10:30 AM-12:30 PM
(This session will run until 12:45 PM)
Law School, Room 290
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
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