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<p>In this paper, we develop new conic scalarization theorems to characterize approximate proper efficiency relative to improvement sets in a real locally convex space. By leveraging seminorm-linear separation functions and Bishop-Phelps-type separating cones introduced by Günther, Khazayel, and Tammer [SIAM J. Optim., 34 (2024), pp. 225-250], we establish and rigorously prove these results. Notably, our theorems extend Kasimbeyli’s foundational conic scalarization framework – originally formulated for normed spaces (Kasimbeyli [SIAM J. Optim., 20 (2010), pp. 1591-1619]) – to the broader context of real locally convex spaces.</p>

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Characterization of Approximate Efficient Solutions of Nonconvex Vector Optimization Problems

  • 期刊论文

  • 发表日期：

    2026年3月14日

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  • Wen-Bin Wei,
  • Jian-Wen Peng,
  • Elisabeth Köbis,
  • Jen-Chih Yao

摘要

In this paper, we develop new conic scalarization theorems to characterize approximate proper efficiency relative to improvement sets in a real locally convex space. By leveraging seminorm-linear separation functions and Bishop-Phelps-type separating cones introduced by Günther, Khazayel, and Tammer [SIAM J. Optim., 34 (2024), pp. 225-250], we establish and rigorously prove these results. Notably, our theorems extend Kasimbeyli’s foundational conic scalarization framework – originally formulated for normed spaces (Kasimbeyli [SIAM J. Optim., 20 (2010), pp. 1591-1619]) – to the broader context of real locally convex spaces.