Remarks on solutions to a nonconvex quadratic programming test problem. (English) Zbl 1220.90078
Summary: A recent paper of H. Tuy and N. T. Hoai-Phuong [J. Glob. Optim. 37, No. 4, 557–569 (2007; Zbl 1198.90316)] presents an algorithm for nonconvex quadratic programming with quadratic constraints. The performance of this algorithm is illustrated by solving, among others, a test problem from a paper of C. Audet, P. Hansen, B. Jaumard and G. Savard [Math. Program. 87, No. 1 (A), 131–152 (2000; Zbl 0966.90057)]. This test problem is a reformulation of a problem from a paper of R. S. Dembo [Math. Program. 10, 192–213 (1976; Zbl 0349.90066)]. Tuy and Hoai-Phuong observe that the optimal solution reported by Audet et al. is very far from the optimal one for this reformulation. The discrepancy between the reported optimal solutions is not due to selection of an almost feasible solution far from the optimal one nor to cumulation of termwise approximation errors. It is, in fact, simply due to a typographical error.
Keywords:
signomial geometric program; nonconvex quadratic program; outer approximation; approximation error; successive incumbent transcendingReferences:
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| [6] | Tuy H., Hoai-Phuong N.: A robust algorithm for quadratic optimization under quadratic constraints. J. Global Optim. 37(4), 557–569 (2007) · Zbl 1198.90316 · doi:10.1007/s10898-006-9063-7 |
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