Some NP-complete problems in quadratic and nonlinear programming
Mathematical Programming: Series A and B
The expected length of a shortest path
Information Processing Letters
Resistance bounds for first-passage percolation and maximum flow
Journal of Combinatorial Theory Series A
The ζ (2) limit in the random assignment problem
Random Structures & Algorithms
Approximation of the Stability Number of a Graph via Copositive Programming
SIAM Journal on Optimization
On Copositive Programming and Standard Quadratic Optimization Problems
Journal of Global Optimization
On the Value of a Random Minimum Weight Steiner Tree
Combinatorica
Probabilistic Combinatorial Optimization: Moments, Semidefinite Programming, and Asymptotic Bounds
SIAM Journal on Optimization
Optimal Inequalities in Probability Theory: A Convex Optimization Approach
SIAM Journal on Optimization
A Conic Programming Approach to Generalized Tchebycheff Inequalities
Mathematics of Operations Research
Proofs of the Parisi and Coppersmith-Sorkin random assignment conjectures
Random Structures & Algorithms
Persistence in discrete optimization under data uncertainty
Mathematical Programming: Series A and B
Robust Mean-Covariance Solutions for Stochastic Optimization
Operations Research
Persistency Model and Its Applications in Choice Modeling
Management Science
On the copositive representation of binary and continuous nonconvex quadratic programs
Mathematical Programming: Series A and B
A “Joint+Marginal” Approach to Parametric Polynomial Optimization
SIAM Journal on Optimization
Journal of Global Optimization
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In this paper, we analyze mixed 0-1 linear programs under objective uncertainty. The mean vector and the second-moment matrix of the nonnegative objective coefficients are assumed to be known, but the exact form of the distribution is unknown. Our main result shows that computing a tight upper bound on the expected value of a mixed 0-1 linear program in maximization form with random objective is a completely positive program. This naturally leads to semidefinite programming relaxations that are solvable in polynomial time but provide weaker bounds. The result can be extended to deal with uncertainty in the moments and more complicated objective functions. Examples from order statistics and project networks highlight the applications of the model. Our belief is that the model will open an interesting direction for future research in discrete and linear optimization under uncertainty.