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In this chapter, we consider set-valued optimization problems and discuss some results on the existence of solutions. It is well-known that there are two major approaches to understand solutions in set-valued optimization, namely the vector approach and the set approach. We focus on the set approach in this chapter and consider the notion of l-minimal and u-minimal solutions. We provide a survey of various continuity and semi-continuity properties of set-valued maps and their applications in the existence of solutions for set-valued optimization.

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Results on Existence of l-Minimal and u-Minimal Solutions in Set-Valued Optimization: A Brief Survey

  • 会议论文

  • 发表日期：

    2025年

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  • Kuntal Som,
  • V. Vetrivel

摘要

In this chapter, we consider set-valued optimization problems and discuss some results on the existence of solutions. It is well-known that there are two major approaches to understand solutions in set-valued optimization, namely the vector approach and the set approach. We focus on the set approach in this chapter and consider the notion of l-minimal and u-minimal solutions. We provide a survey of various continuity and semi-continuity properties of set-valued maps and their applications in the existence of solutions for set-valued optimization.