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Sensitivity analysis for parametric vector optimization problems using differential equations approach. (English) Zbl 0999.90040

This paper deals with a parametric vector optimization problem (VOP)\(_\nu\), with parameters in the objective functions and in the constraints. The purpose of the paper is to investigate, using the technique of trajectory continuation, the behaviour of a local solution \(x'{^*}\) of (VOP)\(_{\overline{\nu}}\) for slight perturbations of the parameters. Sensitivity information for the first order estimation of solutions is discussed by introducing the autonomous system of differential equations corresponding to (VOP). In particular, a first order approximation of the solution of (VOP)\(_{\nu}\) for \(\nu\) in a neighborhood of \(\overline{ \nu}\) can be easily obtained. Finally, to clarify the theory developed in the paper, two illustrative numerical examples are provided.
Reviewer: Rita Pini (Milano)

MSC:

90C31 Sensitivity, stability, parametric optimization
90C29 Multi-objective and goal programming
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