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Analysis of a quadratic programming decomposition algorithm

Abstract : We analyze a decomposition algorithm for minimizing a quadratic objective function, separable in x1 and x2, subject to the constraint that x1 and x2 are orthogonal vectors on the unit sphere. Our algorithm consists of a local step where we minimize the objective function in either variable separately, while enforcing the constraints, followed by a global step where we minimize over a subspace generated by solutions to the local subproblems. We establish a local convergence result when the global minimizers nondegenerate. Our analysis employs necessary and sufficient conditions and continuity properties for a global optimum of a quadratic objective function subject to a sphere constraint and a linear constraint. The analysis is connected with a new domain decomposition algorithm for electronic structure calculations.
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https://hal.inria.fr/inria-00169080
Contributor : Guy Bencteux <>
Submitted on : Tuesday, June 2, 2009 - 4:44:56 PM
Last modification on : Friday, May 21, 2021 - 7:36:03 PM
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  • HAL Id : inria-00169080, version 5

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William Hager, Guy Bencteux, Eric Cancès, Claude Le Bris. Analysis of a quadratic programming decomposition algorithm. [Research Report] RR-6288, INRIA. 2007. ⟨inria-00169080v5⟩

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