The Implicit Complementarity Problem: Part I.
Management science research rept.,
CARNEGIE-MELLON UNIV PITTSBURGH PA MANAGEMENT SCIENCES RESEARCH GROUP
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Given an n by n matrix A,n-vector b and a mapping m from R superscript n into R superscript n, the implicit complementary problem is to find a vector x in R superscript n so that Ax b or 0, X or mx and Ax b transposed x - mx 0. This is the first of two papers in which we study this complementarity problem via an implicitly defined mapping F which depends on a given splitting of the matrix A. In the present paper, we derive sufficient conditions for the problem to have a unique solution for each vector b and study the problem in connection with a least-element theory. Author
- Theoretical Mathematics