The penalized Fischer-Burmeister SOC complementarity function
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In this paper, we study the properties of the penalized Fischer-Burmeister (FB) second-order cone (SOC) complementarity function. We show that the function possesses similar desirable properties of the FB SOC complementarity function for local convergence; for example, with the function the second-order cone complementarity problem (SOCCP) can be reformulated as a (strongly) semismooth system of equations, and the corresponding nonsmooth Newton method has local quadratic convergence without strict complementarity of solutions. In addition, the penalized FB merit function has bounded level sets under a rather weak condition which can be satisfied by strictly feasible monotone SOCCPs or SOCCPs with the Cartesian R 01-property, although it is not continuously differentiable. Numerical results are included to illustrate the theoretical considerations.
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- 9.Facchinei, F., Pang, J.-S.: Finite-Dimensional Variational Inequalities and Complementarity Problems, vols. I and II. Springer, New York (2003) Google Scholar
- 21.Pan, S.-H., Chen, J.-S.: Quadratic convergence of semismooth methods based on the FB function for SOCPs without strict complementarity condition. IMA J. Numer. Anal. (2009, submitted) Google Scholar
- 22.Pang, J.-S., Sun, D., Sun, J.: Semismooth homeomorphisms and strong stability of semidefinite and Lorentz complementarity problems. Math. Oper. Res. 284, 193–228 (2002) Google Scholar
- 23.Pataki, G., Schmieta, S.: The DIMACS library of semidefinite-quadratic-linear programs. Preliminary draft, Computational Optimization Research Center, Columbia University, New York (2002). http://dimacs.rutgers.edu/Challenges/Seventh/Instances/