Convex Relaxations for Gas Expansion Planning

Convex Relaxations for Gas Expansion Planning

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Convex Relaxations for Subset Selection

We use convex relaxation techniques to produce lower bounds on the optimal value of subset selection problems and generate good approximate solutions. We then explicitly bound the quality of these relaxations by studying the approximation ratio of sparse eigenvalue relaxations. Our results are used to improve the performance of branch-and-bound algorithms to produce exact solutions to subset se...

Convex Relaxations for Permutation Problems

Seriation seeks to reconstruct a linear order between variables using unsorted, pairwise similarity information. It has direct applications in archeology and shotgun gene sequencing, for example. We write seriation as an optimization problem by proving the equivalence between the seriation and combinatorial 2-SUM problems on similarity matrices (2-SUM is a quadratic minimization problem over pe...

Convex relaxations for cubic polynomial problems

On Convex Programming Relaxations for the Permanent

In recent years, several convex programming relaxations have been proposed to estimate the permanent of a non-negative matrix, notably in the works of [GS02, Gur11, GS14]. However, the origins of these relaxations and their relationships to each other have remained somewhat mysterious. We present a conceptual framework, implicit in the belief propagation literature, to systematically arrive at ...