testfunctions: Test Functions in gek

Description

Overview of test functions and their associated gradients available in gek.

Arguments

2-dimensional test functions for optimization

branin: Branin-Hoo function
camel3: Three-hump camel function
camel6: Six-hump camel function
himmelblau: Himmelblaus's function

Multi-dimensional test functions for optimization

banana: Rosenbrock's Banana function
cigar: Bent Cigar function
griewank: Griewank function
qing: Qing function
rastrigin: Rastrigin function
schwefel: Schwefel function
sphere: Sphere function
styblinski: Styblinski-Tang function

Test functions for uncertainty quantification

borehole: Borehole function
steel: Steel column function
short: Short column function
sulfur: Sulfur model function

Author

Carmen van Meegen

References

Branin, Jr., F. H. (1972). Widely Convergent Method of Finding Multiple Solutions of Simultaneous Nonlinear Equations. IBM Journal of Research and Development, 16(5):504--522.

Jamil, M. and Yang, X.-S. (2013). A Literature Survey of Benchmark Functions for Global Optimization Problems. International Journal of Mathematical Modelling and Numerical Optimisation, 4(2):150-–194. tools:::Rd_expr_doi("10.1504/IJMMNO.2013.055204").

Harper, W. V. and Gupta, S. K. (1983). Sensitivity/Uncertainty Analysis of a Borehole Scenario Comparing Latin Hypercube Sampling and Deterministic Sensitivity Approaches. BMI/ONWI-516, Office of Nuclear Waste Isolation, Battelle Memorial Institute, Columbus, OH.

Himmelblau, D. (1972). Applied Nonlinear Programming. McGraw-Hill. ISBN 0-07-028921-2.

Kuschel, N. and Rackwitz, R. (1997). Two Basic Problems in Reliability-Based Structural Optimization. Mathematical Methods of Operations Research, 46(3):309--333.

Morris, M., Mitchell, T., and Ylvisaker, D. (1993). Bayesian Design and Analysis of Computer Experiments: Use of Derivatives in Surface Prediction. Technometrics, 35(3):243--255. tools:::Rd_expr_doi("10.1080/00401706.1993.10485320").

Plevris, V. and Solorzano, G. (2022). A Collection of 30 Multidimensional Functions for Global Optimization Benchmarking. Data, 7(4):46. tools:::Rd_expr_doi("10.3390/data7040046").

Rosenbrock, H. H. (1960). An Automatic Method for Finding the Greatest or least Value of a Function. The Computer Journal, 3(3):175--184. tools:::Rd_expr_doi("10.1093/comjnl/3.3.175").

Surjanovic, S. and Bingham, D. (2013). Virtual Library of Simulation Experiments: Test Functions and Datasets. https://www.sfu.ca/~ssurjano/ (retrieved January 19, 2024).