Alternative theorem for sequences of functions and applications to optimisation

Mohammed Bachir; Rongzhen Lyu

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arXiv · 2412.05614

Alternative theorem for sequences of functions and applications to optimisation

Mohammed Bachir·Rongzhen Lyu

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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.

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Mohammed Bachir, Rongzhen Lyu. 2024-12-07. Alternative theorem for sequences of functions and applications to optimisation. https://arxiv.org/abs/2412.05614

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