SEMISMOOTH METHODS FOR LINEAR AND NONLINEAR SECOND-ORDER CONE PROGRAMS

作者: Masao Fukushima , Christian Kanzow

DOI:

关键词:

摘要: The optimality conditions of a nonlinear second-order cone program can be reformulated as nonsmooth system equations using projection mapping. This allows the application Newton methods for solution program. Conditions local quadratic convergence these are investigated. Related also given special case linear An interesting and important feature is that they do not require strict complementarity solution.

参考文章(21)
Robert J. Vanderbei, Hande Yurttan, USING LOQO TO SOLVE SECOND-ORDER CONE PROGRAMMING PROBLEMS ,(2007)
Frank H. Clarke, Optimization and nonsmooth analysis ,(1983)
Jein-Shan Chen, Paul Tseng, An unconstrained smooth minimization reformulation of the second-order cone complementarity problem Mathematical Programming. ,vol. 104, pp. 293- 327 ,(2005) , 10.1007/S10107-005-0617-0
Jos F. Sturm, Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones Optimization Methods & Software. ,vol. 11, pp. 625- 653 ,(1999) , 10.1080/10556789908805766
Hiroshi Yamashita, Hiroshi Yabe, A primal-dual interior point method for nonlinear optimization over second-order cones Optimization Methods & Software. ,vol. 24, pp. 407- 426 ,(2009) , 10.1080/10556780902752447
Liqun Qi, Jie Sun, A nonsmooth version of Newton's method Mathematical Programming. ,vol. 58, pp. 353- 367 ,(1993) , 10.1007/BF01581275
F. Alizadeh, D. Goldfarb, Second-order cone programming Mathematical Programming. ,vol. 95, pp. 3- 51 ,(2003) , 10.1007/S10107-002-0339-5