Seminar

Title: Asymmetric Latin squares, Steiner triple systems, and 1-factorizations

Abstract:

We outline how the Van der Waerden permanent theorem can be used to show that almost all Latin squares, Steiner triple systems, and 1-factorizations of the complete graph admit only trivial automorphisms. 

Title: Fragility and circuit-hyperplane relaxation

Abstract:

I will briefly discuss the problem of trying to determine the excluded minors for the class of GF(5)-representable matroids, highlighting the roles of N-fragility and of circuit-hyperplane relaxations.

Title: Efficient First-Order Methods for Linear Programming and Semidefinite Programming 

Abstract:

We will be discussing the paper (bearing the same title) of James Reneger.  We present a simple transformation of any linear program or semidefinite program into an equivalent convex optimization problem whose only constraints are linear equations. The objective function is defined on the whole space, making virtually all subgradient methods be immediately applicable.

Title: Orientations, Pseudoforests, Flows, and the Densest Subgraph
 

Abstract:

Given an undirected graph, consider the problem of finding an orientation such that the max-imum indegree is minimized. The Gabow-Westermann algorithm can solve it by exploiting the matroid structure of pseudoforests.

Title: Sum-of-Squares Proofs in Optimization

Abstract:

The old concept of sum-of-squares found its way into optimization and even machine learning. I will talk about this quickly evolving research area known as convex algebraic geometry.

Title: Nash-Williams

Abstract:

Crispin Nash-Williams was one of the founding professors of C&O. The talk will cover a small sample of his mathematical work, and also his association with C&O.

Title: Alternating Direction Method of Multipliers for the SDP Relaxation of the Quadratic Assignment Problem

Abstract:

The semidefinite programming (SDP) relaxation has proven to be extremely strong for many hard discrete optimization problems. This is in particular true for the quadratic assignment problem (QAP), arguably one of the hardest NP-hard discrete optimization problems.

Title: Ramsey theory for biased graphs

Abstract:

We discuss the unavoidable subgraphs of biased graphs whose underlying graph is a clique.

Title: Recent Advances in Frank-Wolfe Optimization

Abstract:

The Frank-Wolfe (FW) optimization algorithm has lately re-gained popularity thanks in particular to its ability to nicely handle the structured constraints appearing in machine learning and signal processing applications. However, its convergence rate is known to be slow (sublinear) when the solution lies at the boundary.

Title: Convex drawings of complete graphs:  topology meets geometry

Abstract:

A drawing D of the complete graph K(n) is the sphere is characterized by, for each isomorph J of K(5), D[J] is homeomorphic to one of the three rectilinear drawings of K(5).  Every drawing of K(n) in the plane with all edges straight-line segments is obviously convex.  Thus, convex drawings generalize planar point sets that are in general position.