Relaxed optimality conditions for mu-differentiable functions

TL;DR

This paper explores fundamental properties of mu-differentiable functions, introducing new notions of local extrema and formulating extremum conditions using nonstandard analysis techniques.

Contribution

It introduces a novel concept of local extrema for mu-differentiable functions and establishes extremum conditions within a nonstandard analysis framework.

Findings

New notion of local minimizer and maximizer

Formulation of extremum conditions using nonstandard analysis

Fundamental properties of mu-differentiable functions

Abstract

We prove some fundamental properties of mu-differentiable functions. A new notion of local minimizer and maximizer is introduced and several extremum conditions are formulated using the language of nonstandard analysis.