Abstract
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.
Highlights
Optimizing a real valued function over an efficient set associated with a vector optimization problem could be a very useful tool for a decision maker
Beginning with the work of Philip [25], the problem of optimizing a scalar objective over the efficient set of a multicriteria programming problem has been intensively studied in the last decades
In all these papers the efficient set is associated with a multicriteria mathematical programming problem, not with a multiobjective control problem
Summary
Optimizing a real valued function over an efficient set (or Pareto frontier) associated with a vector (multiobjective) optimization problem could be a very useful tool for a decision maker. Our paper continues the research initiated in [10], and is probably the second paper dealing with the much more difficult problem of optimizing a scalar objective over the (weakly or properly) efficient set associated with a multiobjective control problem. Multi-objective Control and Optimization, Grand coalition p-player cooperative differential game, Optimizing over the Pareto set. We are led to consider the problem min J0(x, u) over the set of Pareto processes associated with the grand coalition cooperative p-player differential game. The problem min J0(x, u) over the set of (weakly or properly) Pareto processes associated to the p-objective convex control problem becomes the finite dimensional problem minθ J0(θ) := J0(x(·, θ), u(·, θ)). To illustrate our approach we present some examples using Wolfram Mathematica 7
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Journal of Industrial & Management Optimization
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
