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

Henri Bonnel (henri.bonnel***at***univ-nc.nc)
Ngoc Sang Pham (sang.pham***at***univ-nc.nc)

Abstract: 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.

Keywords: Multi-objective Control and Optimization, Grand coalition p-player cooperative differential game, Optimizing over the Pareto set.

Category 1: Other Topics (Multi-Criteria Optimization )

Category 2: Convex and Nonsmooth Optimization

Category 3: Nonlinear Optimization (Systems governed by Differential Equations Optimization )

Citation: JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION Volume 7, Number 4, November 2011, pp. 789809

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Entry Submitted: 10/23/2010
Entry Accepted: 10/25/2010
Entry Last Modified: 08/10/2011

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