Profesor Investigador. Titulo: Hadamard Well-posedness of Multiobjective Optimization Problems
When studying the correctness of formulations of problems of mathematical physics, Hadamard has introduced in  a notion of well-posedness. He considered that as problems of mathematical physics describe real physical processes, their mathematical formulations must satisfy the following natural requirements:
(a) the solution must exist within a class of functions C1;
(b) the solution must be unique within a class of functions C2;
(c) the solution must depend continuously on the data of the problem.
We say that a problem is Hadamard well-posed if satisfies the requirements (a)-(c). The set of functions C1 ∩ C2 is called the Hadamard well-posedness class. By dropping the uniqueness condition we obtain the notion of generalized Hadamard well-posed. The existence of solutions postulated in (a) indicates that the model is coherent and the uniqueness and stability postulated in (b)-(c) facilitate the development of accurate numerical approximations.
In this work, we study the well-posedness of families of nite dimensional multiobjective optimization problems. For these problems, two Hadamard well-posedness concepts are introduced. These concepts involve the existence and uniqueness of ecient/weak ecient solutions, and also the continuous behavior of these solutions with respect to perturbations of the data.
The perturbations in the last property are formulated through a variational convergence notion of the objective functions (see [4, 5]) and by considering approximate solutions of the perturbed problems (see ). Necessary and sufficient conditions for the well-posedness of Pareto optimization problems are obtained in general, and also under convexity and quasiconvexity assumptions.
Finally, it is proved that the convex multiobjective optimization problems are essentially well-posed in the sense of category theory.Palabras clave: Hadamard well-posed Orientación Temática: Optimization Adjunto: PDF Tipo de Presentación: Subplenaria