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Separable Spherical Constraints and the Decrease of a Quadratic Function in the Gradient Projection Step

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Abstract

We examine the decrease of a strictly convex quadratic function along the projected-gradient path and show that our earlier estimates obtained for the bound constraints are valid for more general feasible sets including those defined by separable spherical constraints. The result is useful for the development of in a sense optimal algorithms for the solution of some QPQC problems with separable constraints and is an important ingredient in the development of scalable algorithms for contact problems with friction.

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Acknowledgements

This research has been supported by the Ministry of Education of the Czech Republic No. MSM6198910027 and by the IT4Innovations Center of Excellence project, reg. no. CZ.1.05/1.1.00/02.0070 within Operational Programme ‘Research and Development for Innovations’ funded by Structural Funds of the European Union and the budget of the Czech Republic.

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  1. VŠB–Technical University of Ostrava, 17. listopadu 15, 70833, Ostrava, Czech Republic

    J. Bouchala, Z. Dostál & P. Vodstrčil

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  1. J. Bouchala
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  2. Z. Dostál
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  3. P. Vodstrčil
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Correspondence to Z. Dostál.

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Bouchala, J., Dostál, Z. & Vodstrčil, P. Separable Spherical Constraints and the Decrease of a Quadratic Function in the Gradient Projection Step. J Optim Theory Appl 157, 132–140 (2013). https://doi.org/10.1007/s10957-012-0178-3

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  • DOI: https://doi.org/10.1007/s10957-012-0178-3

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