# American Institute of Mathematical Sciences

October  2011, 7(4): 789-809. doi: 10.3934/jimo.2011.7.789

## Nonsmooth optimization over the (weakly or properly) Pareto set of a linear-quadratic multi-objective control problem: Explicit optimality conditions

 1 Equipe de Recherhce en Informatique et Mathématiques (ERIM), University of New Caledonia (France), B.P. R4, F98851, Nouméa Cedex, New Caledonia (French), New Caledonia (French)

Received  October 2010 Revised  May 2011 Published  August 2011

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.
Citation: Henri Bonnel, Ngoc Sang Pham. Nonsmooth optimization over the (weakly or properly) Pareto set of a linear-quadratic multi-objective control problem: Explicit optimality conditions. Journal of Industrial & Management Optimization, 2011, 7 (4) : 789-809. doi: 10.3934/jimo.2011.7.789
##### References:

show all references

##### References:

2018 Impact Factor: 1.025