Future students

Title: Towards Large-Scale Nonconvex/Stochastic Discrete Optimization

Abstract:

Modern data analytics is powered by scalable mathematical optimization methods. For decision-making, we want to be able to solve large-scale mathematical problems that include discrete choices or structures. These can already be very challenging to solve exactly even when the objective and feasible region are convex.

Title: Generalized Conditional Gradient for Sparse Estimation

Abstract:

We will be discussing the paper (bearing the same title) of Yaoliang Yu, Xinhua Zhang, and Dale Schuurmans.  Structured sparsity is an important modelling tool that expands the applicability of convex formulations for data analysis, however it also creates significant challenges for efficient algorithm design.

Title: Continuous Quantum Walks and Symmetric Powers

Abstract:

The k-th symmetric power of a graph X has the k-subsets of V(X) as its vertices, and two k-subsets are adjacent if their symmetric difference is an edge in X. A continuous quantum walk on a graph gives rise in a natural walk to walks on it symmetric powers.

Title: Signal Recovery by Proximal Forward-Backward Splitting

Abstract:

We will be discussing the paper (bearing the same title) of Patrick Combettes and Valérie Wajs.  We show that various inverse problems in signal recovery can be formulated as the generic problem of minimizing the sum of two convex functions with certain regularity properties.

Title: Turan problems for matroids

Abstract:

Given a fixed simple binary matroid N, what is the maximum size of a simple rank-r binary matroid that does not contain N a restriction?

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.