Inoltro avviso di Seminario a me pervenuto. Cordiali saluti Liviana Paoletti

----- Original Message ----- From: panicucc@mail.dm.unipi.it To: curciare@dm.unipi.it Sent: Tuesday, March 31, 2009 10:25 AM Subject: seminari

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il Prof. Boris Mordukhovich (Wayne State University) terrà un ciclo di seminari presso il Dipartimento di Matematica Applicata "U. Dini". La pregherei di darne diffusione. Grazie, Barbara Panicucci. __________________________________________________________________

April 8, 10.00 AM:"New trends and developments in variational analysis"

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. Nonlinear systems and variational systems in applied sciences also give rise to nonsmooth structures and motivate the development of new forms of analysis that rely on generalized differentiation. In this talk we discuss some new trends and developments in variational analysis and its numerous applications in both finite-dimensional and infinite-dimensional spaces, emphasizing those to optimization and equilibrium problems, robust stability and error bounds, and optimal control. _________________________________________________________________________

April 15,10.00 AM:"Variational principles in multiobjective optimization"

This talk concerns new variational principles for set-valued and vector-valued mappings, which are of their own interest while being mainly motivated by applications to problems of multiobjective optimization and equilibria. Formulations and proofs of some of these results require developing and applications of appropriate tools of generalized differentiation for nonsmooth and set-valued mappings. _________________________________________________________________________

April 16,11.00 AM:"New existence theorems and optimality conditions in multiobjective optimization and equilibria"

This talk discusses new applications of advanced variational analysis to trends in multiobjective optimization and equilibria from the viewpoint of applications modern variational principle and generalized differentiation. We mainly study Pareto-type concepts of solutions (efficient, weakly efficient, relative efficient) to multiobjective optimization and equilibrium problems and present existence theorems and necessary optimality conditions for them with and without conventional assumptions on nonempty interiors of ordering cones.

April 30,11.00 AM:"Hybrid approximate proximal method for vector optimization and variational inequalities" This talk mainly concerns vector optimization problems (VOP) of finding weakly efficient points for mappings from Hilbert spaces to Banach spaces ordered by convex and closed cones with nonempty interiors. We develop several versions of the Hybrid Approximate Proximal Method (HAPM) to find weakly efficient solutions to VOP, which all involve solving auxiliary variational inequalities _________________________________________________________________________

May 19,10.00 AM:"Variational analysis and discrete approximations in calculus of variations and optimal control"

Modern variational analysis can be viewed as a certain outgrowth of the classical calculus of variations, optimal control and mathematical programming, where perturbation-approximation methods and stability-sensitivity issues play a crucial role. In this talk we discuss recent advances in variational analysis and its applications in dynamic optimization models governed by nonconvex differential inclusions in both finite and infinite dimensions, which happen to be a natural framework for the unifying study of various problems in the calculus of variations and optimal control. We discuss an approach to such problems based on finite difference/discrete approximations of differential systems and thus related to both numerical and theoretical issues in optimization and control. Developing this approach, we reduce continuous-time optimal control problems to sequences of constrained mathematical programs of a special type, which are comprehensively studied by using modern methods of variational analysis and generalized differentiation. The main results justify well-posedness-stability of discrete approximations and establish necessary optimality conditions of Euler-Lagrange and Weierstrass-Pontryagin types for nonconvex differential inclusions employing advanced tools of variational analysis. ___________________________________________________________________ May 21,11.00 AM:"New applications of variational analysis to economic modeling" In this talk we consider recent applications of advanced variational analysis to convex and nonconvex models of microeconomics, particularly of welfare economics, with finite-dimensional and infinite-dimensional commodity spaces. Based on variational principles and generalized differentiation, we show 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.

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