Alternative theorem for sequences of functions and applications to optimisation
Optimization and Control
2024-12-10 v1
Abstract
We present a new alternative theorems for sequences of functions. As applications, we extend recent results in the literature related to first-order necessary conditions for optimality problems. Our contributions involve extending well-known results, previously established for a finite number of inequality constraints to a countable number of inequality constraints. This extension is achieved using the Dini differentiability concept which is more general than Fr\'echet or G\^ateaux differentiability. We will illustrate our results by giving examples of optimisation problems with a finite or countable number of inequality constraints where the functions are not Gateaux-differentiable but only upper Dini-differentiable.
Cite
@article{arxiv.2412.05614,
title = {Alternative theorem for sequences of functions and applications to optimisation},
author = {Mohammed Bachir and Rongzhen Lyu},
journal= {arXiv preprint arXiv:2412.05614},
year = {2024}
}