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A Survey on Proximal Point Type Algorithms for Solving Vector Optimization Problems

  • Sorin-Mihai GradEmail author
Chapter

Abstract

In this survey paper we present the existing generalizations of the proximal point method from scalar to vector optimization problems, discussing some of their advantages and drawbacks, respectively, presenting some open challenges and sketching some possible directions for future research.

Keywords

Vector optimization problem Proximal point algorithm Weakly efficient solution Efficient solution Splitting method Multiobjective optimization problem Vector function Scalarization function 

AMS 2010 Subject Classification

90C25 90C29 90C46 

Notes

Acknowledgements

This work was partially supported by FWF (Austrian Science Fund), project M-2045 and DFG (German Research Foundation), project GR3367∕4 − 1 The author is grateful to an anonymous reviewer for making him aware of the paper [73] and for carefully reading this survey, and to the editors of this volume for the invitation to the CMO-BIRS Workshop on Splitting Algorithms, Modern Operator Theory, and Applications (17w5030) in Oaxaca.

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Authors and Affiliations

  1. 1.Faculty of MathematicsUniversity of ViennaViennaAustria

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