The magic of Nash social welfare in optimization: Do not sum, just multiply!

Hadi Charkhgard; Kimia Keshanian; Rasul Esmaeilbeigi; Parisa Charkhgard

doi:10.21914/anziamj.v64.16439

Authors

Hadi Charkhgard University of South Florida https://orcid.org/0000-0001-5416-6960
Kimia Keshanian University of Tampa https://orcid.org/0000-0002-1969-3391
Rasul Esmaeilbeigi Deakin University https://orcid.org/0000-0003-3460-7954
Parisa Charkhgard University of Newcastle https://orcid.org/0000-0002-5659-4229

DOI:

https://doi.org/10.21914/anziamj.v64.16439

Keywords:

Nash social welfare, equity, single-objective optimization, multi-objective optimization, multiplicative program

Abstract

We explain some key challenges when dealing with a single- or multi-objective optimization problem in practice. To overcome these challenges, we present a mathematical program that optimizes the Nash social welfare function. We refer to this mathematical program as the Nash social welfare program (NSWP). An interesting property of the NSWP is that it can be constructed for any single- or multi-objective optimization problem. We show that solving the NSWP could result in more desirable solutions in practice than its single- or multi-objective counterpart. We also discuss several promising approaches that could be employed to solve the NSWP in practice.

doi:10.1017/S1446181122000074

Author Biographies

Hadi Charkhgard, University of South Florida

Department of Industrial and Management Systems Engineering, The University of South Florida, Tampa, FL USA.

Kimia Keshanian, University of Tampa

Information and Technology Management Department, University of Tampa, Tampa, FL USA.

Rasul Esmaeilbeigi, Deakin University

School of Information Technology, Deakin University, Geelong, VIC Australia.

Parisa Charkhgard, University of Newcastle

School of Mathematical and Physical Sciences, University of Newcastle, NSW Australia.