Current Research
Main current fields of interest:
The
study of non-convex optimization problems: from the existence of solutions
to the use of the Relaxation method to describe the asymptotic behaviour
of the minimizing sequences, the so-called relaxed functional plays a prominent
role on this regard. With special interest in studying the consequences
of the lack of (convexity or quasiconvexity) weak lower semicontinuity and
coercivity (superlinear growth condition) of the function to be minimized.
A non minor interest relies on generalized conjugation schemes for single
and set-valued maps, together with its main implications in Optimization
theory.
- Optimization theory: existence, strong duality, first and second order optimality conditions, duality theory.
- Convex analysis and first and second order asymptotic analysis in convex and quasi-convex optimization,
- Calculus of Variations without convexity or coercivity