Probabilistic Combinatorial Optimization: Moments, Semidefinite Programming, and Asymptotic Bounds

Authors:
Dimitris Bertsimas;Karthik Natarajan;Chung-Piaw Teo
Affiliations:
-;-;-
Venue:
SIAM Journal on Optimization
Year:
2005

Citing 0
Cited 7

Tight Bounds On Expected Order Statistics

Probability in the Engineering and Informational Sciences
A semidefinite optimization approach to the steady-state analysis of queueing systems

Queueing Systems: Theory and Applications
Persistency Model and Its Applications in Choice Modeling

Management Science
Mixed 0-1 Linear Programs Under Objective Uncertainty: A Completely Positive Representation

Operations Research
Stochastic 0-1 linear programming under limited distributional information

Operations Research Letters
On the Complexity of Nonoverlapping Multivariate Marginal Bounds for Probabilistic Combinatorial Optimization Problems

Operations Research
Price of Correlations in Stochastic Optimization

Operations Research

Quantified Score

Hi-index	0.00

Visualization

Abstract

We address the problem of evaluating the expected optimal objective value of a 0-1 optimization problem under uncertainty in the objective coefficients. The probabilistic model we consider prescribes limited marginal distribution information for the objective coefficients in the form of moments. We show that for a fairly general class of marginal information, a tight upper (lower) bound on the expected optimal objective value of a 0-1 maximization (minimization) problem can be computed in polynomial time if the corresponding deterministic problem is solvable in polynomial time. We provide an efficiently solvable semidefinite programming formulation to compute this tight bound. We also analyze the asymptotic behavior of a general class of combinatorial problems that includes the linear assignment, spanning tree, and traveling salesman problems, under knowledge of complete marginal distributions, with and without independence. We calculate the limiting constants exactly.