Paper Info
Title
A Combined Smoothing and Regularization Method for Monotone Second-Order Cone Complementarity Problems
Abstract
The second-order cone complementarity problem (SOCCP) is a wide class of problems containing the nonlinear complementarity problem (NCP) and the second-order cone programming problem (SOCP). Recently, Fukushima, Luo, and Tseng [SIAM J. Optim., 12 (2001), pp. 436--460] extended some merit functions and their smoothing functions for NCP to SOCCP. Moreover, they derived computable formulas for the Jacobians of the smoothing functions and gave conditions for the Jacobians to be invertible. In this paper, we propose a globally and quadratically convergent algorithm, which is based on smoothing and regularization methods, for solving monotone SOCCP. In particular, we study strong semismoothness and Jacobian consistency, which play an important role in establishing quadratic convergence of the algorithm. Furthermore, we examine the effectiveness of the algorithm by means of numerical experiments.
Year
DOI
Venue
2005
10.1137/S1052623403421516
SIAM Journal on Optimization
Keywords
Field
DocType
second-order cone complementarity problem,siam j. optim,monotone soccp,combined smoothing,jacobian consistency,monotone second-order cone complementarity,regularization method,complementarity problem,computable formula,important role,second-order cone,second-order cone programming problem,smoothing function,smoothing method,nonlinear complementarity problem,quadratically convergent algorithm,quadratic convergence
Mathematical optimization,Quadratic growth,Jacobian matrix and determinant,Complementarity theory,Smoothing,Rate of convergence,Mixed complementarity problem,Monotone polygon,Mathematics,Nonlinear complementarity problem
Journal
Volume
Issue
ISSN
15
2
1052-6234
Citations 
PageRank 
References 
69
2.34
10
Authors
3
Name
Order
Citations
PageRank
Shunsuke Hayashi1865.31
Nobuo Yamashita217216.39
Masao Fukushima32050172.73