Deriving collinear scaling algorithms as extensions of quasi-Newton methods and the local convergence of DFP- and BFGS-related collinear scaling algorithms

DOI10.1007/BF01588777zbMath0724.90059MaRDI QIDQ2277145

Ariyawansa, K. A.

Publication date: 1990

Published in: Mathematical Programming. Series A. Series B (Search for Journal in Brave)

zbMATH Keywords

unconstrained minimizationquasi-Newton methodscollinear scaling algorithmsconic approximationslocal and q-superlinear convergence

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Nonlinear programming (90C30) Newton-type methods (49M15) Computational methods for problems pertaining to operations research and mathematical programming (90-08)

Related Items (26)

On Davidon's collinear scaling algorithms for optimization ⋮ A class of collinear scaling algorithms for bound-constrained optimization: convergence theorems ⋮ Interpolation by conic model for unconstrained optimization ⋮ A quasi-Newton trust region method with a new conic model for the unconstrained optimization ⋮ An efficient algorithm for globally minimizing sum of quadratic ratios problem with nonconvex quadratic constraints ⋮ A trust region method with a conic model for nonlinearly constrained optimization ⋮ A fractional programming algorithm based on conic quasi-Newton trust region method for unconstrained minimization ⋮ A conic trust-region method for optimization with nonlinear equality and inequality constrains via active-set strategy ⋮ A new nonmonotone trust-region method of conic model for solving unconstrained optimization ⋮ Some convergence properties of descent methods ⋮ A numerical evaluation of some collinear scaling algorithms for unconstrained ⋮ A nonmonotone adaptive trust region method for unconstrained optimization based on conic model ⋮ Exact two steps SOCP/SDP formulation for a modified conic trust region subproblem ⋮ A model-hybrid approach for unconstrained optimization problems ⋮ Local andQ-superlinear convergence of a class of collinear scaling algorithms that extends quasi-newton methods with broyden's bounded-⊘ class of updates† ‡ ⋮ An improved hybrid quantum optimization algorithm for solving nonlinear equations ⋮ A global optimization algorithm for sum of quadratic ratios problem with coefficients ⋮ A trust-region method with a conic model for unconstrained optimization ⋮ A nonmonotone trust-region method of conic model for unconstrained optimization ⋮ Nonmonotone adaptive trust region method based on simple conic model for unconstrained optimization ⋮ A nonmonotone conic trust region method based on line search for solving unconstrained optimization ⋮ An adaptive conic trust-region method for unconstrained optimization ⋮ A variant of trust-region methods for unconstrained optimization ⋮ A class of collinear scaling algorithms for bound-constrained optimization: Derivation and computational results ⋮ A subspace minimization conjugate gradient method based on conic model for unconstrained optimization ⋮ On the updating scheme in a class of collinear scaling algorithms for sparse minimization

Cites Work

• Unnamed Item
• Convergence Theorems for Least-Change Secant Update Methods
• On statistical control of optimization
• Conic Approximations and Collinear Scalings for Optimizers
• The Q-Superlinear Convergence of a Collinear Scaling Algorithm for Unconstrained Optimization
• Quasi-Newton Methods, Motivation and Theory
• Collinear scaling and sequential estimation in sparse optimization algorithms
• On the Local and Superlinear Convergence of Quasi-Newton Methods
• A Characterization of Superlinear Convergence and Its Application to Quasi-Newton Methods

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