Dipartimento di Ingegneria informatica, automatica e gestionale

For single-objective quadratic optimization problems, much is known about the existence of optimal solutions and the topological properties of the image set. For instance, in the unconstrained case, the image set is always a closed convex interval, and either a minimizer exists or the problem is unbounded from below. This situation changes substantially as soon as two or more objective functions are considered: the image set may be neither closed nor open, and it need not be convex. Moreover, a multiobjective problem may be unbounded from below and still have efficient solutions.

The aim of this talk is to contribute to a better understanding of quadratic multiobjective optimization problems. One tool in this analysis is provided by conic lifting-and-relaxation techniques, through which certain nonconvex quadratic problems can be reformulated exactly as convex problems over suitable cones. We use such ideas to identify a class of quadratic multiobjective problems for which all nondominated points are supported, that is, they can be obtained by weighted-sum scalarization.