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A reduced subgradient algorithm
1987The authors describe an iterative method for the approximate solution of nondifferentiable convex programming problems. The problems incorporate linear equality and inequality constraints \((Ax=b\), \(x\geq 0)\); the method combines Wolfe's well-known reduced gradient algorithm with the bundle method of nonsmooth optimization.
Bihain, André +2 more
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Likelihood Subgradient Densities
Journal of the American Statistical Association, 2006We introduce likelihood subgradient densities and explore their basic properties. Using mixtures of likelihood subgradient densities, we propose an approach for constructing tight enveloping functions in the Bayesian context. In the case of normal priors with normal data, the area underneath the resulting enveloping function is bounded above by .
Nygren, Kjell, Nygren, Lan Ma
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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 Algorithm on Riemannian Manifolds
Journal of Optimization Theory and Applications, 1998zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ferreira, O. P., Oliveira, P. R.
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The Proximal Subgradient and Constancy
Canadian Mathematical Bulletin, 1993AbstractIf f is a lower semicontinuous function mapping a connected open subset of ℝn to (—∞, ∞], and if the proximal subgradient of f reduces to zero wherever it exists, then f is constant.
Clarke, F. H., Redheffer, R. M.
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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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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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Subgradient Projection Algorithm
2016In this chapter we study the subgradient projection algorithm for minimization of convex and nonsmooth functions and for computing the saddle points of convex–concave 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
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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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Fixed Point Subgradient Algorithm
2021In this chapter we consider a minimization of a convex function on a common fixed point set of a finite family of quasi-nonexpansive mappings in a Hilbert space. Our goal is to obtain a good approximate solution of the problem in the presence of computational errors.
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