May 28, 2013, 4:00pm
Christopher Jordan-Squire, Department of Mathematics, University of Washington
Convex Optimization on Probability Measures
Abstract: We consider a class of convex optimization problems over the space of regular Borel measures on a compact subset of n dimensional Euclidean space where the measures are restricted to be probability measures. Applications of this class of problems are discussed including mixing density estimation, maximum entropy, and optimal design. We provide a complete duality theory using perturbational techniques, establish the equivalence of these problems to associated nonconvex finite dimensional problems, and then establish the equivalence between the finite and infinite dimensional optimality conditions. Finally, some implications for numerical methods are discussed.
May 21, 2013, 4:00pm
Yang Song, Department of Mathematics, University of Washington
Stochastic Programming in Finance
Abstract: In financial markets, many assets have seemingly random behavior, such as the price of stocks, options and commodities. Therefore, financial optimization problems are often formulated as stochastic optimization problems, i.e. stochastic programming problems. This presentation introduces 3 of such financial optimization problems: credit risk optimization, asset/liability management and synthetic options, and discusses the corresponding stochastic programming models and algorithms.
May 14, 2013, 4:00pm
Jing Hong, Department of Mathematics, University of Washington
Low Rank Estimation for Matrices with Missing Diagonal
Abstract: A matrix completion problem is a matrix estimation problem where the data is a subset of the matrix entries. Such problems arise in many applications, e.g., international commerce, customer service (products/service rating analysis) and image recovery. Our study focuses on problem coming from international commerce where the diagonal entries in the model have no meaning and so are not given. Nonetheless, we wish to estimate this matrix by a low rank matrix. We present several algorithmic approaches to solving this estimation problem and present the results of our numerical experimentation.
May 3, 2013, 3:30pm
Kane Hall 220
Richard Tapia, Department of Computational and Applied Mathematics, Rice University
Math at top speed: exploring and breaking myths in the drag racing folklore
Abstract: In this talk the speaker will identify elementary mathematical frameworks for the study of old and new drag racing beliefs. In this manner some myths are validated, while others are destroyed. The first part of the talk will be a historical account of the development of drag racing and will include several lively videos and pictures depicting the speaker’s involvement in the early days of the sport.
Part of the Math Across Campus series.
April 30, 2013, 4:00pm
Ido Bright, Department of Applied Mathematics, University of Washington
Periodic Optimization Suffices for Infinite Horizon Planar Optimal Control
Abstract: We start by presenting a new result on the average velocity of long Jordan curves in plane, which is then applied to establish a Poincare-Bendixson type result for infinite horizon planar systems, where the criteria for optimization is the averaged cost.The latter result is then applied to the convex set of empirical measures of a control system. An extension to higher dimensions will be discussed.
April 23, 2013, 4:00pm
De Dennis Meng, Department of Electrical Engineering, University of Washington
Max-min Cost Flow Problem and Maximizing the Length of Geodesic via Convex Optimization
Abstract: Given a graph with edge weights or a continuous field with metric, we can find the shortest path/geodesic between a source set and destination set. In a variety of applications including network interdiction, geometric optics, landscape design, wild fire suppression, we want to design weights to change the geodesic such that all possible paths connecting the source set and destination set have the same length. In this talk, we consider the problem of optimizing weights to maximize the length of the geodesic. This problem turns out to be a convex optimization problem, and by using duality, the graph problem can be formulated as a network linear program and the discretized continuous problem can be formulated as a second-order cone program. Furthermore, we propose the convex formulation to a related but different problem: maximize the minimum total cost to transport a commodity from sources with assigned supplies to destinations with assigned demands. We show that our convex formulation is linked to the mass transportation prevention problem and traffic congestion problem which have been historically studied in the combinatorial formulation.