## 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:

**ore
11. **

**30**

**Robust Solutions of Uncertainty Affected Conic**

Optimization Problems

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
Problems**

**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.

Tutti gli interessati sono

invitati a intervenire. Per informazioni rivolgersi a grippo@dis.uniroma1.it

**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 Approac*h (Wiley-Interscience, 1981)*Lectures on Modern Convex Optimization: Analysis, Algorithms and Engineering Applications* (SIAM-MPS

series on optimization, 2001) and *Robust
Optimization* (Princeton

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

of Operations Research

(1993-1999), member of the Editorial Board of

*SIAM J. Optimization, J.*

Convex Analysis, OR Letters,

Convex Analysis, OR Letters

*Mathematical Programming, Management*

Scienceand

Science

*Math. Modeling and Numerical Analysis, European J. of*

Operations Research and Computational Management Science.In

Operations Research and Computational Management Science.

*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.*