Multi-Composed Programming with Applications to Facility Location

Abstract

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A sequential formula for the $\varepsilon$-subdifferential of multi-composed functions via a perturbation approach with an application to location problems

“…Motivated by the location models examined in [17,3], the aim of this section is to give the sequential ε-optimality conditions of the following location problem with geometric constraint…”

“…Multi-composed optimization problems deal with optimization models whose objective functions are written as the compositions of more than two functions (see [1,2,3]). In fact, the study of multi-composed optimization problems has been a subject matter of great interest because this new class of mathematical optimization models can be applied to many practical problems that arise in different fields of modern research, such as deep learning [4], facility location theory [5,6], fractional programming problems, and entropy optimization [2], etc.…”

A note on the subdifferential of convex multi-composite functionals

“…The origin of interest in such calculus rules comes from the recent contribution of Wanka and Wilfer [6] that introduced and examined the optimality conditions of the so-called multi-composed convex optimization problems via conjugate duality approach in 2016. For more details regarding this new branch of convex optimization, we refer to a recent book on multi-composed programming [7].…”