Stability of the linear complementarity problem at a solution point
Article
Received:
Revised:
- 76 Downloads
- 16 Citations
Abstract
In this paper we study the behavior of a solution of the linear complementarity problem when data are perturbed. We give characterizations of strong stability of the linear complementarity problem at a solution. In the case of stability we give sufficient and necessary conditions.
Key words
Linear Complementarity Problem Stability PerturbationPreview
Unable to display preview. Download preview PDF.
References
- [1]M. Aganagic and R.W. Cottle, “A note onQ-matrices”,Mathematical Programming 16 (1979) 374–377.MATHCrossRefMathSciNetGoogle Scholar
- [2]R.D. Doverspike, “Some perturbation results for the linear complementarity problem”,Mathematical Programming 23 (1982) 181–192.MATHCrossRefMathSciNetGoogle Scholar
- [3]R.D. Doverspike and C.E. Lemke, “A partial characterization of a class of matrices defined by solutions to the linear complementarity problem”,Mathematics of Operations Research 7 (1982) 272–294.MATHMathSciNetGoogle Scholar
- [4]B.C. Eaves, “The linear complementarity problem”,Management Science 17 (1971) 612–634.MathSciNetMATHGoogle Scholar
- [5]C.B. Garcia, “Some classes of matrices in linear complementarity theory”,Mathematical Programming 5 (1974) 299–310.CrossRefGoogle Scholar
- [6]L.M. Kelly and L.T. Watson, “Erratum: Some perturbation theorems forQ-matrices”,SIAM Journal on Applied Mathematics 34 (1978) 320–321.MATHCrossRefMathSciNetGoogle Scholar
- [7]L.M. Kelly and L.T. Watson, “Q-matrices and spherical geometry”,Linear Algebra and its Applications 25 (1979) 175–190.MATHCrossRefMathSciNetGoogle Scholar
- [8]C.E. Lemke, “Bimatrix equilibrium points and mathematical programming”,Management Science 11 (1965) 681–689.MathSciNetGoogle Scholar
- [9]O.L. Mangasarian, “Locally unique solutions of quadratic programs, linear and nonlinear complementarity problems”,Mathematical Programming 19 (1980) 200–212.MATHCrossRefMathSciNetGoogle Scholar
- [10]O.L. Mangasarian, “Characterizations of bounded solutions of linear complementarity problems”,Mathematical Programming Study 19 (1982) 153–166.MathSciNetGoogle Scholar
- [11]K.G. Murty, “On the number of solutions to the complementarity problem and spanning properties of complementarity cones”,Linear Algebra and its Applications 5 (1972) 65–108.MATHCrossRefMathSciNetGoogle Scholar
- [12]J.S. Pang, “OnQ-matrices”,Mathematical Programming 17 (1979) 243–247.MATHCrossRefMathSciNetGoogle Scholar
- [13]S.M. Robinson, “Generalized equations and their solutions, Part I: basic theory”,Mathematical Programming Study 10 (1979) 128–141.MATHGoogle Scholar
- [14]S.M. Robinson, “Strongly regular generalized equations”,Mathematics of Operations Research 5 (1980) 43–62.MATHMathSciNetCrossRefGoogle Scholar
- [15]S.M. Robinson, “Some continuity properties of polyhedral multifunctions”,Mathematical Programming Study 14 (1981) 206–214.MATHGoogle Scholar
- [16]A. Tamir, “The complementarity problem of mathematical programming”, Doctoral dissertation, Case Western Reserve University (Cleveland, OH, 1973).Google Scholar
- [17]L.T. Watson, “A variational approach to the linear complementarity problem”, Doctoral thesis, Department of Mathematics, University of Michigan (Ann Arbor, MI, 1974).Google Scholar
- [18]L.T. Watson, “Some perturbation theorems forQ-matrices”,SIAM Journal on Applied Mathematics 31 (1976) 379–384.MATHCrossRefMathSciNetGoogle Scholar
Copyright information
© The Mathematical Programming Society, Inc. 1985