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A superlinear space decomposition algorithm for constrained nonsmooth convex program. (English) Zbl 1226.65056
Summary: A class of constrained nonsmooth convex optimization problems, that is, piecewise $C^{2}$ convex objectives with smooth convex inequality constraints are transformed into unconstrained nonsmooth convex programs with the help of exact penalty function. The objective functions of these unconstrained programs are particular cases of functions with primal-dual gradient structure which has connection with $\cal {VU}$ space decomposition. Then a $\cal{VU}$ space decomposition method for solving this unconstrained program is presented. This method is proved to converge with local superlinear rate under certain assumptions. An illustrative example is given to show how this method works.

MSC:
65K05Mathematical programming (numerical methods)
90C25Convex programming
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References:
[1] Meng, Fanwen; Zhao, Gongyun: On second-order properties of the moreau--yosida regulation for constrained nonsmooth convex programs, Numerical functional analysis and optimization 25, 515-530 (2007) · Zbl 1071.90030
[2] Lemaréchal, C.; Oustry, F.; Sagastizábal, C.: The U-Lagrangian of a convex function, Transactions of the American mathematical society 352, 711-729 (2000) · Zbl 0939.49014 · doi:10.1090/S0002-9947-99-02243-6
[3] Mifflin, R.; Sagastizábal, C.: VU-decomposition derivatives for convex MAX-functions, Lecture notes in economics and mathematical systems 477, 167-186 (1999) · Zbl 0944.65069
[4] Mifflin, R.; Sagastizábal, C.: Proximal points are on the fast track, Journal of convex analysis 9, No. 2, 563-579 (2002) · Zbl 1037.49031
[5] Mifflin, R.; Sagastizábal, C.: VU-smoothness and proximal point results for some nonconvex functions, Optimization methods and software 19, No. 5, 463-478 (2004) · Zbl 1097.90059 · doi:10.1080/10556780410001704902
[6] Mifflin, R.; Sagastizábal, C.: On VU-theory for functions with primal-dual gradient structure, SIAM journal on optimization 11, No. 2, 547-571 (2000) · Zbl 1015.90084 · doi:10.1137/S1052623499350967
[7] Yuan Lu, Wei Wang, The VU-decomposition to the proper convex function. http://www.springerlink.com/content/t750736057402lw6/ · Zbl 1209.90290
[8] Mifflin, R.; Sagastizábal, C.: Primal-dual gradient structured functions: second-order results; links to epi-derivatives and partly smooth functions, SIAM journal on optimization 13, 1174-1197 (2003) · Zbl 1036.90067 · doi:10.1137/S1052623402412441
[9] Mifflin, R.; Sagastizábal, C.: A VU-algorihtm for convex minimization, Mathematical programming, series B 104, 583-608 (2005) · Zbl 1085.65051 · doi:10.1007/s10107-005-0630-3