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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[Research Report] RR-6288, INRIA. 2007
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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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