Abstract
Grapiglia et al. (2013) proved subspace properties for the Celis-Dennis-Tapia (CDT) problem. If a subspace with lower dimension is appropriately chosen to satisfy subspace properties, then one can solve the CDT problem in that subspace so that the computational cost can be reduced. We show how to find subspaces that satisfy subspace properties for the CDT problem, by using the eigendecomposition of the Hessian matrix of the objection function. The dimensions of the subspaces are investigated. We also apply the subspace technologies to the trust region subproblem and the quadratic optimization with two quadratic constraints.
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Acknowledgements
This work was supported by National Natural Science Foundation of China (Grant Nos. 11171217 and 11571234).
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Zhao, X., Fan, J. Subspace choices for the Celis-Dennis-Tapia problem. Sci. China Math. 60, 1717–1732 (2017). https://doi.org/10.1007/s11425-016-0012-1
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DOI: https://doi.org/10.1007/s11425-016-0012-1