Abstract
In this paper, we consider the interval bounded generalized trust region subproblem (GTRS) which is the problem of minimizing a general quadratic function subject to an upper and lower bounded general quadratic constraint. Under the assumption that two matrices from the objective and the constraint functions can be simultaneously diagonalizable via congruence, a diagonalization-based algorithm is introduced to solve it by showing that GTRS is indeed equivalent to a linearly constrained convex univariate problem. Some numerical experiments are given to show the effectiveness of the proposed method and to compare it with the extended Rendl–Wolkowicz algorithm due to Pong and Wolkowicz.
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Notes
GTRS_ codes are available from http://www.math.uwaterloo.ca/~ptingkei/GTRS_codes/.
eigifp is a MATLAB program for computing a few algebraically smallest or largest eigenvalues and their corresponding eigenvectors of the generalized eigenvalue problem, available from http://www.ms.uky.edu/~qye/software.html.
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Acknowledgments
The authors would like to thank the reviewer for his/her useful comments and Prof. Wolkowicz for his suggestions on the early version of this work. The first author also would like to thank University of Guilan for supporting his sabbatical leave 2015–2016, hosted by Prof. H. Wolkowicz at the Department of Combinatorics and Optimization, University of Waterloo.
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Communicated by Natasa Krejic.
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Salahi, M., Taati, A. An efficient algorithm for solving the generalized trust region subproblem. Comp. Appl. Math. 37, 395–413 (2018). https://doi.org/10.1007/s40314-016-0349-1
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DOI: https://doi.org/10.1007/s40314-016-0349-1