Seminar

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. 

Title: Constructing cospectral graphs with a different switching

Abstract:

Many years ago, Brendan McKay and I introduced a construction of pairs of cospectral graphs, sometimes known as local switching. In the same paper we introduced a second switching technique which produces, as special cases, the smallest pair of cospectral graphs and the smallest pair of connected cospectral graphs.

Title: Proximal alternating linearized minimization for nonconvex and nonsmooth problems

Abstract:

We will be discussing the paper (having the same title) by Jerome Bolte, Shoham Sabach and Marc Teboulle.  We introduce a proximal alternating linearized minimization (PALM) algorithm for solving a broad class of nonconvex and nonsmooth minimization problems.

Title: A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems 

Abstract:

We will be discussing the paper (having the same title) by Amir Beck and Marc Teboulle. We consider the class of iterative shrinkage-thresholding algorithms (ISTA) for solving linear inverse problems arising in signal/image processing. This class of methods, which can be viewed as an extension of the classical gradient algorithm, is attractive due to its simplicity and thus is adequate for solving large-scale problems even with dense matrix data.

Title: An application of graph "recolouring”

Abstract:

I will prove that for any graph G, if there is an edge e such that G-e has less than (k-1)!/2 cycles of length zero mod k, then the chromatic number of G is less or equal to k.