A method of linearizations for linearly constrained nonconvex nonsmooth minimization |
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Authors: | Krzysztof C. Kiwiel |
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Affiliation: | (1) Systems Research Institute, Polish Academy of Sciences, Newelska 6, 01-447 Warsaw, Poland |
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Abstract: | A readily implementable algorithm is given for minimizing a (possibly nondifferentiable and nonconvex) locally Lipschitz continuous functionf subject to linear constraints. At each iteration a polyhedral approximation tof is constructed from a few previously computed subgradients and an aggregate subgradient, which accumulates the past subgradient information. This aproximation and the linear constraints generate constraints in the search direction finding subproblem that is a quadratic programming problem. Then a stepsize is found by an approximate line search. All the algorithm's accumulation points are stationary. Moreover, the algorithm converges whenf happens to be convex. |
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Keywords: | Primary 65K05 Secondary 90C25 |
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