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A subgradient method for multiobjective optimization
Computational Optimization and Applications, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
João Xavier da Cruz Neto +3 more
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An Incremental Subgradient Method on Riemannian Manifolds
Journal of Optimization Theory and Applications, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Peng Zhang 0036, Gejun Bao
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Subgradient Methods for Saddle-Point Problems
Journal of Optimization Theory and Applications, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Angelia Nedic, Asuman E. Ozdaglar
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Convergence of a simple subgradient level method
Mathematical Programming, 1999zbMATH 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, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Evgeni A. Nurminskii, David Tien
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Variable target value subgradient method
Mathematical Programming, 1990Polyak'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
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Subgradient and ε-Subgradient Methods
1998Let 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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Subgradient methods with perturbations in network problems
2016 54th Annual Allerton Conference on Communication, Control, and Computing (Allerton), 2016We study the impact of perturbations on the convergence of the subgradient method for the dual problem in constrained convex optimisation. Perturbations are likely to be present in practical implementations of the subgradient method and can affect either the computation of a subgradient, the update of the dual variables, or both.
Víctor Valls, Douglas J. Leith
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1985
Let f be a convex function defined on E n . The subgradient method is an algorithm which generates a sequence \(\{{x_k}\}_{k = 0}^\infty\) according to the formula $${x_{k + 1}} = {x_k} - {h_{k + 1}}\,({x_k})\,gf(x_k^{\rm{r}}),$$ (2.1) where x0 is a given starting point.
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Let f be a convex function defined on E n . The subgradient method is an algorithm which generates a sequence \(\{{x_k}\}_{k = 0}^\infty\) according to the formula $${x_{k + 1}} = {x_k} - {h_{k + 1}}\,({x_k})\,gf(x_k^{\rm{r}}),$$ (2.1) where x0 is a given starting point.
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On convergence rates of subgradient optimization methods
Mathematical Programming, 1977Rates of convergence of subgradient optimization are studied. If the step size is chosen to be a geometric progression with ratioρ the convergence, if it occurs, is geometric with rateρ. For convergence to occur, it is necessary that the initial step size be large enough, and that the ratioρ be greater than a sustainable ratez(μ), which depends upon a ...
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