Welcome (J. Nocedal and Sanjay Mehrotra)
Overview of Don Goldfarb's Contributions
J. Dennis, Rice University
M. Todd, Cornell University
Title: Solutions of Linear programs by Krylov Space Method
S. Mehrotra (co-author Zhifeng Li), Northwestern University
We will present result for an extension of Mehrotra's predictor-corrector method that generates interesting directions by appropriately considering a Krylov space associated with the direction finding problem in interior point methods. Our approach results in a stable and efficient implementation significantly reducing matrix factorizations and computational times.
Solving Convex Quadratic Programming Problems arising in Support Vector Machine Framework
Katya Scheinberg, IBM
At the core of support vector machine techniques to solve a classification problem lies a convex quadratic program. This convex QP is often very large and the Hessian of the objective function is completely dense. We will discuss two main approaches to solve these problems, and show how to use the inherent structure of the problem to design efficient algorithms.
Robust Quadratically Constrained Quadratic Programming and Applications
Garud Iyengar, Columbia University
(co-author Donald Goldfarb)
We show that for a number of interesting classes of uncertainty sets robust quadratically constrained quadratic programming problem (RQCQP) can be formulated as a second-order cone program (SOCP). This is important because the complexity of SOCP is an order of magnitude smaller than that of RQCQP. We discuss applications of RQCQP in portfolio selection, antenna array design, robust-truss design, robust linear-quadratic controller design etc.