Research Reports from the Department of Operations
Document Type
Dissertation
Publication Date
6-6-1973
Abstract
We consider the nonlinear complementarity problem: Find x in R^n such that: x ≥ 0 , f(x) ≥ 0 (1) x^T(f(x))=0 (2) where f is a given mapping satisfying f(0) = 0 and q is a vector in R^n. We say that the problem is feasible if (1) has a solution. f is said to be a Q-function if (1)-(2) has a solution for each q in R^n, and it is a P-function if the solution is unique for each q. Classes of functions are defined using properties of the complementarity problem (1)-(2), and sufficient conditions which guarantee that a function belongs to one of these classes are given. In particular, a nonlinear generalization of square matrices with nonpositive off-diagonal elements is presented, and an algorithm to solve the corresponding complementarity problem is suggested. Focusing on the linear complementarity problem we introduce additional characterizations of existing classes of matrices. We also extend the class of matrices which are known to be processed by Lemke's algorithm.
Keywords
Operations research, Mathematical optimization, Nonlinear programming, Complementarity (Physics), Linear complementarity problem, Algorithms, Functions, Mathematical analysis
Publication Title
Dissertation/Technical Memorandums from the Department of Operations, School of Management, Case Western Reserve University
Issue
Technical memorandum no. 301 ; Submitted in partial fulfillment of the requirements for the Degree of Doctor of Philosophy.
Rights
This work is in the public domain and may be freely downloaded for personal or academic use
Recommended Citation
Tamir, Arie, "The Complementarity Problem of Mathematical Programming" (1973). Research Reports from the Department of Operations. 82.
https://commons.case.edu/wsom-ops-reports/82