On VU-theory for functions with primal-dual gradient structure

Citation
R. Mifflin et C. Sagastizabal, On VU-theory for functions with primal-dual gradient structure, SIAM J OPTI, 11(2), 2000, pp. 547-571
Citations number
23
Categorie Soggetti
Mathematics
Journal title
SIAM JOURNAL ON OPTIMIZATION
ISSN journal
10526234 → ACNP
Volume
11
Issue
2
Year of publication
2000
Pages
547 - 571
Database
ISI
SICI code
1052-6234(20001110)11:2<547:OVFFWP>2.0.ZU;2-W
Abstract
We consider a general class of convex functions having what we call primal- dual gradient structure. It includes finitely determined max-functions and maximum eigenvalue functions as well as other in finitely defined max-funct ions. For a function in this class, we discuss a space decomposition that a llows us to identify a subspace on which the function appears to be smooth. Moreover, using the special structure of such a function, we compute smoot h trajectories along which certain second-order expansions can be obtained. We also give an explicit expression for the Hessian of a related Lagrangia n.