Asymptotic analysis of scalarization functions and applications

Genghua Li; Shengjie Li; Manxue You

doi:10.3934/jimo.2022046

Article Contents

2023, Volume 19, Issue 4: 2367-2380. Doi: 10.3934/jimo.2022046

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Asymptotic analysis of scalarization functions and applications

1.
Chongqing Key Laboratory of Social Economic and Applied Statistics, School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China
2.
College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China
3.
College of Mathematics and Information, China West Normal University, Nanchong 637009, Sichuan, China

^*Corresponding author: Shengjie Li
^*Corresponding author: Shengjie Li

Received: September 2021

Revised: January 2022

Published: April 2023

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Abstract

In this paper, we consider two common scalarization functions and their applications via asymptotic analysis. We mainly analyze the recession and asymptotic properties of translation invariant function and oriented distance function, and discuss their monotonicity and Lipschitz continuity in terms of recession functions. Finally, we apply these scalarization functions to the characterization of the nonemptiness and boundedness of the solution set for a general constrained nonconvex optimization problem.

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Mathematics Subject Classification: Primary: 26B35; Secondary: 90C26; 90C30.

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