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arXiv · 1801.06946

Yet Another Convex Sets Subtraction with Application in Nondifferentiable Optimization

Evgeni Nurminski·Stan Uryasev
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Abstract

This paper introduces a new subtraction operation for convex sets, which defines their difference as a collection of inclusion-minimal convex sets with appropriate definitions of linear operations on them. With these operations the set of collections becomes a linear vector space with common zero and possibility to invert Minkowski summation. As the demonstration of usability of this concept the Lipschitz continuity of \(ε\)-subdifferentials of convex analysis is proved in a novel way.

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Evgeni Nurminski, Stan Uryasev. 2018-06-15. Yet Another Convex Sets Subtraction with Application in Nondifferentiable Optimization. https://arxiv.org/abs/1801.06946

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