Name
Title | ||
|---|---|---|
Equivalence of Complementarity Problems to Differentiable Minimization: A Unified Approach |
Abstract | ||
|---|---|---|
We consider two merit functions for a generalized nonlinear complementarity problem (GNCP) based on quadratic regularization of the standard linearized gap function. The first extends Fukushima's merit function for variational inequality problems [Fukushima, Math. Programming, 53 (1992), pp. 99-110] and the second extends Mangasarian and Solodov's implicit Lagrangian for complementarity problems [Mangasarian and Solodov, Math. Programming, 62 (1993), pp, 277-297]. We show, among other things, that the second merit function is in the order of the natural residual squared and we give conditions under which the stationary points of this function are the solutions to GNCP. These results extend those of Luo et al. [Math. Oper, Res,, 19 (1994), pp, 880-892] and of Yamashita and Fukushima [J. Optim. Theory Appl., 84 (1995), pp. 653-663] on the properties of the implicit Lagrangian. |
Year | DOI | Venue |
|---|---|---|
1996 | 10.1137/0806024 | SIAM JOURNAL ON OPTIMIZATION |
Keywords | Field | DocType |
complementarity problem,merit function,error bound,natural residual,quadratic regularization | Complementarity (molecular biology),Mathematical optimization,Nonlinear programming,Complementarity theory,Differentiable function,Stationary point,Mixed complementarity problem,Mathematics,Nonlinear complementarity problem,Variational inequality | Journal |
Volume | Issue | ISSN |
6 | 2 | 1052-6234 |
Citations | PageRank | References |
20 | 2.98 | 2 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Paul Tseng | 1 | 623 | 77.30 |
| Nobuo Yamashita | 2 | 172 | 16.39 |
| Masao Fukushima | 3 | 2050 | 172.73 |