Tuesday, May 21

8:00-10:00 AM

Oak Bay 2
## MS18

Algorithms for Multilevel Programming

In a multilevel programming problem, successive subsets of the variables are constrained to be optimal solutions of other mathematical programs, parameterized by the preceding blocks of variables. Bilevel problems arise in economics and mechanics, while general multilevel problems are encountered in multiobjective optimization and distributed engineering design optimization.
The engineering community's interest in largescale multilevel programming coupled with the ad hoc nature of many approaches indicates that there is a need for further work in this field by nonlinear programmers.

The focus of this minisymposium is practical algorithms for solving multilevel programs. The speakers will discuss convergence theory as well as practical issues encountered in the implementation of algorithms.

**Organizer: Robert Michael Lewis, **

NASA Langley Research Center

**A Two-Level Approach to Computing Worst Case Optimum Designs**
- J.R. Jagannatha Rao and K. Badhrinath, University of Houston
**Solving Nonlinear Bilevel Programs Using Trust Regions and an Exact Penalty Function**
- Paul Calamai and Lori M. Case, University of Waterloo; and Andrew R. Conn, IBM T.J. Watson Research Center
**General Nonlinear Multilevel Optimization for MDO**
- Natalia Alexandrov, NASA Langley Research Center
**Applications of a Bilevel Algorithm to Systems Governed by PDE**
- Robert Michael Lewis, Organizer

*MEM, 3/18 /96*