Abstract
In this article, we extend two classes of merit functions for the second-order complementarity problem (SOCP) to infinite-dimensional SOCP. These two classes of merit functions include several popular merit functions, which are used in nonlinear complementarity problem, (NCP)/(SDCP) semidefinite complementarity problem, and SOCP, as special cases. We give conditions under which the infinite-dimensional SOCP has a unique solution and show that all these merit functions provide an error bound for infinite-dimensional SOCP and have bounded level sets. These results are very useful for designing solution methods for infinite-dimensional SOCP.
Original language | English |
---|---|
Pages (from-to) | 387-413 |
Number of pages | 27 |
Journal | Numerical Functional Analysis and Optimization |
Volume | 31 |
Issue number | 4 |
DOIs | |
Publication status | Published - 2010 Apr |
Keywords
- Error bound
- Fixed point
- Hilbert space
- Level set
- Merit functions
- Second-order cone
ASJC Scopus subject areas
- Analysis
- Signal Processing
- Computer Science Applications
- Control and Optimization