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arXiv · 1710.10187

A general representation of delta-normal sets to sublevels of convex functions

Abderrahim Hantoute·Anton Svensson
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Abstract

The (delta-) normal cone to an arbitrary intersection of sublevel sets of proper, lower semicontinuous, and convex functions is characterized, using either epsilon-subdifferentials at the nominal point or exact subdifferentials at nearby points. Our tools include (epsilon-) calculus rules for sup/max functions. The framework of this work is that of a locally convex space, however, formulas using exact subdifferentials require some restriction either on the space (e.g. Banach), or on the function (e.g. epi-pointed).

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Abderrahim Hantoute, Anton Svensson. 2017-10-27. A general representation of delta-normal sets to sublevels of convex functions. https://arxiv.org/abs/1710.10187

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