Seminar

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.

Title: An Introduction to Discrete Quantum Walks

Abstract:

We will introduce the concept of a discrete quantum walk, prove some of its properties, discuss its relation to different graph structures, and construct interesting walks from these structures such as self-dual embeddings.

Title: Coloring (cap even hole)-free graphs

Abstract:

An even cycle of length 4 or more is called an even hole. A cap is a cycle of length at least 5 with exactly one chord and that chord creates a triangle with the cycle. In this talk we consider (cap, even hole)-free graphs, i.e., graphs that do not contain any even hole or cap as an induced subgraph.

Title: A short proof of a forgotten result

Abstract:

Title: A Stochastic Gradient Method with an Exponential Convergence Rate for Finite Training Sets

Abstract:

We will be discussing the paper (having the same title) by Roux, Schmidt, and Bach.  The authors propose a new stochastic gradient method for optimizing the sum of
 a finite set of smooth functions, where the sum is strongly convex.


Title: How we solve linear programs

Abstract:

Linear programming is one of the most fundamental tools in optimization, and its theoretical complexity is well understood. In practice though, things are quite different: Which types of problems can we really solve? What sizes? With what algorithms?

Title: Coordinate Descent Algorithms

Abstract:

We will be discussing the survey of Stephen J. Wright on coordinate descent algorithms. Coordinate descent algorithms solve optimization problems by successively performing approximate minimization along coordinate directions or coordinate hyperplanes. They have been used in applications for many years, and their popularity continues to grow because of their usefulness in data analysis, machine learning, and other areas of current interest.