2003 Lagrange Prize Citation
"Nonsmooth Analysis of Eigenvalues,"
Mathematical Programming 84 (1999), pp. 1-24.
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.