[CvGmt News] [Notiziario] [Settimanale] Fw: seminari

Liviana Paoletti paoletti at dm.unipi.it
Tue Mar 31 10:32:53 CEST 2009

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

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