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Minimizing an indefinite quadratic function subject to a single indefinite quadratic constraint

Abstract In this paper, we consider the problem of minimizing an indefinite quadratic function subject to a single indefinite quadratic constraint. A key difficulty with this problem is its nonconvexity.… Click to show full abstract

Abstract In this paper, we consider the problem of minimizing an indefinite quadratic function subject to a single indefinite quadratic constraint. A key difficulty with this problem is its nonconvexity. Using Lagrange duality, we show that under a mild assumption, this problem can be solved by solving a linearly constrained convex univariate minimization problem. Finally, the superior efficiency of the new approach compared to the known semidefinite relaxation and a known approach from the literature is demonstrated by solving several randomly generated test problems.

Keywords: indefinite quadratic; minimizing indefinite; function subject; subject single; single indefinite; quadratic function

Journal Title: Optimization
Year Published: 2018

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