Mixed Zero-one Linear Programs Under Objective Uncertainty: A Completely Positive Representation

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 is 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 … Read more

On the computational complexity of gap-free duals for semidefinite programming

We consider the complexity of gap-free duals in semidefinite programming. Using the theory of homogeneous cones we provide a new representation of Ramana’s gap-free dual and show that the new formulation has a much better complexity than originally proved by Ramana. Citation COR@L Technical Report, Lehigh University Article Download View On the computational complexity of … Read more

Quasi-Newton methods on Grassmannians and multilinear approximations of tensors

In this paper we proposed quasi-Newton and limited memory quasi-Newton methods for objective functions defined on Grassmannians or a product of Grassmannians. Specifically we defined BFGS and L-BFGS updates in local and global coordinates on Grassmannians or a product of these. We proved that, when local coordinates are used, our BFGS updates on Grassmannians share … Read more

Transmission Expansion Planning with Re-design

Expanding an electrical transmission network requires heavy investments that need to be carefully planned, often at a regional or national level. We study relevant theoretical and practical aspects of transmission expansion planning, set as a bilinear programming problem with mixed 0-1 variables. We show that the problem is NP-hard and that, unlike the so-called Network … Read more