2003
Lagrange Prize in Continuous Optimization Citation
Adrian
Lewis, "Nonsmooth Analysis of Eigenvalues," Mathematical Programming
84 (1999), pp. 124.
Using
tools from convex and nonsmooth analysis, this paper establishes
an elegant and compact chain rule to find the subdifferential of
virtually any function of the spectrum of a symmetric matrix. It
shows that a somewhat unusual view of symmetric matrices (as being
largely functions of their eigenvalues) is the key to developing
conceptual and technical tools for optimization over the symmetric
matrices. The paper crowns a series of papers by Lewis on the analysis
of spectral functions. Like the other papers in this series, it
does a superb job of connecting optimization to important currents
in modern mathematics and in conveying the spirit of the underlying
mathematics to its optimization audience. It exposes the highly
technical subject matter forcefully and uncompromisingly, yet is
written in a remarkably lucid and engaging style.
