Analyse par intervalles et optimisation convexe pour résoudre un problème général de faisabilité d'une contrainte robuste

Translated title of the contribution: Interval analysis and convex optimization to solve a robust constraint feasibility problem

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6 Citations (Scopus)

Abstract

This paper deals with the Robust Constraint Feasibility (RCF) problem which aims finding all θ such that there exists a vector x satisfying the constraint f(x, θ) < 0. An interval based algorithm will answer the question but with a crippling computational complexity which is exponential with respect to the dimension of the vector (x, θ). If the constraint function is assumed to be convex in x when θ is fixed, the paper shows that the complexity of the problem becomes polynomial with respect to the dimension of vector x and exponential with respect to the dimension of vector θ. Another contribution of the paper is to provide an algorithm which combines convex optimization and interval analysis to solve the problem with the reduced complexity. As an illustration, a simple numerical example is given.

Translated title of the contributionInterval analysis and convex optimization to solve a robust constraint feasibility problem
Original languageFrench
Pages (from-to)381-395
Number of pages15
JournalJournal Europeen des Systemes Automatises
Volume46
Issue number4-5
DOIs
Publication statusPublished - 2012
Externally publishedYes

Keywords

  • Convex optimization
  • Interval analysis
  • Robust constraint feasibility

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