Local nonglobal minima for solving large-scale extended trust-region subproblems

Maziar Salahi (), Akram Taati and Henry Wolkowicz
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Maziar Salahi: University of Guilan
Akram Taati: University of Guilan
Henry Wolkowicz: University of Waterloo

Computational Optimization and Applications, 2017, vol. 66, issue 2, No 1, 223-244

Abstract: Abstract We study large-scale extended trust-region subproblems (eTRS) i.e., the minimization of a general quadratic function subject to a norm constraint, known as the trust-region subproblem (TRS) but with an additional linear inequality constraint. It is well known that strong duality holds for the TRS and that there are efficient algorithms for solving large-scale TRS problems. It is also known that there can exist at most one local non-global minimizer (LNGM) for TRS. We combine this with known characterizations for strong duality for eTRS and, in particular, connect this with the so-called hard case for TRS. We begin with a recent characterization of the minimum for the TRS via a generalized eigenvalue problem and extend this result to the LNGM. We then use this to derive an efficient algorithm that finds the global minimum for eTRS by solving at most three generalized eigenvalue problems.

Keywords: Trust-region subproblem; Linear inequality constraint; Large-scale optimization; Generalized eigenvalue problem; 90C26; 90C30; 90C46; 65F15 (search for similar items in EconPapers)
Date: 2017
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10589-016-9867-4

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