Quadratic optimization with a ball and a reverse ball constraints

Document Type : Original paper

Authors

1 Department of Mathematics and Statistics, College of Art and Science, Qatar University, Doha, Qatar

2 Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran

Abstract

In this paper, we study a quadratic minimization problem over the intersection of a ball and a reverse ball constraints that includes generalized trust-region subproblem (TRS). Using the structure of the problem, we prove that it can be solved to global optimality by solving at most three TRS or two TRS with an extra linear constraint. Then we present an efficient TRS-based algorithm to solve it. Computational experiments illustrate that our new algorithm outperforms the ones in the literature, specially the algorithm for generalized TRS, on three widely used test classes.

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Main Subjects


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