A one-parametric class of merit functions for the second-order cone complementarity problem

Computational Optimization and Applications

Volumn 45, Issue 3, 2010, Pages 581-606

  Chen, Jein Shan ^a,b   Pan, Shaohua ^c  

^a NATIONAL TAIWAN NORMAL UNIVERSITY   (Taiwan)

^b NATIONAL CENTER FOR THEORETICAL SCIENCES   (Taiwan)

^c SOUTH CHINA UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Complementarity; Jordan product; Merit function; Second order cone

Indexed keywords

JORDAN PRODUCT; KKT OPTIMALITY CONDITIONS; MERIT FUNCTION; NONSMOOTH SYSTEMS; NUMERICAL RESULTS; SECOND ORDER CONE; SECOND-ORDER CONE COMPLEMENTARITY PROBLEM; SECOND-ORDER CONE PROGRAM; UNCONSTRAINED MINIMIZATION;

NUMERICAL ANALYSIS; TIME VARYING CONTROL SYSTEMS;

FLOATING BREAKWATERS;

EID: 77950521302     PISSN: 09266003     EISSN: 15732894     Source Type: Journal    
DOI: 10.1007/s10589-008-9182-9     Document Type: Article

References (19)

1. F. Alizadeh D. Goldfarb 2003 Second-order cone programming Math. Program. 95 3 51 1153.90522 10.1007/s10107-002-0339-5 1971381 (Pubitemid 44757862)
2. Alizadeh, F., Schmieta, S.: Symmetric cones, potential reduction methods, and word-by-word extensions. In: Wolkowicz, H., Saigal, R., Vandenberghe, L. (eds.) Handbook of Semidefinite Programming, pp. 195-233. Kluwer Academic, Boston (2000)
3. E.D. Andersen C. Roos T. Terlaky 2003 On implementing a primal-dual interior-point method for conic quadratic optimization Math. Program. 95 249 277 1030.90137 10.1007/s10107-002-0349-3 1976481 (Pubitemid 44757855)
4. J.-S. Chen P. Tseng 2005 An unconstrained smooth minimization reformulation of the second-order cone complementarity problem Math. Program. 104 293 327 1093.90063 10.1007/s10107-005-0617-0 2179239 (Pubitemid 41521377)
5. J.-S. Chen X. Chen P. Tseng 2004 Analysis of nonsmooth vector-valued functions associated with second-order cone Math. Program. 101 95 117 1065.49013 10.1007/s10107-004-0538-3 2085260 (Pubitemid 41201320)
6. X.-D. Chen D. Sun J. Sun 2003 Complementarity functions and numerical experiments for second-order cone complementarity problems Comput. Optim. Appl. 25 39 56 1038.90084 10.1023/A:1022996819381 1996662
7. Facchinei, F., Pang, J.-S.: Finite-Dimensional Variational Inequalities and Complementarity Problems, vols. I and II. Springer, New York (2003)
8. Ferris, M.C., Mangasarian, O.L., Pang, J.-S. (eds.): Complementarity: Applications, Algorithms and Extensions. Kluwer Academic, Dordrecht (2001)
9. M. Fukushima Z.-Q. Luo P. Tseng 2002 Smoothing functions for second-order cone complementarity problems SIAM J. Optim. 12 436 460 10.1137/ S1052623400380365 1885570
10. L. Grippo F. Lampariello S. Lucidi 1986 A nonmonotone line search technique for Newton's method SIAM J. Numer. Anal. 23 707 716 0616.65067 10.1137/0723046 849278 (Pubitemid 16604645)
11. S. Hayashi N. Yamashita M. Fukushima 2005 A combined smoothing and regularization method for monotone second-order cone complementarity problems SIAM J. Optim. 15 593 615 1114.90139 10.1137/S1052623403421516 2144183 (Pubitemid 40672814)
12. C. Kanzow H. Kleinmichel 1998 A new class of semismooth Newton-type methods for nonlinear complementarity problems Comput. Optim. Appl. 11 227 251 0913.90250 10.1023/A:1026424918464 1651699 (Pubitemid 128523314)
13. M.S. Lobo L. Vandenberghe S. Boyd H. Lebret 1998 Application of second-order cone programming Linear Algebra Appl. 284 193 228 0946.90050 10.1016/S0024-3795(98)10032-0 1655138
14. Luo, Z.-Q., Tseng, P.: A new class of merit functions for the nonlinear complementarity problem. In: Ferris, M.C., Pang, J.-S. (eds.) Complementarity and Variational Problems: State of the Art, pp. 204-225. SIAM, Philadelphia (1997)
15. H.D. Mittelmann 2003 An independent benchmarking of SDP and SOCP solvers Math. Program. 95 407 430 1030.90080 10.1007/s10107-002-0355-5 1976487 (Pubitemid 44757861)
16. R.D.C. Monteiro T. Tsuchiya 2000 Polynomial convergence of primal-dual algorithms for the second-order cone programs based on the MZ-family of directions Math. Program. 88 61 83 0967.65077 10.1007/PL00011378 1765893
17. Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, New York (1999)
18. Pataki, G., Schmieta, S.: The DIMACS library of semidefinite-quadratic- linear programs. Preliminary draft, Computational Optimization Research Center, Columbia University, New York. http://dimacs.rutgers.edu/Challenges
19. T. Tsuchiya 1999 A convergence analysis of the scaling-invariant primal-dual path-following algorithms for second-order cone programming Optim. Methods Softw. 11 141 182 10.1080/10556789908805750 1777456