Abstract
We introduce the Jordan product associated with the second-order cone K into the real Hilbert space H, and then define a one-parametric class of complementarity functions φt on H×H with the parameter t∈[0,2). We show that the squared norm of φt with tφ(0,2) is a continuously F(réchet)-differentiable merit function. By this, the second-order cone complementarity problem (SOCCP) in H can be converted into an unconstrained smooth minimization problem involving this class of merit functions, and furthermore, under the monotonicity assumption, every stationary point of this minimization problem is shown to be a solution of the SOCCP.
Original language | English |
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Pages (from-to) | 159-178 |
Number of pages | 20 |
Journal | Journal of Mathematical Analysis and Applications |
Volume | 383 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2011 Nov 1 |
Keywords
- Complementarity
- Hilbert space
- Merit functions
- Second-order cone
ASJC Scopus subject areas
- Analysis
- Applied Mathematics