An Automatic Method for Finding the Greatest or Least Value of a Function
1960/03/01 by H.H. Rosenbrock, H. H. Rosenbrock · 2,954 citations
Computer Science · Engineering · Mathematics · #Biology #Computer science #Function (biology) #Manufacturing Process and Optimization #Mathematics #Neural Networks and Applications #Numerical Methods and Algorithms #Statistics #Value (mathematics)
paper · doi:10.1093/comjnl/3.3.175
published in The Computer Journal 3(3), 175-184 (Oxford University Press)
openalex publication_date 1960/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Abstract
The greatest or least value of a function of several variables is to be found when the variables are restricted to a given region. A method is developed for dealing with this problem and is compared with possible alternatives. The method can be used on a digital computer, and is incorporated in a program for Mercury.
Cited by
- A Simplex Method for Function Minimization
- Optimization of Control Parameters for Genetic Algorithms
- Rosenbrock artificial bee colony algorithm for accurate global optimization of numerical functions
- On search directions for minimization algorithms
- Threshold estimation in two-alternative forced-choice (2AFC) tasks: The Spearman-Kärber method
- On the analysis of psychometric functions: The Spearman-Kärber method
- Optimization by Direct Search: New Perspectives on Some Classical and Modern Methods
- Some Efficient Algorithms for Solving Systems of Nonlinear Equations
- A methodology for creating multidisciplinary design optimization benchmark problems from optimization ones
- An n-dimensional Rosenbrock Distribution for MCMC Testing
- Feasible-side global convergence in experimental optimization
- When Rates Are Geometric: Rate-Certificate Transfer for Contact Splittings in Optimization
- Robust Gradient Descent via Heavy-Ball Momentum with Predictive Extrapolation
- Parameter-Free Accelerated Quasi-Newton Method for Nonconvex Optimization
- Contraction methods for continuous optimization
- HVAdam: A Full-Dimension Adaptive Optimizer
- Efficient Search for Diverse Coherent Explanations
- Bayesian Imaging With Data-Driven Priors Encoded by Neural Networks: Theory, Methods, and Algorithms
- A modular approach to addressing model design, scale, and parameter estimation issues in distributed hydrological modelling
- Simulated Tom Thumb, the Rule Of Thumb for Autonomous Robots
- Flexible numerical optimization with ensmallen
- High-Dimensional Gaussian Process Inference with Derivatives
- Harris hawks optimization: Algorithm and applications
- Adaptive Conditional Gradient Descent
- A Constrained Multi-Fidelity Bayesian Optimization Method
- Polynomial-Chaos-based Kriging
- Efficient Douglas-Rachford Methods on Hadamard Manifolds with Applications to the Heron Problems
- Nested Rˆ: Assessing the Convergence of Markov Chain Monte Carlo When Running Many Short Chains
- New Hoopoe Heuristic Optimization
- Decoupled-Value Attention for Prior-Data Fitted Networks: GP Inference for Physical Equations
- Nested sampling for physical scientists
- DREAM(LoAX): Simultaneous Calibration and Diagnosis for Tracer‐Aided Ecohydrological Models Under the Equifinality Thesis
- The Multi-Query Paradox in Zeroth-Order Optimization
- Modified Bee Colony optimization algorithm for computational parameter identification for pore scale transport in periodic porous media
- AngularGrad: A New Optimization Technique for Angular Convergence of Convolutional Neural Networks
- Spherical latent space models for social network analysis
- The Optimiser Hidden in Plain Sight: Training with the Loss Landscape's Induced Metric
- Heavy Ball Neural Ordinary Differential Equations
- Reverse engineering learned optimizers reveals known and novel mechanisms
- A Self-Taught Artificial Agent for Multi-Physics Computational Model Personalization
- Mixing ADAM and SGD: a Combined Optimization Method
- Visualization of hypersurfaces and multivariable (objective) functions by partial global optimization
- Distributed stochastic optimization with large delays
- evortran: a modern Fortran package for genetic algorithms with applications from LHC data fitting to LISA signal reconstruction
- GPU-based complete search for nonlinear minimization subject to bounds
- Hindsight-Guided Momentum (HGM) Optimizer: An Approach to Adaptive Learning Rate
- Gradient-Normalized Smoothness for Optimization with Approximate Hessians
- Limited-Memory BFGS with Displacement Aggregation
- SoftAdapt: Techniques for Adaptive Loss Weighting of Neural Networks with Multi-Part Loss Functions
- A Probabilistically Motivated Learning Rate Adaptation for Stochastic Optimization
- On the convergence of mirror descent beyond stochastic convex programming
- Solving a linear program via a single unconstrained minimization
- Backpropagation-Free Metropolis-Adjusted Langevin Algorithm
- Modeling, Simulating, and Parameter Fitting of Biochemical Kinetic Experiments
- DeepOBS: A Deep Learning Optimizer Benchmark Suite
- AdamP: Slowing Down the Slowdown for Momentum Optimizers on Scale-invariant Weights
- Projection Pursuit Regression
- Learning Low-Dimensional Embeddings for Black-Box Optimization
- Properties of the Affine Invariant Ensemble Sampler in high dimensions
- Evaluation of the precipitation-runoff modeling system, Beaver Creek basin, Kentucky
- A general cost-benefit-based adaptation framework for multimeme algorithms
- Accounting for potassium and magnesium in irrigation water quality assessment
- Exploiting Separability in Multi-Scale Grey-Box Bayesian Optimization
- Dynamic Proximal Point Method for Unconstrained Minimization
- The Impact of Move Schemes on Simulated Annealing Performance
- Diffeomorphic Markov Chain Monte Carlo: fast mixing for heavy-tailed distributions
- Covariant Gradient Descent
- Deep Neural Network Accelerated Implicit Filtering
- Influence of electronic correlations on orbital polarizations in the parent and doped iron pnictides
- Hessian-Free High-Resolution Nesterov Acceleration for Sampling
- Neural Architecture Transfer
- Bregman Linearized Augmented Lagrangian Method for Nonconvex Constrained Stochastic Zeroth-order Optimization
- Nested sampling cross-checks using order statistics
- An improved parameter estimation and comparison for soft tissue constitutive models containing an exponential function. [europepmc]
- On-demand serum-free media formulations for human hematopoietic cell expansion using a high dimensional search algorithm. [europepmc]
- Arbitrarily tight α BB underestimators of general non-linear functions over sub-optimal domains. [europepmc]
- Development of Supervised Learning Predictive Models for Highly Non-linear Biological, Biomedical, and General Datasets. [europepmc]
- NEO: NEuro-Inspired Optimization-A Fractional Time Series Approach. [europepmc]
- A Framework for Stochastic Optimization of Parameters for Integrative Modeling of Macromolecular Assemblies. [europepmc]
- AutoMH: Automatically Create Evolutionary Metaheuristic Algorithms Using Reinforcement Learning. [europepmc]
- High-dimensional normalized data profiles for testing derivative-free optimization algorithms. [europepmc]
- An Enhanced Hunger Games Search Optimization with Application to Constrained Engineering Optimization Problems. [europepmc]
- Surrogate-assisted global and distributed local collaborative optimization algorithm for expensive constrained optimization problems. [europepmc]
- Optimization of non-smooth functions via differentiable surrogates. [europepmc]
- IBKA-MSM: A Novel Multimodal Fake News Detection Model Based on Improved Swarm Intelligence Optimization Algorithm, Loop-Verified Semantic Alignment and Confidence-Aware Fusion. [europepmc]
Related