Results 161 to 170 of about 19,600 (195)
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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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A Subgradient Method for Vector Optimization Problems
SIAM Journal on Optimization, 2013Vector optimization problems are a significant extension of scalar optimization and have many real life applications. We consider an extension of the projected subgradient method to convex vector optimization, which works directly with vector-valued functions, without using scalar-valued objectives.
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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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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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Subgradient Method for Convex Feasibility on Riemannian Manifolds
Journal of Optimization Theory and Applications, 2011zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Glaydston de Carvalho Bento +1 more
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A Subgradient Method for Multiobjective Optimization on Riemannian Manifolds
Journal of Optimization Theory and Applications, 2013The authors propose a subgradient-type method for solving a multiobjective optimization problem whose objective function, \(F=(f_1,\dots,f_m) : M \to \mathbb{R}^m\), is convex on an \(n\)-dimensional Riemannian manifold \(M\) (i.e., componentwise convex along geodesic segments joining any points of \(M\)).
Glaydston de Carvalho Bento +1 more
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A generalized subgradient method with relaxation step
Mathematical Programming, 1995zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Subgradient Methods for the Service Network Design Problem
Transportation Science, 1994We present local-improvement heuristics for a Service Network Design Problem encountered in the motor carrier industry. The scheduled set of vehicle departures determines the right hand side of the capacity constraints of the shipment routing subproblem which is modeled as a multicommodity network flow problem.
Judith M. Farvolden, Warren B. Powell
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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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