Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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FINDING EXPLICIT SOLUTIONS FOR LINEAR REGRESSION WITHOUT CORRESPONDENCES BASED ON REARRANGEMENT INEQUALITY

  • MIJIN KIM (Department of Mathematics, Kyungpook National University) ;
  • HYUNGU LEE (Department of Mathematics, Kyungpook National University) ;
  • HAYOUNG CHOI (Department of Mathematics, Kyungpook National University)
  • Received : 2023.10.21
  • Accepted : 2024.01.05
  • Published : 2024.01.30
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Abstract

A least squares problem without correspondences is expressed as the following optimization: Π∈Pminm, x∈ℝn ║Ax-Πy║, where A ∈ ℝm×n and y ∈ ℝm are given. In general, solving such an optimization problem is highly challenging. In this paper we use the rearrangement inequalities to find the closed form of solutions for certain cases. Moreover, despite the stringent constraints, we successfully tackle the nonlinear least squares problem without correspondences by leveraging rearrangement inequalities.

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Acknowledgement

The authors are deeply grateful to the referee for suggestions that led to significant improvements in the presentation.

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