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).