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<p>This note proposes a new reformulation of complex semidefinite programs (SDP) as real SDPs. As an application, we present an economical reformulation of complex SDP relaxations of complex polynomial optimization problems as real SDPs and derive some further reductions by exploiting inner structure of the complex SDP relaxations. Various numerical examples demonstrate that our new reformulation runs significantly faster than the usual popular reformulation.</p>

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A more efficient reformulation of complex SDP as real SDP

  • 期刊论文

  • 发表日期：

    2026年4月13日

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  • Jie Wang

摘要

This note proposes a new reformulation of complex semidefinite programs (SDP) as real SDPs. As an application, we present an economical reformulation of complex SDP relaxations of complex polynomial optimization problems as real SDPs and derive some further reductions by exploiting inner structure of the complex SDP relaxations. Various numerical examples demonstrate that our new reformulation runs significantly faster than the usual popular reformulation.