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關于二次約束二次規劃問題強對偶性的幾個結果
楊慶之; 樂航睿 喀什大學數學與統計學院數學系; 喀什市844006; 南開大學數學學院科學與工程計算系; 天津300071
- qcqp
- decomposition
- of
- matrix
- slater
摘要：In this paper, we revisit the strong duality of the quadratically constrained quadratic programming(QCQP) problem. We first generalize a known result for the rank-one decomposition of matrices and then apply it to consider the strong duality for more general QCQP scenarios, including the cases with one constraint, two constraints while at least one being inactive on the optimal solution point, multiple constraints, and an interval constraint. A sufficient condition ensuring the strong duality of more general QCQP problems is studied as well. We also extend our results to the QCQP problems with complex variables.
- qcqp
- decomposition
- of
- matrix
- slater
摘要：In this paper, we revisit the strong duality of the quadratically constrained quadratic programming(QCQP) problem. We first generalize a known result for the rank-one decomposition of matrices and then apply it to consider the strong duality for more general QCQP scenarios, including the cases with one constraint, two constraints while at least one being inactive on the optimal solution point, multiple constraints, and an interval constraint. A sufficient condition ensuring the strong duality of more general QCQP problems is studied as well. We also extend our results to the QCQP problems with complex variables.
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