University of South Florida
College of Arts and Sciences
Title: Projection Methods for Monotone Mappings in Nonsmooth Optimization
Speaker: Oday Hazaimah, Visiting Assistant Professor, Saint Louis University
Optimization algorithms are at the core of machine learning models in which gradients and subgradients play a crucial role in nonsmooth optimization and variational inequalities. In this talk, preliminaries and relations between optimization and inclusions are introduced, important and existing methods are presented. The proposed analytical iteration is a natural modification of the classical extragradient algorithm in which it finds the solution of the sum of two monotone operators by evaluating the smooth operator twice per iteration. The convergence and complexity rates are established. To perform the projection process for monotone operators, a suitable separating hyperplane must be found in the spirit of the cutting-plane idea.
Title: Creation & annihilation of sinks in gradient dynamics related to statistical learning
Speaker: Mike Field, Research Associate, UC Santa Barbara
The talk is, for the most part, introductory with minimal prerequisites. We begin with a review of some ideas from bifurcation theory — illustrated by basic examples. Motivated by a problem in statistical learning, we then look carefully at a specific bifurcation problem involving the symmetric group. The approach here is new and some results are surprising. Discussion of the motivating problem — which originates from neural networks and machine learning — is left to the end of the talk.
The talk is based on joint work with Yossi Arjevani (School of Engineering and Computer Science, The Hebrew University, Israel).
Title: Direct and Indirect Methods for Optimal Control of Virus Propagation in Plants
Speaker: Benito Chen-Charpentier, University of Texas at Arlington
In many applications of mathematical modeling to biology, economics, social sciences and engineering, the objective is to find optimal solutions. Usually, we want to minimize an objective function depending on a number of functions subject to constraints given, for example, by systems of differential equations. Two main numerical approaches are used to solve these optimal control problems, depending on whether the problem is optimized first and then discretized, or vice versa. Each of these two approaches has its advantages and disadvantages. In this paper we describe both methods an apply them to a plant virus propagation model, where the virus is propagated through a vector that bites the infected plants. The model includes delays due to the time the virus takes to infect the plant and the vector, and seasonality due to the dependence of the behavior on the seasons.
The objective function is the total cost to a farmer of having infected plants and includes the actual cost of a plant plus the cost of the controls which are insecticides and a predator species that preys on the insects. Numerical simulations are done using both methods and comparisons are made.
Title: From Calculus to Optimal Control: Optimization for Sustainable Fishery Harvest
Speaker: Suzanne Lenhart, University of Tennessee
Marine fisheries are a significant source of protein for many human populations, and models can suggest management policies for natural renewable food resources. We will start with the concept of maximum sustainable yield modeled with one ordinary differential equation including constant proportional harvesting using calculus. Optimal control techniques can be used to design time varying harvest rates in systems of ordinary differential equations. We will illustrate these techniques with an example of a food chain model on the Turkish coast of the Black Sea. Incorporating data from the anchovy landings in Turkey, optimal control of the harvesting rate of the anchovy population in a system of three ordinary differential equations (anchovy, jellyfish, and zooplankton) gives management strategies. Finally, the idea of marine reserves in simple spatial models will be introduced.