Upper and lower approximations of the second order. Exhausters of the second order

I. M. Prudnikov

Upper and lower approximations of the second order. Exhausters of the second order

Optimization and Control 2026-06-25 v1

Authors: I. M. Prudnikov

Abstract

The upper and lower approximations of the second order are defined for a function differentiable in the directions. Exhausters of the second order are introduced. The relation between the second-order Frechet subdifferentials and the second-order exhausters is given. A rule for constructing exhausters of the first and second orders is given for Lipschitz functions.Necessary and sufficient extremum conditions through exhausters are given. It is discussed about the use of Exhausters in optimization.

Keywords

second order upper approximation second order lower approximation exhausters frechet subdifferential lipschitz functions extremum conditions optimization

Cite

@article{arxiv.2607.22647,
  title  = {Upper and lower approximations of the second order. Exhausters of the second order},
  author = {I. M. Prudnikov},
  journal= {arXiv preprint arXiv:2607.22647},
  year   = {2026}
}