4:00 PM / Salon A/B

Monday, May 20

## IP2

Differential-Algebraic Equations and Continuous Optimization

Significant advances have been made in recent years in the two fields of continuous optimization and of differential equations with algebraic constraints. These advances are both in terms of development of new, efficient algorithms, and in developing a better mathematical understanding of the issues involved.
Somewhat surprisingly, the vast majority of these developments were made independently in each of the two fields, even when similar issues are involved. An example is the simulation of the dynamics of constrained mechanical systems: The time-dependent differential system arises from an optimization principle, and at each time step one is faced with the inversion of a KT matrix ("forward dynamics"). But the connection between forward dynamics and the following motion integration algorithm can be important too, and this latter connection falls outside the traditional domain of continuous optimizers. Another example is the interpretation of path following as approximating a differential system with an explicitly defined invariant.

The speaker will survey the basic
issues, structure and algorithms for differential equations with equality and inequality constraints and explore their relationship with continuous optimization techniques.

**Uri M. Ascher**

Department of Computer Science

University of British Columbia, Canada

*MEM, 3/11/96*