Abstract
For minimizing a convex max-function f we consider, at a minimizer, a space decomposition. That is, we distinguish a subspace V, where f’s nonsmoothness is concentrated, from its orthogonal complement, U. We characterize smooth trajectories, tangent to U, along which f has a second order expansion. We give conditions (weaker than typical strong second order sufficient conditions for optimality) guaranteeing the existence of a Hessian of a related U-Lagrangian. We also prove, under weak assumptions and for a general convex function, superlinear convergence of a conceptual algorithm for minimizing f using VU-decomposition derivatives.
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© 1999 Springer-Verlag Berlin Heidelberg
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Mifflin, R., Sagastizábal, C. (1999). VU-Decomposition Derivatives for Convex Max-Functions. In: Théra, M., Tichatschke, R. (eds) Ill-posed Variational Problems and Regularization Techniques. Lecture Notes in Economics and Mathematical Systems, vol 477. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45780-7_11
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DOI: https://doi.org/10.1007/978-3-642-45780-7_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66323-2
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