Descent algorithm for nonsmooth stochastic multiobjective optimization

An algorithm for solving the expectation formulation of stochastic nonsmooth multiobjective optimization problems is proposed. The proposed method is an extension of the classical stochastic gradient algorithm to multiobjective optimization using the properties of a common descent vector defined in...

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Bibliographic Details
Published inComputational optimization and applications Vol. 68; no. 2; pp. 317 - 331
Main Authors Poirion, Fabrice, Mercier, Quentin, Désidéri, Jean-Antoine
Format Journal Article
LanguageEnglish
Published New York Springer US 01.11.2017
Springer Nature B.V
Springer Verlag
Subjects
Algorithms
Analysis of PDEs
Convex and Discrete Geometry
Descent
Fluid mechanics
Management Science
Mathematical programming
Mathematics
Mathematics and Statistics
Mechanics
Multiple objective analysis
Operations Research
Operations Research/Decision Theory
Optimization
Pareto optimum
Physics
Statistics
Stochastic models
Nonsmooth
Almost sure convergence
Stochastic
Multiobjective optimization
15
Multiobjective optimization · Stochastic · Nonsmooth · Almost
sure convergence
Online AccessGet full text
ISSN0926-6003
1573-2894
1573-2894
DOI10.1007/s10589-017-9921-x

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Summary:An algorithm for solving the expectation formulation of stochastic nonsmooth multiobjective optimization problems is proposed. The proposed method is an extension of the classical stochastic gradient algorithm to multiobjective optimization using the properties of a common descent vector defined in the deterministic context. The mean square and the almost sure convergence of the algorithm are proven. The algorithm efficiency is illustrated and assessed on an academic example.
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ISSN:0926-6003
1573-2894
1573-2894
DOI:10.1007/s10589-017-9921-x