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
Journal of Industrial & Management Optimization 2011, 7(4): 789-809 doi: 10.3934/jimo.2011.7.789
We present explicit optimality conditions for a nonsmooth functional defined over the (properly or weakly) Pareto set associated with a multi-objective 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 various 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: Grand coalition $p$-player cooperative differential game Optimizing over the Pareto set. Multi-objective Control and Optimization

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