- Research Summary
Rothblum's Ph.D. dissertation concerned the analysis of growth decision
processes, extending Markov decision chains. A book entitled
Markov
Population Decision
Chains, co-authored with Prof. Veinott from Stanford, is about to be
published by Springer. The thesis includes an extension of the classical
Perron-Frobenius Theorem, which dates back to the beginning of the century.
A major theme of Rothblum's work has been the identification of
properties of optimal solutions/policies in a variety of (structured)
optimization problems. Examples of such properties include stationarity,
"cut across the board", interleaving, clustering, monotonicity, and priority
rules. Prof. Rothblum is currently co-authoring a book with Dr. Hwang from
Bell Labs on Partitions: Optimality and Clustering, to be published
by World Scientific. More recent work concerns the use of rewards and
penalties to induce cooperation in multi-agent systems and the comparison
of performance of Nash-equilibrium and optimal behavior.
Particular applications included supply chains.
Prof. Rothblum's Master thesis was done in Game Theory and he continues to
contribute to this area. In recent years he worked on the Stable Matching
Problem, which is an important model used to study junior labor markets.
He introduced linear algebra tools to the analysis of the model, developed
new algorithms for computing stable
matchings, and extended the model to allow for the study of senior-level
markets. Recently, jointly with S. Onn, he introduced the class of
"convex combinatorial optimization" problems and developed an efficient
approach to solve such problems, extending techniques developed to solve
partitioning problems.
Rothblum has had an extensive collaboration with Prof. Eaves
from Stanford University on computational methods over ordered fields.
They developed a framework for studying computability and solvability
of problems over ordered fields. In particular, they obtained a one-to-one
correspondence of problems with a "linear syntax" and a class of
algorithms that can solve them completely, that is, with randomization,
generate all solutions. The subject has applications in designing
algorithms for solving parametric problems.
Rothblum has published over 150 papers in (peer-reviewed) scientific journals and
collaborated with over 50 co-authors.
