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Akademický článek
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Autor:
Ioffe, A. D.
The key element of the approach to the theory of necessary conditions in optimal control discussed in the paper is reduction of the original constrained problem to unconstrained minimization with subsequent application of a suitable mechanism of loca
Externí odkaz:
http://arxiv.org/abs/1904.10647
Nonsmooth optimization using Taylor-like models: error bounds, convergence, and termination criteria
We consider optimization algorithms that successively minimize simple Taylor-like models of the objective function. Methods of Gauss-Newton type for minimizing the composition of a convex function and a smooth map are common examples. Our main result
Externí odkaz:
http://arxiv.org/abs/1610.03446
Autor:
Ioffe, Alexander D.
The regularity theory for variational inequalities over polyhedral sets developed in a series of papers by Robinson, Ralph and Dontchev-Rockafellar in the 90s has long become classics of variational analysis. But in the available proofs of almost all
Externí odkaz:
http://arxiv.org/abs/1508.06607
Autor:
Ioffe, A. D.
Metric regularity has emerged during last 2-3 decades as one of the central concepts of variational analysis. The roots of this concept go back to a circle of fundamental regularity ideas of classical analysis embodied in such results as the implicit
Externí odkaz:
http://arxiv.org/abs/1505.07920
We present a theorem of Sard type for semi-algebraic set-valued mappings whose graphs have dimension no larger than that of their range space: the inverse of such a mapping admits a single-valued analytic localization around any pair in the graph, fo
Externí odkaz:
http://arxiv.org/abs/1504.07694
Akademický článek
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We consider the method of alternating projections for finding a point in the intersection of two closed sets, possibly nonconvex. Assuming only the standard transversality condition (or a weaker version thereof), we prove local linear convergence. Wh
Externí odkaz:
http://arxiv.org/abs/1401.7569
Publikováno v:
Proceedings of the American Mathematical Society, 2018 Dec 01. 146(12), 5157-5167.
Externí odkaz:
https://www.jstor.org/stable/90026451
Autor:
Drusvyatskiy, D., Ioffe, A. D.
We show that quadratic growth of a semi-algebraic function is equivalent to strong metric subregularity of the subdifferential --- a kind of stability of generalized critical points. In contrast, this equivalence can easily fail outside of the semi-a
Externí odkaz:
http://arxiv.org/abs/1309.1446