Abstract
Recently Tseng (Math Program 83:159-185, 1998) extended a class of merit functions, proposed by Luo and Tseng (A new class of merit functions for the nonlinear complementarity problem, in Complementarity and Variational Problems: State of the Art, pp. 204-225, 1997), for the nonlinear complementarity problem (NCP) to the semidefinite complementarity problem (SDCP) and showed several related properties. In this paper, we extend this class of merit functions to the second-order cone complementarity problem (SOCCP) and show analogous properties as in NCP and SDCP cases. In addition, we study another class of merit functions which are based on a slight modification of the aforementioned class of merit functions. Both classes of merit functions provide an error bound for the SOCCP and have bounded level sets.
Original language | English |
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Pages (from-to) | 495-519 |
Number of pages | 25 |
Journal | Mathematical Methods of Operations Research |
Volume | 64 |
Issue number | 3 |
DOIs | |
Publication status | Published - 2006 Dec |
Keywords
- Error bound
- Jordan product
- Level set
- Merit function
- Second-order cone
- Spectral factorization
ASJC Scopus subject areas
- Software
- General Mathematics
- Management Science and Operations Research