Geodesic
A Proximity Control Algorithm to Minimize Nonsmooth and Nonconvex Semi-Infinite Maximum Eigenvalue Functions
Journal of convex analysis, Tome 16 (2009) no. 3, pp. 641-666.

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Proximity control is a well-known mechanism in bundle method for nonsmooth optimization. Here we show that it can be used to optimize a large class of nonconvex and nonsmooth functions with additional structure. This includes for instance nonconvex maximum eigenvalue functions, and also infinite suprema of such functions.
Mots-clés : Nonsmooth calculus, nonsmooth optimization, Clarke subdifferential, spectral bundle method, maximum eigenvalue function, semi-infinite problem, H-infinity-norm 
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     author = {P. Apkarian and D. Noll and O. Prot},
     title = {A {Proximity} {Control} {Algorithm} to {Minimize} {Nonsmooth} and {Nonconvex} {Semi-Infinite} {Maximum} {Eigenvalue} {Functions}},
     journal = {Journal of convex analysis},
     pages = {641--666},
     publisher = {mathdoc},
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     number = {3},
     year = {2009},
     url = {http://geodesic.mathdoc.fr/item/JCA_2009_16_3_JCA_2009_16_3_a2/}
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P. Apkarian; D. Noll; O. Prot. A Proximity Control Algorithm to Minimize Nonsmooth and Nonconvex Semi-Infinite Maximum Eigenvalue Functions. Journal of convex analysis, Tome 16 (2009) no. 3, pp. 641-666. http://geodesic.mathdoc.fr/item/JCA_2009_16_3_JCA_2009_16_3_a2/