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<p>This paper presents a computationally efficient optimization framework for complex quadratic fractional minimax problems with second-order cone constraints. Our approach combines semidefinite relaxation with accelerated bisection and generalized Dinkelbach–type algorithms to guarantee provable global optimality and achieve an improved <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(O(k^{-1.5})\)</EquationSource> </InlineEquation> convergence rate. Extensive numerical experiments demonstrate the framework’s superior performance in both solution quality and computational efficiency, particularly for large–scale problems. The theoretical advances are validated through practical applications in wireless communication beamforming design, showing consistent improvements over existing methods across various problem scales.</p>

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Beamforming design via complex quadratic double–ratio minimax optimization: theory and algorithms

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • Arezu Zare,
  • Bahram Sadeghi Bigham

摘要

This paper presents a computationally efficient optimization framework for complex quadratic fractional minimax problems with second-order cone constraints. Our approach combines semidefinite relaxation with accelerated bisection and generalized Dinkelbach–type algorithms to guarantee provable global optimality and achieve an improved \(O(k^{-1.5})\) convergence rate. Extensive numerical experiments demonstrate the framework’s superior performance in both solution quality and computational efficiency, particularly for large–scale problems. The theoretical advances are validated through practical applications in wireless communication beamforming design, showing consistent improvements over existing methods across various problem scales.