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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 $$\mathcal {VU}$$ space decomposition. Then a $$\mathcal{VU}$$ 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:
 65K05 Numerical mathematical programming methods 90C25 Convex programming
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##### References:
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