Analysis of a quadratic programming decomposition algorithm

William Hager (1) , Guy Bencteux (2) , Eric Cancès (2) , Claude Le Bris (2)

1 UF|Math - Department of Mathematics [Gainesville]
2 MICMAC - Methods and engineering of multiscale computing from atom to continuum

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.

Domaines: Analyse numérique [math.NA]

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