Nonlinear Optimization

Research grant POCTI/35059/MAT/2000 funded by FCT.

January 2001 - December 2004

Doctoral Members: Joaquim Joăo Júdice and Luís Nunes Vicente (PI)
Graduate Students: Catarina Avelino, Maria C. Brás, Ana M. Monteiro, and Renata D. Silva
Consultants: Matthias Heinkenschloss, Michael Ulbrich, Stefan Ulbrich, and Stephen J. Wright

This grant deals with research in numerical solution of nonlinear programming problems (optimization problems where an objective function of several variables is minimized in a set defined by a number of equality and inequality constraints). The objective and constraint functions are assumed smooth, nonlinear, and not necessarily convex. The goal is to find a stationary or critical point (preferably a local minimizer). It is assumed that the optimization problem is posed in finite dimension, although it might result from the discretization of an infinite dimensional optimization problem. We are not concerned with "global optimization", where the best local minimizer is sought.

Many nonlinear optimization problems, typically those arising from applications, pose several difficulties to nonlinear optimization algorithms and codes, that can include numerical instability, convergence to spurious minimizers, and slow convergence. The algorithms developed and analyzed in this project consider, depending on the origin of the problem, some of following pitfalls:

Research that is already underway includes: