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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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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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On the solution of the generalized steiner problem by the subgradient method
ZOR Zeitschrift f�r Operations Research Methods and Models of Operations Research, 1990The paper is concerned with the problem of constructing a minimal cost weighted tree connecting a set of n given terminal vertices on a Euclidean plane. The authors prove that the problem is convex and that its solution is in the convex hull of the given terminal vertices and that the necessary and sufficient optimality conditions can be expressed by ...
Flavia Donno, Giancarlo Pesamosca
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A Note on the Convergence of Subgradient Optimization Methods
Mathematische Operationsforschung und Statistik. Series Optimization, 1983The author considers the problem of minimizing a closed proper convex function on \({\mathbb{R}}^ n\) over a closed convex set C. For this purpose the subgradient algorithm can be used. The theoretical convergence of this algorithm and its rate depends essentially on the choice of the step size. The purpose of this note is to present conditions for the
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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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A Proximal Bundle Method Based on Approximate Subgradients
Computational Optimization and Applications, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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