### Optimization and Systems Theory Seminar

Friday, January 31, 2003, 11.00-12.00, Room 3721, Lindstedtsv. 25

**Göran Sporre**

Division of Optimization and Systems Theory

Department of Mathematics

KTH

E-mail: sporre@math.kth.se

####
On some properties of interior methods for optimization

This talk gives an overview of the four papers included in my
thesis. To begin with, a brief introduction to interior methods, which
is the common theme of the thesis, is given. Then. the main result of
each of the papers is described. Focus is put on explaining the
results rather than describing the technical details of the
derivations.
The four papers deal with convex quadratic programming, nonconvex
nonlinear programming, linear semidefinite programming and linear
programming, respectively. The first three have a theoretical flavor,
while in the fourth and final paper a number of computational ideas
are investigated.

To be more precise, the first paper concerns a boundedness result for
sequences of weighted linear least-squares problems related to
interior methods for convex quadratic programming. The second one
gives a characterization of the behavior of the updates of the
multipliers when convergence to infeasible points occur for nonconvex
problems. The third paper gives a characterization of the limit point
of the central path in linear semidefinite programming, extending
previous results to the case where strict complementarity need not
hold. The computational experiments in the fourth paper concerns the
possibility of using information available through a previous
factorization to improve performance of interior methods for linear
programming.

Calendar of seminars

*Last update: January 17, 2003 by
Anders Forsgren,
anders.forsgren@math.kth.se.
*