Abstract
This paper introduces examples of convex functions in a general class of functions having what we call primal-dual gradient structure. The class contains finitely defined maximum value functions and maximum eigenvalue functions as well as other infinitely determined max-functions. For such a function there is a space decomposition that allows us to identify a subspace u on which the function appears smooth. Moreover, the special structure combined with sufficiency conditions implies the existence of smooth trajectories on which the function has a certain second order expansion. This results in an explicit expression for the Hessian of a related u-Lagrangian.
Research supported by the National Science Foundation under Grant No. DMS-9703952 and by FAPERJ (Brazil) under Grant No. E-26/171.393/97.
Research supported by FAPERJ (Brazil) under Grant No.E26/150.205/98.
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Mifflin, R., Sagastizábal, C. (2000). Functions with Primal-Dual Gradient Structure and u-Hessians. In: Pillo, G.D., Giannessi, F. (eds) Nonlinear Optimization and Related Topics. Applied Optimization, vol 36. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3226-9_12
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DOI: https://doi.org/10.1007/978-1-4757-3226-9_12
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