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

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 d...

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Bibliographic Details
Published inJournal of optimization theory and applications Vol. 157; no. 1; pp. 132 - 140
Main Authors Bouchala, J., Dostál, Z., Vodstrčil, P.
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.04.2013
Springer Nature B.V
Subjects
Algorithms
Analysis
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Contact
Engineering
Estimates
Euclidean space
Friction
Ingredients
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Projection
Quadratic programming
Studies
Theory of Computation
Theory of constraints
Quadratic programming with separable constraints
Rate of convergence
Euclidean gradient projection
Spherical constraints
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ISSN0022-3239
1573-2878
DOI10.1007/s10957-012-0178-3

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Summary: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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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-012-0178-3