## Research Profile: Jonathan Eckstein

My research interests fall into two related areas. The first area is
quite broad: I am interested in the practical, effective use of
parallel computing technology to solve realistic numerical
optimization problems. My publications in this area have concentrated
on parallel branch and bound algorithms for mixed integer programming
[1,4], but include other topics [3]. In general, I am interested in
practical results on computer systems that have a large number (at
least several dozen) processors and lack shared memory; these systems
present the greatest implementation challenges.
My other area of interest is in proximal algorithms for convex
programming, and the related theory of monotone operators. Monotone
operators are rather under-appreciated in the optimization community.
In my view, their theory is quite elegant, and they provide great
insights into otherwise confusing topics such as convex programming
duality. My work relating to monotone operators has mostly concerned
various kinds of proximal algorithms. Examples are [2,5].

Both of these research areas grew out of my dissertation work, in
which I studied decomposition variants of proximal methods as a way
to derive parallel optimization algorithms.

[1] Distributed versus Centralized Storage and Control
for Parallel Branch and Bound: Mixed Integer Programming on the
CM-5.
*Computational Optimization and Applications*, 7(2):199-220 (1997).

[2] Operator Splitting Methods for Monotone Affine
Variational Inequalities, with a Parallel Application to Optimal
Control. With M. C. Ferris.
*INFORMS Journal on
Computing*, to appear.

[3] "Data-Parallel Implementations of Dense Simplex Methods on the
Connection Machine CM-2," with I. Boduroglu, L. Polymenakos, and
D. Goldfarb. *ORSA Journal on Computing* 7(4):402-416 (1995).

[4] "Parallel Branch-and-Bound Methods for Mixed-Integer Programming on
the CM-5," *SIAM Journal on Optimization* 4(4):794-814 (1994).

[5] "Nonlinear Proximal Point Algorithms using Bregman Functions, with
Applications to Convex Programming", *Mathematics of Operations
Research* 18(1):202-226 (1993).