ANALYSIS OF A QUADRATIC PROGRAMMING DECOMPOSITION ALGORITHM

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 separatel...

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Veröffentlicht in:SIAM journal on numerical analysis Jg. 47; H. 6; S. 4517 - 4539
Hauptverfasser: BENCTEUX, G., CANCÉS, E., HAGER, W. W., LE BRIS, C.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Philadelphia, PA Society for Industrial and Applied Mathematics 01.01.2010
Schlagworte:
Algorithms
Continuity
Convergence
Decomposition
Eigenvalues
Eigenvectors
Electronic structure
Exact sciences and technology
Mathematical analysis
Mathematical minima
Mathematical models
Mathematical vectors
Mathematics
Numerical Analysis
Numerical analysis. Scientific computation
Objective functions
Optimization
Orthogonality
Partial differential equations, boundary value problems
Partial differential equations, initial value problems and time-dependant initial-boundary value problems
Quadratic programming
Sciences and techniques of general use
Unit vectors
Variables
domain decomposition method
65K05
Necessary and sufficient condition
Initial value problem
Decomposition method
Optimization method
Global optimum
Orthogonality
Quadratic programming
Algorithm
Partial differential equation
Constrained optimization
Sphere
90C20
electronic structure calculations
Numerical analysis
Boundary value problem
90C46
Multigrid
orthogonality constraints
Domain decomposition
quadratic programming
ISSN:0036-1429, 1095-7170
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Beschreibung
Zusammenfassung: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 are 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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ISSN:0036-1429
1095-7170
DOI:10.1137/070701728