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pro vyhledávání: '"49J52, 90C30"'
We consider a composite optimization problem where the sum of a continuously differentiable and a merely lower semicontinuous function has to be minimized. The proximal gradient algorithm is the classical method for solving such a problem numerically
Externí odkaz:
http://arxiv.org/abs/2301.05002
Autor:
Kanzow, Christian, Mehlitz, Patrick
Composite optimization problems, where the sum of a smooth and a merely lower semicontinuous function has to be minimized, are often tackled numerically by means of proximal gradient methods as soon as the lower semicontinuous part of the objective f
Externí odkaz:
http://arxiv.org/abs/2112.01798
Using tools provided by the theory of abstract convexity, we extend conditions for zero duality gap to the context of nonconvex and nonsmooth optimization. Mimicking the classical setting, an abstract convex function is the upper envelope of a family
Externí odkaz:
http://arxiv.org/abs/1910.08156
In this short paper, we show that the solution set of a combination of equilibrium problems is not necessary contained in the intersection of a finite family of solution sets of equilibrium problems. As a corollary, we deduce that statements in recen
Externí odkaz:
http://arxiv.org/abs/1904.06013
This paper is devoted to second-order variational analysis of a rather broad class of extended-real-valued piecewise liner functions and their applications to various issues of optimization and stability. Based on our recent explicit calculations of
Externí odkaz:
http://arxiv.org/abs/1507.05350
Around a solution of an optimization problem, an "identifiable" subset of the feasible region is one containing all nearby solutions after small perturbations to the problem. A quest for only the most essential ingredients of sensitivity analysis lea
Externí odkaz:
http://arxiv.org/abs/1207.6628
We prove that uniform second order growth, tilt stability, and strong metric regularity of the limiting subdifferential --- three notions that have appeared in entirely different settings --- are all essentially equivalent for any lower-semicontinuou
Externí odkaz:
http://arxiv.org/abs/1204.5794
Autor:
Christian Kanzow, Patrick Mehlitz
Publikováno v:
Journal of Optimization Theory and Applications. 195:624-646
Composite optimization problems, where the sum of a smooth and a merely lower semicontinuous function has to be minimized, are often tackled numerically by means of proximal gradient methods as soon as the lower semicontinuous part of the objective f
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::44954d5b0d263c759727913759bee9cd
https://doi.org/10.1007/s10957-022-02101-3
https://doi.org/10.1007/s10957-022-02101-3
In this short paper, we show that the solution set of a combination of equilibrium problems is not necessary contained in the intersection of a finite family of solution sets of equilibrium problems. As a corollary, we deduce that statements in recen
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::17c2f23f2b37d8fd0a3c3fa76c9c2b02
Autor:
Adrian S. Lewis, Dmitriy Drusvyatskiy
Publikováno v:
Mathematical Programming. 147:467-498
Around a solution of an optimization problem, an "identifiable" subset of the feasible region is one containing all nearby solutions after small perturbations to the problem. A quest for only the most essential ingredients of sensitivity analysis lea
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::24cba300da8dc7a13121fe2d18618ab1
https://doi.org/10.1007/s10107-013-0730-4
https://doi.org/10.1007/s10107-013-0730-4