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<p>In this paper, we study a class of vector polynomial optimization over a linear matrix inequality (LMI in short) constraint. We show that the weakly efficient solution set can be characterized as the zero level set of a type of merit function, which admits polynomial approximations from above with coefficients computed via semidefinite programming (SDP) problems. An example is given to illustrate our method.</p>

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Merit function as a tool for vector polynomial optimization over an LMI constraint

  • 期刊论文

  • 发表日期：

    2025年11月20日

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  • Jian Huang,
  • Liguo Jiao,
  • Do Sang Kim,
  • Junping Yin

摘要

In this paper, we study a class of vector polynomial optimization over a linear matrix inequality (LMI in short) constraint. We show that the weakly efficient solution set can be characterized as the zero level set of a type of merit function, which admits polynomial approximations from above with coefficients computed via semidefinite programming (SDP) problems. An example is given to illustrate our method.