# References for Unconstrained Minimisation Problems

## Problem: akiva.py
- Ben-Akiva and Lerman, "Discrete Choice Analysis", MIT Press, 1985.

## Problem: argtrigls.py
- J.J. More', B.S. Garbow and K.E. Hillstrom, "Testing Unconstrained Optimization Software", ACM Transactions on Mathematical Software, vol. 7(1), pp. 17-41, 1981.

## Problem: bard.py
- J.J. More', B.S. Garbow and K.E. Hillstrom, "Testing Unconstrained Optimization Software", ACM Transactions on Mathematical Software, vol. 7(1), pp. 17-41, 1981.
- Buckley#16

## Problem: beale.py
- J.J. More', B.S. Garbow and K.E. Hillstrom, "Testing Unconstrained Optimization Software", ACM Transactions on Mathematical Software, vol. 7(1), pp. 17-41, 1981.

## Problem: bennett.py
- Bennett, L., L. Swartzendruber, H. Brown, NIST (1994). Superconductivity Magnetization Modeling.

## Problem: biggs.py
- A.R. Buckley, "Test functions for unconstrained minimization", TR 1989CS-3, Mathematics, statistics and computing centre, Dalhousie University, Halifax (CDN), 1989.

## Problem: box.py
- N. Gould, private communication.
- J.J. More', B.S. Garbow and K.E. Hillstrom, "Testing Unconstrained Optimization Software", ACM Transactions on Mathematical Software, vol. 7(1), pp. 17-41, 1981.
- Buckley#BOX663
- Box, G. P., W. G. Hunter, and J. S. Hunter (1978). Statistics for Experimenters, New York, NY: Wiley, pp. 483-487.

## Problem: broydn.py
- J.J. More', B.S. Garbow and K.E. Hillstrom, "Testing Unconstrained Optimization Software", ACM Transactions on Mathematical Software, vol. 7(1), pp. 17-41, 1981.
- Toint#17
- Buckley#78
- Ph.L. Toint, "Some numerical results using a sparse matrix updating formula in unconstrained optimization", Mathematics of Computation, vol. 32(114), pp. 839-852, 1978.
- Buckley#84
- Buckley#73
- Toint#18

## Problem: chwirut.py
- Chwirut, D., NIST (197?). Ultrasonic Reference Block Study.

## Problem: cosine.py
- N. Gould, private communication.

## Problem: curly.py
- Nick Gould, September 1997.

## Problem: dixon3dq.py
- A.R. Buckley, "Test functions for unconstrained minimization", TR 1989CS-3, Mathematics, statistics and computing centre, Dalhousie University, Halifax (CDN), 1989.

## Problem: dixmaa.py
- L.C.W. Dixon and Z. Maany, "A family of test problems with sparse Hessians for unconstrained optimization", TR 206, Numerical Optimization Centre, Hatfield Polytechnic, 1988.

## Problem: eckerle4ls.py
- Problem 7 from NIST nonlinear least squares test set http://www.itl.nist.gov/div898/strd/nls/nls_main.shtml

## Problem: elatvidu.py
- Problem from the SCIPY benchmark set https://github.com/scipy/scipy/tree/master/benchmarks/benchmarks/go_benchmark_functions

## Problem: engval.py
- Ph.L. Toint, "Test problems for partially separable optimization and results for the routine PSPMIN", Report 83/4, Department of Mathematics, FUNDP (Namur, B), 1983.
- A.R. Buckley, "Test functions for unconstrained minimization", TR 1989CS-3, Mathematics, statistics and computing centre, Dalhousie University, Halifax (CDN), 1989.

## Problem: errinros.py
- L. Luksan, C. Matonoha and J. Vlcek, "Modified CUTE problems for sparse unconstrained optimization", Technical Report 1081, Institute of Computer Science, Academy of Science of the Czech Republic

## Problem: fletch.py
- R. Fletcher, "An optimal positive definite update for sparse Hessian matrices" Numerical Analysis report NA/145, University of Dundee, 1992.
- L. Luksan, C. Matonoha and J. Vlcek, "Modified CUTE problems for sparse unconstrained optimization", Technical Report 1081, Institute of Computer Science, Academy of Science of the Czech Republic.

## Problem: gauss.py
- Rust, B., NIST (1996).

## Problem: gaussian.py
- J.J. More', B.S. Garbow and K.E. Hillstrom, "Testing Unconstrained Optimization Software", ACM Transactions on Mathematical Software, vol. 7(1), pp. 17-41, 1981.
- Buckley#28

## Problem: genhumps.py
- Ph. Toint, private communication, 1997.

## Problem: genrose.py
- S. Nash, "Newton-type minimization via the Lanczos process", SIAM J. Num. Anal. 21, 1984, 770-788.

## Problem: hahn1ls.py
- Hahn, T., NIST (197?). Copper Thermal Expansion Study.

## Problem: heart.py
- J. E. Dennis, Jr., D. M. Gay, P. A. Vu, "A New Nonlinear Equations Test Problem". Tech. Rep. 83-16, Dept. of Math. Sci., Rice Univ., Houston, TX June 1983, revised May 1985.

## Problem: helix.py
- J.J. More', B.S. Garbow and K.E. Hillstrom, "Testing Unconstrained Optimization Software", ACM Transactions on Mathematical Software, vol. 7(1), pp. 17-41, 1981.

## Problem: himmelblau.py
- D.H. Himmelblau, "Applied nonlinear programming", McGraw-Hill, New-York, 1972.
- W. Hock and K. Schittkowski, "Test examples for nonlinear programming codes", Lecture Notes in Economics and Mathematical Systems 187, Springer Verlag, Berlin, 1981.

## Problem: kirby.py
- Kirby, R., NIST (197?). Scanning electron microscope line width standards.

## Problem: kowosb.py
- J.J. More', B.S. Garbow and K.E. Hillstrom, "Testing Unconstrained Optimization Software", ACM Transactions on Mathematical Software, vol. 7(1), pp. 17-41, 1981.

## Problem: lanczos.py
- Lanczos, C. (1956). Applied Analysis. Englewood Cliffs, NJ: Prentice Hall, pp. 272-280.

## Problem: rosenbr.py
- J.J. More', B.S. Garbow and K.E. Hillstrom, "Testing Unconstrained Optimization Software", ACM Transactions on Mathematical Software, vol. 7(1), pp. 17-41, 1981.

## Frequently Cited Papers

1. J.J. More', B.S. Garbow and K.E. Hillstrom, "Testing Unconstrained Optimization Software", ACM Transactions on Mathematical Software, vol. 7(1), pp. 17-41, 1981.
   - Referenced in: argtrigls.py, beale.py, bard.py, broydn.py, box.py, gaussian.py, helix.py, kowosb.py, rosenbr.py

2. A.R. Buckley, "Test functions for unconstrained minimization", TR 1989CS-3, Mathematics, statistics and computing centre, Dalhousie University, Halifax (CDN), 1989.
   - Referenced in: dixon3dq.py, engval.py, biggs.py

3. L. Luksan, C. Matonoha and J. Vlcek, "Modified CUTE problems for sparse unconstrained optimization", Technical Report 1081, Institute of Computer Science, Academy of Science of the Czech Republic.
   - Referenced in: fletch.py, errinros.py

4. Nick Gould (private communications)
   - Referenced in: cosine.py, box.py 

5. NIST test problems
   - Referenced in: chwirut.py, bennett.py, gauss.py, hahn1ls.py, kirby.py, eckerle4ls.py