Generalized linear complementarity problems treated without fixed-point theory
We study the (monotone) linear complementarity problem in reflexive Banach space. The problem is treated as a quadratic program and shown to satisfy appropriate constraint qualifications. This leads to a theory of the generalized monotone linear complementarity problem which is independent of Brouwer's fixed-point theorem. Certain related results on linear systems are given. The final section concerns copositive operators.
Key WordsComplementarity dual inequality systems convex duality quadratic programming
- 2.Lemke, C. E.,A Brief Survey of Complementarity Theory, Constructive Approaches to Mathematical Models, Edited by C. V. Coffman and G. J. Fix, Academic Press, New York, New York, 1979.Google Scholar
- 12.Lemke, C. E.,Recent Results in Complementarity Problems, Nonlinear Programming, Edited by J. B. Rosen, O. L. Mangasarian, and K. Ritter, Academic Press, New York, New York, 1970.Google Scholar
- 18.McLinden, L.,The Complementarity Problem for Maximal Monotone Multifunctions, Variational Inequalities and Complementarity Problems, Edited by R. W. Cottle, F. Giannessi, and J. L. Lions, Wiley, Chichester, England, 1980.Google Scholar
- 20.Borwein, J. M.,Convex Relations in Analysis and Optimization, Generalized Concavity in Optimization and Economics, Edited by S. Schaible and W. T. Ziemba, Academic Press, New York, New York, pp. 335–377, 1981.Google Scholar
- 24.Mangasarian, O. L.,Characterizations of Bounded Solutions of Linear Complementarity Problems, Mathematical Programming Studies (to appear).Google Scholar