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On Poljak's improved subgradient method
Journal of Optimization Theory and Applications, 1988\textit{B. T. Polyak} [USSR Comput. Math. Math. Phys. 9 (1969), No.3, 14-29 (1971; Zbl 0229.65056)] has suggested an improved subgradient method and provided a lower bound on the improvement of the Euclidean distance to an optimal solution. In this paper, we provide a stronger lower bound and show that the direction of movement in this method forms a ...
Kim, S. Kim, Sehun, Koh, S.
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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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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, Gejun Bao
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2016
In this chapter we study the continuous subgradient algorithm for minimization of convex functions, under the presence of computational errors. We show that our algorithms generate a good approximate solution, if computational errors are bounded from above by a small positive constant.
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In this chapter we study the continuous subgradient algorithm for minimization of convex functions, under the presence of computational errors. We show that our algorithms generate a good approximate solution, if computational errors are bounded from above by a small positive constant.
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Nondifferentiable Optimisation Subgradient and ε — Subgradient Methods
1976We give some ideas which lead to descent methods for minimizing nondifferentiable functions. Such methods have been published in several papers and they all involve the same concept, namely the e — subdifferential.
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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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A subgradient method for multiobjective optimization
Computational Optimization and Applications, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Da Cruz Neto, J. X. +3 more
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On Convergence Properties of a Subgradient Method
Optimization Methods and Software, 2003In this article, we consider convergence properties of the normalized subgradient method which employs the stepsize rule based on a priori knowledge of the optimal value of the cost function. We show that the normalized subgradients possess additional information about the problem under consideration, which can be used for improving convergence rates ...
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(Online) Subgradient Methods for Structured Prediction
2007Promising approaches to structured learning problems have recently been developed in the maximum margin framework. Unfortunately, algorithms that are computationally and memory efficient enough to solve large scale problems have lagged behind. We propose using simple subgradient-based techniques for optimizing a regularized risk formulation of these ...
Ratliff, Nathan D. +2 more
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Scaling techniques for $��$-subgradient projection methods
2014The recent literature on first order methods for smooth optimization shows that significant improvements on the practical convergence behaviour can be achieved with variable stepsize and scaling for the gradient, making this class of algorithms attractive for a variety of relevant applications.
Bonettini, Silvia +2 more
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