Publication | Open Access
A new approach to variable metric algorithms
4K
Citations
0
References
1970
Year
Mathematical ProgrammingNumerical AnalysisQuadratic TerminationLarge-scale Global OptimizationEngineeringUnconstrained OptimizationOptimization-based Data MiningData ScienceData MiningPattern RecognitionCombinatorial OptimizationApproximation TheoryVariable Metric AlgorithmsContinuous OptimizationKnowledge DiscoveryInverse ProblemsComputer ScienceDimensionality ReductionVariable Neighborhood SearchConic OptimizationConvex OptimizationLinear Search
An approach to variable metric algorithms has been investigated in which the linear search sub-problem no longer becomes necessary. The property of quadratic termination has been replaced by one of monotonic convergence of the eigenvalues of the approximating matrix to the inverse hessian. A convex class of updating formulae which possess this property has been established, and a strategy has been indicated for choosing a member of the class so as to keep the approximation away from both singularity and unboundedness. A FORTRAN program has been tested extensively with encouraging results.