Function minimization by conjugate gradients

1964/02/01 by R. Fletcher · 42 citations
Mathematics · #Advanced Optimization Algorithms Research #Numerical methods in inverse problems #Iterative Methods for Nonlinear Equations

paper · pdf · doi:10.1093/comjnl/7.2.149

Abstract

A quadratically convergent gradient method for locating an unconstrained local minimum of a function of several variables is described. Particular advantages are its simplicity and its modest demands on storage, space for only three vectors being required. An ALGOL procedure is presented, and the paper includes a discussion of results obtained by its used on various test functions.

Cited by

• A Modified Hestenes and Stiefel Conjugate Gradient Algorithm for Large-Scale Nonsmooth Minimizations and Nonlinear Equations
• An Inertial Three-term Derivative-free Projection Algorithm for Nonlinear Equations without Pseudo-monotonicity
• Global convergence of a modified Fletcher–Reeves conjugate gradient method with Armijo-type line search
• An Accelerated Double Step Size model in unconstrained optimization
• WINO: A Weak-Form Physics Informed Neural Operator for Hyperelasticity on Variable Domains
• Health risk modelling by transforming a multi-dimensional unknown distribution to a multi-dimensional Gaussian
• Enhanced simulated annealing for globally minimizing functions of many-continuous variables
• The Dynamic ECME Algorithm
• Minimization algorithm in the simulation of the Wall Touching Kink Modes
• Algorithm 851
• Stability of Planar Slits in Multilayer Graphite Crystals
• A Convexity-dependent Two-Phase Training Algorithm for Deep Neural Networks
• Crustal and upper mantle model of the Middle East based on full-waveform inversion
• Stochastic choice of basis functions in adaptive function approximation and the functional-link net
• A unified convergence bound for conjugate gradient and accelerated gradient
• Solving Optimization Problems over the Stiefel Manifold by Smooth Exact Penalty Function
• A Second-Order Energy Stable Backward Differentiation Formula Method for the Epitaxial Thin Film Equation with Slope Selection
• Four Generations of High-Dimensional Neural Network Potentials
• KKT Conditions, First-Order and Second-Order Optimization, and Distributed Optimization: Tutorial and Survey
• Optimization in Theory and Practice
• SGDR: Stochastic Gradient Descent with Warm Restarts
• Line Search Fixed Point Algorithms Based on Nonlinear Conjugate Gradient\n Directions: Application to Constrained Smooth Convex Optimization
• Square-Domain Area-Preserving Parameterization for Genus-Zero and Genus-One Closed Surfaces
• Model-driven reconstruction with phase-constrained highly-oversampled MRI
• Reconstruction of a potential parameter in subdiffusion via a Kohn--Vogelius type functional: Theory and computation
• A Parallel Auxiliary Grid AMG Method for GPU
• Introducing the method of ellipcenters, a new first order technique for unconstrained optimization
• A Meshing Framework for Digital Twins for Extrusion based Additive Manufacturing
• Simpler Grassmannian optimization
• A Riemannian conjugate subgradient method for nonconvex and nonsmooth optimization on manifolds
• Near-Optimal Methods for Minimizing Star-Convex Functions and Beyond
• On the extension of the Hager–Zhang conjugate gradient method for vector optimization
• Spectral conjugate gradient methods for vector optimization problems
• Escape over a saddle by coloured noise: theory and numerics
• Numerical Optimization for Tensor Disentanglement
• Physics-Informed Tolerance Allocation: A Surrogate-Based Framework for the Control of Geometric Variation on System Performance
• Toroidal area-preserving parameterizations of genus-one closed surfaces
• Structural and helix reversal defects of carbon nanosprings
• Triangularized Orthogonalization-free Method for Solving Extreme Eigenvalue Problems
• Intrinsic structure of liquid surface and capillary waves on the Density\n Functional Theory
• Probabilistic Line Searches for Stochastic Optimization
• Complexity Guarantees for Polyak Steps with Momentum

Related

• An efficient method for finding the minimum of a function of several variables without calculating derivatives
• Been Down So Long it Looks Like Up to Me: A Unified Derivation of Conjugate Gradient and Variable Metric Minimization
• A Principle for Global Optimization with Gradients
• Conjugate Gradients and Accelerated Methods Unified: The Approximate Duality Gap View
• An optimization derivation of the method of conjugate gradients