2000 / Accepted: November 2000?Published online January 17, 2001 相似文献
15.
16.
Alexander Shapiro 《Mathematical Programming》1995,70(1-3):149-157
In this paper, directional differentiability properties of the optimal value function of a parameterized semi-infinite programming problem are studied. It is shown that if the unperturbed semi-infinite programming problem is convex, then the corresponding optimal value function is directionally differentiable under mild regularity assumptions. A max-min formula for the directional derivatives, well-known in the finite convex case, is given. 相似文献
17.
We prove that a general convex quadratic program (QP) can be reduced to the problem of finding the nearest point on a simplicial cone inO(n
3 +n logL) steps, wheren andL are, respectively, the dimension and the encoding length of QP. The proof is quite simple and uses duality and repeated perturbation. The implication, however, is nontrivial since the problem of finding the nearest point on a simplicial cone has been considered a simpler problem to solve in the practical sense due to its special structure. Also we show that, theoretically, this reduction implies that (i) if an algorithm solves QP in a polynomial number of elementary arithmetic operations that is independent of the encoding length of data in the objective function then it can be used to solve QP in strongly polynomial time, and (ii) ifL is bounded by a first order exponential function ofn then (i) can be stated even in stronger terms: to solve QP in strongly polynomial time, it suffices to find an algorithm running in polynomial time that is independent of the encoding length of the quadratic term matrix or constraint matrix. Finally, based on these results, we propose a conjecture.corresponding author. The research was done when the author was at the Department of IE & OR, University of California at Berkeley, and partially supported by ONR grant N00014-91-j-1241. 相似文献
18.
M. C. Ferris 《Journal of Optimization Theory and Applications》1990,65(1):53-65
An iterative linear programming algorithm for the solution of the convex programming problem is proposed. The algorithm partially solves a sequence of linear programming subproblems whose solution is shown to converge quadratically, superlinearly, or linearly to the solution of the convex program, depending on the accuracy to which the subproblems are solved. The given algorithm is related to inexact Newton methods for the nonlinear complementarity problem. Preliminary results for an implementation of the algorithm are given.This material is based on research supported by the National Science Foundation, Grants DCR-8521228 and CCR-8723091, and by the Air Force Office of Scientific Research, Grant AFOSR-86-0172. The author would like to thank Professor O. L. Mangasarian for stimulating discussions during the preparation of this paper. 相似文献
19.
20.
The problem of minimizing a quadratic form over the standard simplex is known as the standard quadratic optimization problem (SQO). It is NP-hard, and contains the maximum stable set problem in graphs as a special case. In this note, we show that the SQO problem may be reformulated as an (exponentially sized) linear program (LP). This reformulation also suggests a hierarchy of polynomial-time solvable LP’s whose optimal values converge finitely to the optimal value of the SQO problem. The hierarchies of LP relaxations from the literature do not share this finite convergence property for SQO, and we review the relevant counterexamples. 相似文献