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 , , Short URL: https://optimization-online.org/?p=11300

    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 be considered as a response for a decision maker when he has to choose a solution over the solution set of the grand coalition p-player cooperative differential game.

    Citation

    JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION Volume 7, Number 4, November 2011, pp. 789–809