- Wayne State University
Friday, February 6, 2009
Biblioteca DSE c/o Palazzina 32 (Ex Caserma Passalacqua)
Variational analysis has been well recognized as a rapidly growing and fruitful area in mathematics motivated mainly by the study of constrained optimization and equilibrium problems, while also applying perturbation ideas and variational principles to a broad class of problems and situations that may be not of a variational nature. One of the most characteristic features of modern variational analysis is the intrinsic presence of nonsmoothness, which naturally enters not only through the initial data of the problems under consideration but largely via variational principles and perturbation techniques applied to a variety of problems with even smooth data.
In this talk we consider recent applications of advanced variational analysis to convex and nonconvex models of welfare economics with finite-dimensional and infinite-dimensional commodity spaces. We show, in particular, that the usage of modern variational principles and techniques allows us to justify the existence of nonlinear prices in nonconvex models, which support decentralized convex-type equilibria at Pareto optimal allocations.