optimizing over the pareto set

POST-PARETO ANALYSIS FOR MULTIOBJECTIVE PARABOLIC CONTROL SYSTEMS

  • Henri Bonnel
    • Categories Distributed Control, Multi-Criteria Optimization Tags , , , ,

    In this paper is presented the problem of optimizing a functional over a Pareto control set associated with a convex multiobjective control problem in Hilbert spaces, namely parabolic system. This approach generalizes for this setting some results obtained in finite dimensions. Some examples are presented. General optimality results are obtained, and a special attention is … Read more

    NONSMOOTH OPTIMIZATION OVER THE (WEAKLY OR PROPERLY) PARETO SET OF A LINEAR-QUADRATIC MULTI-OBJECTIVE CONTROL PROBLEM : EXPLICIT OPTIMALITY CONDITIONS

  • Henri Bonnel
  • Ngoc Sang Pham
    • Categories Convex and Nonsmooth Optimization, Multi-Criteria Optimization, Systems governed by Differential Equations Optimization Tags , ,

    We present explicit optimality conditions for a nonsmooth functional defined over the (properly or weakly) Pareto set associated to a multiobjective linear-quadratic control problem. This problem is very difficult even in a finite dimensional setting, i.e. when, instead of a control problem, we deal with a mathematical programming problem. Amongst different applications, our problem may … Read more