 |
Primal-dual approximation algorithm for network design |
Louis Billera (Department of Mathematics) works on a variety of problems arising from trying to understand fundamental combinatorial properties of convex polyhedra. These arise in many areas of mathematics, including optimization theory.
Robert Bland is interested in combinatorial and discrete optimization. He laid foundations in the study of oriented matroids, and has made key contributions to linear programming. Bland also studies apportionment, where he focuses on equitable allocation of indivisible goods among competing claimants. He is especially interested in problems of legislative apportionment, in the connections between apportionment methods and issues in local/global optimization, and in axiomatic approaches and related impossibility theorems.
Eric Friedman studies the optimization of networks and reputation systems in the context of game theoretic information economics.
Shane Henderson does research on simulation optimization, that is, on optimization problems where the objective function and/or constraint functions are evaluated using simulation. Specific applications include call center staffing, ambulance redeployment, network control, and adaptive Monte Carlo methods for variance reduction. Henderson, moreover, brings a broad swath of traditional optimization to bear in his applications work.
Adrian Lewis specializes in convex analysis and nonsmooth optimization, areas beyond the realm of traditional calculus. He also focuses on structured optimization problems that blend smooth and nonsmooth features, and on measures of well-posedness (e.g., metric regularity). He is particularly interested in the variational analysis of eigenvalues and, more generally, of spectral functions of symmetric and nonsymmetric matrices. He works on applications in robust control design, where objectives such as the distance to instability and uncontrollability play important roles.
James Renegar is interested in continuous optimization problems having differential-manifold or algebraic structure, such as problems whose constraint functions are multivariate polynomials. He also is intrigued by optimization problems that are naturally viewed from the perspective of functional analysis and its rich duality theory. Presently he is investigating sequences of relaxations of hyperbolic programming problems, of which linear programming and semidefinite programming are special cases.
David Shmoys deals with a wide range of optimization issues arising from problems with underlying combinatorial structure. The problems come in a variety of flavors, including scheduling problems, clustering problems, inventory models, and network design issues. Shmoys has worked on the design of efficient algorithms to obtain optimal and near-optimal solutions for these problems, from both theoretical and empirical perspectives. He has particularly investigated devising special-purpose LP algorithms for combinatorial problems.
Eva Tardos (Department of Computer Science) works on efficient algorithms for problems in combinatorial optimization on graphs and network.
Michael Todd is a scholar of optimization broadly. His myriad research contributions pertain foremost to continuous optimization. Among his interests nowadays are semidefinite programming and second-order cone programming, areas which have rich applications in fields as diverse as structural optimization, control theory, optimal design in statistics, and combinatorial optimization.
Huseyin Topaloglu focuses on large-scale multiperiod stochastic optimization problems. He works on problems that are large in both the number of decision variables and the number of scenarios. He seeks to approximate the recourse functions arising from multiperiod stochastic optimization problems by using ideas from simulation, optimization, and machine-learning.
Leslie Trotter is interested in discrete and combinatorial optimization. He has done considerable research on underlying abstract duality models for linear and integer programming, and on graph theoretic models (particularly structural and algorithmic properties of the stable set model).
David Williamson studies general methods for designing approximation algorithms for a wide variety of hard problems in discrete optimization.