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<p>In this paper, we investigate an adjustable robust counterpart (ARC) of a two-stage uncertain linear problem. A non-adjustable robust form of (ARC) is derived, which allows us to provide a solvable semidefinite programming reformulation (SDP) and evaluate its tractability. Under the local Farkas–Minkowski constraint qualification, optimality conditions and duality results are established. Some applications to robust counterpart (RC) and affinely adjustable robust counterpart (AARC) are obtained. These results are numerically illustrated by considering a practical problem with the support of some optimization packages.</p>

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Linear adjustable robust optimization problem: semidefinite programming reformulation, optimality conditions and duality

  • 期刊论文

  • 发表日期：

    2025年10月27日

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  • Nguyen Minh Tung,
  • Mai Van Duy

摘要

In this paper, we investigate an adjustable robust counterpart (ARC) of a two-stage uncertain linear problem. A non-adjustable robust form of (ARC) is derived, which allows us to provide a solvable semidefinite programming reformulation (SDP) and evaluate its tractability. Under the local Farkas–Minkowski constraint qualification, optimality conditions and duality results are established. Some applications to robust counterpart (RC) and affinely adjustable robust counterpart (AARC) are obtained. These results are numerically illustrated by considering a practical problem with the support of some optimization packages.