Thursday, July 17

10:30 AM-12:30 PM

(This session will run until 12:45 PM)
Law School, Room 290

Nasty Nonsmooth Nonlinear Optimization

For more than 30 years, the Nelder-Mead "simplex" algorithm and several related direct search algorithms have been widely used to minimize nasty nonlinear functions using only function values. Such functions may be discontinuous, nonsmooth, or smooth but corrupted by noise or measurement error; they may involve table lookup, interpolation, and very expensive subproblems, or simply have gradients that are impractical to compute. Despite their popularity, direct search methods were not taken seriously by numerical analysts until recently. Since 1989, however, significant advances have been made toward theoretical understanding of a broad class of direct search algorithms; today, progress is being made on the Nelder-Mead algorithm itself. The speakers in this minisymposium will discuss provably convergent pattern search algorithms, convergence and failure modes of the Nelder-Mead algorithm, and the detection and correction of those failure modes.

The purpose of this minisymposium is to present an up-to-date picture of research about theory and `best practice' for direct search methods applied to difficult optimization problems without gradient information. The intended audience includes researchers in optimization and people who want to solve optimization problems using only function values.

Organizers: C. T. Kelley, North Carolina State University; and Margaret H. Wright, Bell Laboratories

10:30 Introduction
John Ashworth Nelder, Imperial College of Science, Technology and Medicine, United Kingdom
(Cancelled) 10:45 Convergence of the Nelder-Mead Method to a Non-Stationary Point
K. I. M. McKinnon, University of Edinburgh, Scotland
10:45 Rank Ordering and Positive Bases in Pattern Search Methods
Virginia Torczon, College of William & Mary; and Robert Michael Lewis, NASA Langley Research Center
11:15 Recent Results about Theory and Practice for the Nelder-Mead Simplex Algorithm
Margaret H. Wright, Organizer
11:45 Detection and Remediation of Stagnation in the Nelder-Mead Algorithm Using a Sufficient Decrease Condition
C. T. Kelley, Organizer

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MMD, 4/30/97
tjf, 5/30/97
MMD, 7/3/97