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Stochastic Subgradient Method Converges on Tame Functions [PDF]

Foundations of Computational Mathematics, 2019
This work considers the question: what convergence guarantees does the stochastic subgradient method have in the absence of smoothness and convexity? We prove that the stochastic subgradient method, on any semialgebraic locally Lipschitz function, produces limit points that are all first-order stationary.
Damek Davis, Dmitriy Drusvyatskiy, Jason D Lee   +2 more
exaly   +4 more sources

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A subgradient method for multiobjective optimization

Computational Optimization and Applications, 2012
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
João Xavier da Cruz Neto, G. J. P. Da Silva, Orizon Pereira Ferreira, Jurandir O. Lopes   +3 more
openaire   +1 more source

An Incremental Subgradient Method on Riemannian Manifolds

Journal of Optimization Theory and Applications, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Peng Zhang 0036, Gejun Bao
openaire   +2 more sources

Subgradient Methods for Saddle-Point Problems

Journal of Optimization Theory and Applications, 2009
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Angelia Nedic, Asuman E. Ozdaglar
openaire   +2 more sources

An Effective Line Search for the Subgradient Method

Journal of Optimization Theory and Applications, 2005
One of the main drawbacks of the subgradient method is the tuning process to determine the sequence of steplengths. In this paper, the radar subgradient method, a heuristic method designed to compute a tuning-free subgradient steplength, is geometrically motivated and algebraically deduced.
Beltran, C, Heredia, F.-Javier (Francisco Javier)   +1 more
exaly   +4 more sources

Subgradient Method for Nonconvex Nonsmooth Optimization

Journal of Optimization Theory and Applications, 2012
Based on the notion of quasisecants introduced by \textit{A. M. Bagirov} and \textit{A. N. Ganjehlou} [Optim. Methods Softw. 25, No. 1, 3--18 (2010; Zbl 1202.65072)], the authors develop a version of the subgradient method for solving nonconvex nonsmooth optimization problems. Quasisecants are subgradients computed in some neighborhood of a point.
Adil M. Bagirov, L. Jin, Napsu Karmitsa, A. Al Nuaimat, Napsu Sultanova   +4 more
openaire   +2 more sources

Convergence of a simple subgradient level method

Mathematical Programming, 1999
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jean-Louis Goffin, Krzysztof C. Kiwiel
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Method of conjugate subgradients with constrained memory

Automation and Remote Control, 2014
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Evgeni A. Nurminskii, David Tien
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Subgradient and ε-Subgradient Methods

1998
Let us consider a convex programming problem (CPP): $$find{f^*} = \inf {f_0}\left( x \right),x = \left( {{x^{\left( 1 \right)}},...,{x^{\left( n \right)}}} \right) \in {E^n},$$ (2.1) subject to constraints: $${f_i}\left( x \right)\quad 0,\quad i \in \left\{ {1,2, \ldots ,m} \right\} = I;$$ (2.2) $$x \in X\quad \subseteq {E^n},$$
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Variable target value subgradient method

Mathematical Programming, 1990
Polyak's subgradient algorithm for nondifferentiable optimization problems requires prior knowledge of the optimal value of the objective function to find an optimal solution. In this paper we extend the convergence properties of the Polyak's subgradient algorithm with a fixed target value to a more general case with variable target values.
KIM, SH Kim, Sehun, AHN, HU, CHO, SC
openaire   +3 more sources