Abstract
We investigate some properties related to the generalized Newton method for the Fischer-Burmeister (FB) function over second-order cones, which allows us to reformulate the second-order cone complementarity problem (SOCCP) as a semismooth system of equations. Specifically, we characterize the B-subdifferential of the FB function at a general point and study the condition for every element of the B-subdifferential at a solution being nonsingular. In addition, for the induced FB merit function, we establish its coerciveness and provide a weaker condition than Chen and Tseng (Math. Program. 104:293-327, 2005) for each stationary point to be a solution, under suitable Cartesian P-properties of the involved mapping. By this, a damped Gauss-Newton method is proposed, and the global and superlinear convergence results are obtained. Numerical results are reported for the second-order cone programs from the DIMACS library, which verify the good theoretical properties of the method.
| Original language | English |
|---|---|
| Pages (from-to) | 293-318 |
| Number of pages | 26 |
| Journal | Applied Mathematics and Optimization |
| Volume | 59 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2009 Jun 1 |
Keywords
- B-subdifferential
- Complementarity
- Fischer-Burmeister function
- Generalized Newton method
- Second-order cones
ASJC Scopus subject areas
- Applied Mathematics
- Control and Optimization