DEPARTMENT OF COMPUTER SCIENCE

DOCTORAL DISSERTATION DEFENSE

Candidate: Madhu V. Nayakkankuppam

Advisor: Michael L. Overton

DOCTORAL DISSERTATION DEFENSE

Candidate: Madhu V. Nayakkankuppam

Advisor: Michael L. Overton

**Optimization Over Symmetric Cones **

3:00 p.m., Wednesday, August 25, 1999

Room 402, Warren Weaver Hall

Abstract

We consider the problem of optimizing a linear function
over the intersection of an affine space and a special
class of closed, convex cones, namely the symmetric cones
over the reals. This problem subsumes linear programming,
convex quadratically constrained quadratic programming, and
semidefinite programming as special cases. First, we
derive some perturbation results for this problem class.
Then, we discuss two solution methods: an
*interior-point* method capable of delivering highly
accurate solutions to problems of modest size, and a first
order *bundle method* which provides solutions of low
accuracy, but can handle much larger problems. Finally,
we describe an application of semidefinite programming in
electronic structure calculations, and give some numerical
results on sample problems.