Research Reports from the Department of Operations
Document Type
Report
Publication Date
10-1-1969
Abstract
This paper addresses a fundamental problem in linear programming, quadratic programming, and bimatrix games: solving a system involving vectors w and z, subject to complementarity and non-negativity constraints. Existing algorithms solve this problem when the matrix M meets specific properties such as being positive semi-definite, copositive-plus, or adequate. The paper extends the problem to a broader class of matrices, including L-matrices, which are not necessarily copositive-plus, adequate, or positive semi-definite. An efficient algorithm is introduced to solve the problem for this generalized class, and its steps and correctness are detailed.
Keywords
Operations research, Linear programming, Quadratic programming, Matrices, Algorithms
Publication Title
Technical Memorandums from the Department of Operations, School of Management, Case Western Reserve University
Issue
Technical memorandum no. 163
Rights
This work is in the public domain and may be freely downloaded for personal or academic use
Recommended Citation
Chandrasekaran, R., "A Special Case of the Complementary Pivot Problem" (1969). Research Reports from the Department of Operations. 549.
https://commons.case.edu/wsom-ops-reports/549