**5:00-5:05 **

Welcome (J. Nocedal and Sanjay Mehrotra)

**5:05-5:45 **

**Overview of Don Goldfarb's Contributions **

J. Dennis, *Rice University*

M. Todd, *Cornell University*

**5:45-6:05**

**Title: Solutions of Linear programs by Krylov Space Method
**S. Mehrotra (co-author Zhifeng Li),

mehrotra@iems.nwu.edu

Abstract:

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.

**6:05-6:25**

**Solving Convex Quadratic Programming Problems arising in Support Vector Machine
Framework**

Katya Scheinberg, *IBM*

katyas@watson.ibm.com

Abstract:

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.

**6:25-6:45**

**Robust Quadratically Constrained Quadratic Programming and Applications**

Garud Iyengar, *Columbia University*

(co-author Donald Goldfarb)

garud@ieor.columbia .edu

Abstract:

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.