### Optimization and Systems Theory Seminar

Friday, November 28, 1997, 11.00-12.00, Room 3721, Lindstedtsvägen 25

**Michael Patriksson**

Department of Mathematics

Chalmers University of Technology

Göteborg, Sweden

####
Adaptive sequential quadratic programming (SQP) algorithms for
non-strictly monotone variational inequality problems

Sequential quadratic programming (SQP) algorithms are classical
Newton-type methods for the solution of nonlinear optimization
problems with nonlinear constraints. In existing analyses, the
convergence of these methods rely on an exact penalty function for the
problem to be strictly decreasing. Inherent in the analysis of this
property is the requirement that the value of the penalty parameter
chosen must be larger than a problem-specific parameter, which is hard
to estimate a priori. In the talk, we address the (more general)
variational inequality problem, and show how the problem of estimating
the proper value of this penalty parameter can be eliminated entirely
through the introduction of an adaptive scaling parameter; the new
method allows for the penalty parameter to take on any non-negative
value. The new analysis also reveals for the first time that SQP
methods are globally convergent for variational inequality problems
with non-strictly monotone problem mappings.

Calendar of seminars

*Last update: November 17, 1997 by
Anders Forsgren,
andersf@math.kth.se.
*