On the piecewise-concave approximations of functions

2014/03/16 by Gene A. Bunin, Bunin, Gene A.
Engineering · Mathematics · #Advanced Control Systems Optimization #Advanced Optimization Algorithms Research #Control Systems and Identification #FOS: Mathematics #Optimization and Control (math.OC) #math.OC

paper · pdf · doi:10.48550/arxiv.1403.3882

4 pages; written as a supplement to submitted journal paper

openalex publication_date 2014/03/16 · arxiv created 2014/04/16 · arxiv updated 2014/04/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The piecewise-concave function may be used to approximate a wide range of other functions to arbitrary precision over a bounded set. In this short paper, this property is proven for three function classes: (a) the multivariate twice continuously differentiable function, (b) the univariate Lipschitz-continuous function, and (c) the multivariate separable Lipschitz-continuous function.

Citations

• Extended reverse-convex programming: an approximate enumeration approach to global optimization

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