Julien Collonge

Optimization over the Pareto Outcome set associated with a Convex Bi-Objective Optimization Problem: Theoretical Results, Deterministic Algorithm and Application to the Stochastic case

  • Henri Bonnel
  • Julien Collonge
    • Categories Multi-Criteria Optimization, Stochastic Programming

    Our paper consists of two main parts. In the first one, we deal with the deterministic problem of minimizing a real valued function $f$ over the Pareto set associated with a deterministic convex bi-objective optimization problem (BOP), in the particular case where $f$ depends on the objectives of (BOP), i.e. we optimize over the Pareto … Read more

    STOCHASTIC OPTIMIZATION OVER A PARETO SET ASSOCIATED WITH A STOCHASTIC MULTI-OBJECTIVE OPTIMIZATION PROBLEM

  • Henri Bonnel
  • Julien Collonge
    • Categories Multi-Criteria Optimization, Stochastic Approaches Tags , , , ,

    We deal with the problem of minimizing the expectation of a real valued random function over the weakly Pareto or Pareto set associated with a Stochastic Multi-Objective Optimization Problem (SMOP) whose objectives are expectations of random functions. Assuming that the closed form of these expectations is difficult to obtain, we apply the Sample Average Approximation … Read more