Solving Conic Systems via Rescaling

Poor conditioning of problem instances is a well-known difficulty that arises when solving convex optimization problems. Geometrically, this issue is caused by the existence of flat or nearly flat geometries in problem instances. When such geometries are encountered algorithms exhibit very slow convergence rates. The speaker develops rescaling techniques that accelerate the convergence rate of variants of the von Neumann and perceptron algorithms by improving the geometric structure of instances. This acceleration leads to exponential improvements in the convergence rates of these algorithms while maintaining their simple computational steps. This research thus bodes well for using accelerated versions of the von Neumann and perceptron algorithms for solving large scale optimization problems.

Bio: Negar Soheili is a tenure-track Assistant Professor of Business Analytics at the Information and Decision Sciences department in the University of Illinois at Chicago. She has a PhD in Operations Research from Carnegie Mellon University and a Bachelor of Science in Applied Mathematics from University of Tehran. Negar’s research focuses on improving the effectiveness of a class of algorithms with simple computational steps for solving large scale convex optimization.

Event Topic:

Computational Mathematics & Statistics