Computational Combinatorial Optimization, Optimal or Provably Near-Optimal Solutions [based on a Spring School]
Functions and Sets of Smooth Substructure: Relationships and Examples
Computational Optimization and Applications
Non-smoothness in classification problems
Optimization Methods & Software - THE JOINT EUROPT-OMS CONFERENCE ON OPTIMIZATION, 4-7 JULY, 2007, PRAGUE, CZECH REPUBLIC, PART I
A superlinear space decomposition algorithm for constrained nonsmooth convex program
Journal of Computational and Applied Mathematics
An approximate decomposition algorithm for convex minimization
Journal of Computational and Applied Mathematics
Piecewise-quadratic Approximations in Convex Numerical Optimization
SIAM Journal on Optimization
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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 infinitely defined max-functions. For a function in this class, we discuss a space decomposition that allows us to identify a subspace on which the function appears to be smooth. Moreover, using the special structure of such a function, we compute smooth trajectories along which certain second-order expansions can be obtained. We also give an explicit expression for the Hessian of a related Lagrangian.