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Research Experience for Undergraduates 
Project Descriptions - Summer 2010

(1) Shafiu Jibrin – Operations Research

Operations research is concerned with decision-making where one chooses decision variables that maximize or minimize an objective function, subject to the requirement that the decision variables satisfy certain constraints. For example, one may wish to find the amount of each product to produce in a factory in order to maximize the profit subject to restriction on labor, raw materials and demand on the products. A relatively new area of operations research that has many applications is called semidefinite programming. In a semidefinite programming problem one optimizes a linear objective function subject to a system of constraints called linear matrix inequalities. One part of the proposed project would develop an interior point method for solving semidefinite programming problems. The method would use a concept of weighted analytic centers and repelling limits for linear matrix inequalities. The second part would develop an efficient algorithm for computing weighted analytic centers for linear matrix inequalities when some of the weights are relatively large compared to the others. One would have an option to do either part of the project. A weighted analytic center is a minimizer of a strictly convex function as shown in the figure.

Prerequisites: A background in Linear Algebra is required. Some experience with a programming language or mathematics software (e.g., Matlab, C, C++, java, Maple, or Mathematica) is also necessary.

(2) James W. Swift – Dynamical Systems

Please come back soon for details of this fascinating project! It will involve computer simulations and the theory of dynamical systems. A background in differential equations and some knowledge of computer programming is required.