# Thirtieth Annual T.G. Ostrom Lecture

# Roger J-B Wets

#### April 13, 2011, 7:30pm

#### Communications Addition, Room 21 (CADD 21)

### "About an Imperative Evolution of Mathematical Analysis (from equations to inequalities)"

Roger J-B Wets received his Ph. D. in Engineering Sciences in 1965 from the University of California at Berkeley and is now a Distinguished Research Professor of Mathematics at the University of California, Davis with which he has been associated since 1984. His main research interests have been stochastic optimization and variational analysis. During the last decade his research has been focused on equilibrium problems in a stochastic environment, and on nonparametric estimation, in particular in the fusion of hard and soft information. He has published about 200 technical articles, mostly in pure and applied mathematical journals, but also in journals dealing with probability, statistics, economics and ecology.

He received a Guggenheim Fellowship in 1982-83, an Erskine Fellowship in 1991. In 1992, he was made a foreign member of the Ukrainian Academy of Sciences. In 1994, he was awarded the (SIAM-MPS) G.B. Dantzig Prize in Mathematical Programming for his contributions to stochastic programming and variational convergence. In 1998, he received the Lanchester Prize (INFORMS) for the book ‘Variational Analysis’ that he co-authored with R.T. Rockafellar which appeared in Springer’s ‘Grundlehren der mathematischen Wissenschaften.’ In 2002, he was awarded a Doctor Honoris Causa by the University of Vienna for his contributions to mathematics, statistics and economics and in 2004, he was recognized as a pioneer in the field of stochastic optimization at the 10th International Conference on Stochastic Programming.

#### Abstract:

Motivated mostly by applications in Physics and Astronomy, the classical paradigm for Mathematical Analysis can be viewed as one of solving equations including finding maximizers, critical or equilibrium points of smooth functions or of a system of such functions, especially in association with the analysis of differential equations. This, in turn, spurred striking advances in Algebra, Geometry,Topology and so on.

Nearly a century ago, Mathematics expanded its reach to include problems arising in Engineering, Economics, Biology, Operations Management and Control, …In this new landscape, the classical perspective was ill-fitted. Rather than having to solve systems of equations, now it required finding ways to characterize solutions of systems of inequalities. Rather than looking for critical points of smooth functions on an unconstricted (open) domain, one had to deal with non-smooth functions on constrained (closed) domains.

With the advent of computers in the late 1950's, there has been a tremendous expansion of interest in these new problem formulations because rather than closed-form solutions there was now the possibility of designing sophisticated (algorithmic) solution procedures with verification only being required at the conclusion of the procedure. Eventually, the need to consider the environment to be uncertain also took its place necessitating related probabilistic tools and solution procedures.

The lecture will delineate this evolution and the way mathematicians have responded to these new challenges.

#### Background Information for Talk

The background expected of those attending this talk is a general interest in and curiosity about mathematics and its applications. Helpful, but not necessary is a background in elementary university mathematics (calculus). For those with a bit more background, the following reference should satisfy a desire for more depth:

## Ostrom Events

#### Guest Lecture:

"About an Imperative Evolution of Mathematical Analysis (from equations to inequalities)."**When:**April 13, 2011 at 7:30pm

**Where:**Communication Addition, Rm 21 (CADD 21)

Refreshments will follow in the Neill Hall Hacker Lounge (2nd floor).

#### Colloquium:

"Optimization Technologies to Deal with the Fusion of Hard and Soft Information in Statistical Estimation."**Refreshments**

**When:**April 14, 2011 at 3:30pm

**Where:**Neill Hall Hacker Lounge (2nd floor)

**Colloquium**

**When:**April 14, 2011 at 4:10pm

**Where:**Neill Hall 5W