Regularized Lagrangian duality for linearly constrained quadratic optimization and trust-region problems |
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Authors: | V Jeyakumar Guoyin Li |
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Institution: | (3) Univ. Florida, Gainesville, USA;(4) Univ. Iowa, Iowa City, Iowa, USA; |
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Abstract: | In this paper we first establish a Lagrange multiplier condition characterizing a regularized Lagrangian duality for quadratic
minimization problems with finitely many linear equality and quadratic inequality constraints, where the linear constraints
are not relaxed in the regularized Lagrangian dual. In particular, in the case of a quadratic optimization problem with a
single quadratic inequality constraint such as the linearly constrained trust-region problems, we show that the Slater constraint
qualification (SCQ) is necessary and sufficient for the regularized Lagrangian duality in the sense that the regularized duality
holds for each quadratic objective function over the constraints if and only if (SCQ) holds. A new theorem of the alternative
for systems involving both equality constraints and two quadratic inequality constraints plays a key role. We also provide
classes of quadratic programs, including a class of CDT-subproblems with linear equality constraints, where (SCQ) ensures
regularized Lagrangian duality. |
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Keywords: | |
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