Seminario Aharon Ben-Tal

Il giorno 24 novembre 2009, presso l’Aula Magna del Dipartimento di Informatica e Sistemistica, Via Ariosto 25, Roma , il professor Aharon Ben-Tal - MINERVA Optimization Center - Faculty of Industrial Engineering and Management TECHNION-Israel Institute of Technology

terrà i seguenti seminari:

30  Robust Solutions of Uncertainty Affected Conic
Optimization Problems


Abstract. We survey the main developments in Robust Optimization
(RO), a methodology, which is aimed at solving optimization problems(static and
dynamic) affected by uncertainty. We focus primarily on issues of computational
tractability of the robust counterparts emerging from conic optimization
problems(linear, conic quadratic and semidefinite programming). We then show
how results pertaining to the latter issues can be used to solve difficult
chance constrained programs under partial stochastic information. Finally we
discuss the synthesis of uncertainty affected discrete-time linear control
systems by the RO methodology and illustrate the results by treating a supply
chain problem


 ore 12. 30 Some Remedies for Some Intractable Optimization


Abstract. The need to solve real-life optimization problems poses frequently a
severe challenge, as the underlying mathematical programs threaten to be
intractable. The intractability
can be attributed to any of the following properties: large dimensionality of the design dimension; lack of
convexity; parameters affected by uncertainty. In problems of designing optimal mechanical structures
(truss topology design, shape design, free material optimization), the
mathematical programs typically have hundreds of thousands of variables, a fact
which rules out the use of advanced modern solution methods, such as Interior
Point. The same situation occurs
in Medical Imaging (reconstruction of clinically acceptable images from
Positron Emission Tomographs). Some Signal Processing and Estimation problems may result
in nonconvex formulations. In the
wide area of optimization under uncertainty, some classical approaches,
such as chance (probabilistic) constraints, give rise to nonconvex NP-hard
problems. Nonconvexity also occurs
in some Robust Control problems. In all the above applications we
explain how the difficulties were resolved. In some cases this was achieved by mathematical analysis,
which converted the problems (or its dual) to a tractable convex program. In other cases novel approximation
schemes for probability inequalities were used. In the case of huge-scale convex programs, novel algorithms
were employed. In the Robust
Control example, a reparameterization scheme is developed under which the
problem is converted to a tractable deterministic convex program.


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Biographical sketch

Aharon Ben-Tal is a Professor of Operations Research and Head of the
MINERVA Optimization Center at the Faculty of Industrial Engineering and
Management at the Technion – Israel Institute of Technology, and holder of the
Dresner Chair. He received his
Ph.D. in Applied Mathematics from Northwestern University in 1973. He has been a Visiting Professor at the
University of Michigan, University of Copenhagen, Delft University of
Technology and MIT. His interests
are in Continuous Optimization, particularly nonsmooth and large-scale
problems, conic and robust optimization, as well as convex and nonsmooth
analysis. Recently the focus of his research is on optimization problems
affected by uncertainty. In the last 15 years, he has devoted much effort
to engineering applications of
optimization methodology and computational schemes. Some of the algorithms
developed in the MINERVA Optimization Center are in use by Industry ( Medical
Imaging, Aerospace). He has published more than 110 papers in professional
journals and co-authored three books: Optimality in Nonlinear Programming: A Feasible Direction Approach (Wiley-Interscience, 1981)
Lectures on Modern Convex Optimization: Analysis, Algorithms and Engineering Applications (SIAM-MPS
series on optimization, 2001) and Robust
University press,2009). Prof. Ben-Tal was Dean of the Faculty of Industrial
Engineering and Management at the Technion (1989-1992). He served as a council member of the
Mathematical Programming Society (1994-1997). He was Area Editor (Continuous Optimization) of Math.
of Operations Research

(1993-1999), member of the Editorial Board of SIAM J. Optimization, J.
Convex Analysis, OR Letters
, Mathematical Programming, Management
and Math. Modeling and Numerical Analysis, European J. of
Operations Research and Computational Management Science. 
In 2007 Professor Ben-Tal
was awarded the EURO Gold Medal-the highest distinction of Operations Research
within Europe. In 2009 he was named Fellow of INFORMS.