Disclaimer: All software should be regarded as in development
and is made available on an asis basis, without any warranty of any
kind.
A simple threeterm conjugate gradient algorithm for
unconstrained optimization. 

Unconstrained Optimization Test Functions. Algebraic expression. 

Name of test functions. 

THREECG package  threeterm conjugate gradient algorithm
with guaranteed descent and conjugacy conditions. 



THREECG for ElasticPlastic Torsion problem from MINPACK2 collection. 



THREECG for Pressure Distribution in a Journal Bearing problem from MINPACK2 collection. 



THREECG for Optimal Design with Composite Materials problem from MINPACK2 collection. 



THREECG for SteadyState Combustion problem from MINPACK2 collection. 



THREECG for Minimal Surfaces with Enneper Conditions problem from MINPACK2 collection. 



Another Conjugate Gradient Algorithm with Guaranteed
Descent and Conjugacy Conditions for Largescale
Unconstrained Optimization 

Unconstrained Optimization Test Functions. Algebraic expression. 

Name of test functions. 

DESCON package  conjugate gradient algorithm with guaranteed DEScent and CONjugacy
conditions. 

Performances of DESCON for solving a train of 80 unconstrained optimization test functions. 

DESCON for ElasticPlastic Torsion problem from MINPACK2 collection. 



DESCON for Pressure Distribution in a Journal Bearing problem from MINPACK2 collection. 



DESCON for Optimal Design with Composite Materials problem from MINPACK2 collection. 



DESCON for SteadyState Combustion problem from MINPACK2 collection. 



DESCON for Minimal Surfaces with Enneper Conditions problem from MINPACK2 collection. 



A numerical study on efficiency and robustness of some
conjugate gradient algorithms for largescale unconstrained optimization. 



Unconstrained Optimization Test Functions. Algebraic expression. 

Name of test functions. 

ASCALCG package  Accelerated Scaled Conjugate Gradient Algorithm. Main program and subroutines. 

Scaled Conjugate Gradient Algorithm for Unconstrained Optimization (full paper). 



Unconstrained Optimization Test Functions. Algebraic expression. 

Name of test functions. 

AHYBRIDM package  Accelerated Hybrid Conjugate Gradient algorithm with Modified Secant Condition. Main program and subroutines. 

Accelerated hybrid conjugate gradient algorithm with
modified secant condition for unconstrained optimization (full paper). 



Unconstrained Optimization Test Functions. Algebraic expression. 

Name of test functions. 

CONMIN package  Shanno conjugate gradient with Beale restart memoryless variable metric algorithm for Unconstrained Optimization. Main program and subroutines. 



Unconstrained Optimization Test Functions. (old version) 

Fortran expression of test functions. (old version) 

Fortran code with Anticipative and a variant of BarzilaiBorwein algorithms. 

A new gradient descent method with an anticipative scalar
approximation of Hessian for unconstrained 

Numerical experiments with a gradient descent method using
an anticipative scalar approximation of 

Numerical experiments with a variant of BarzilaiBorwein method for unconstrained optimization. 

Performance profiles: Anticipative algorithm versus BarzilaiBorwein algorithm, 310 problems. 



Unconstrained Optimization Test Functions. (old version) 

Fortran expression of test functions. (old version) 

Relaxed Gradient Descent Method with Backtracking for Unconstrained Optimization (full paper). 

Numerical experiments with Relaxed Gradient Descent Algorithm. 430 problems. 

Numerical experiments with Gradient Descent Algorithm. 360 problems. 



HookeJeeves, Powell, Rosenbrock,
NelderMead
in conjunction with unidimensional methods:
Fibonacci, Golden section, Powell's quadratic interpolation, dichotomous search.
UNO package for Unconstrained Optimization using direct search. (Fortran 77) 

Interactive version of UNO package for Unconstrained Optimization using direct search. (Fortran 77) 

NelderMead method for Unconstrained Optimization using direct search. 

HookJeeves method for Unconstrained Optimization using direct search. 

Rosenbrock method for Unconstrained Optimization using direct search. 

Powell method for Unconstrained Optimization using direct search. 

Golden section with interval searching. 

Fibonacci searching technique. 

Quadratic interpolation of Powell technique. 

Dichotomous search technique. 
SPENBAR package for Constrained Optimization using a Sparse Modified PenaltyBarrier method. (Fortran 77) 

SPENPROB COLLECTION  Constrained Optimization Problems solved with SPENBAR Package 

Problem 114, Page 123. Alkylation Problem. W. Hock and K. Schittkowski, Test Examples for Nonlinear Programming. SpringerVerlag, 1981. Lecture Notes in Economics and Mathematical Systems, vol. 187. (Fortran 77) 

Problem N8, pp.800. Neculai Andrei, Advanced Mathematical Programming. Theory, Computational Methods, Applications.Technical Press, Bucharest, 1999. (Fortran 77) 

Problem 1, "Mexican Hat". Brown  BartholomewBiggs, ODE vs SQP methods for constrained optimisation, Technical Report No.179, June 1987. The Hatfield Polytechnic, UK. (Fortran 77) 

Problem 2. Brown  BartholomewBiggs, ODE vs SQP methods for constrained optimisation, Technical Report No.179, June 1987. The Hatfield Polytechnic, UK. (Fortran 77) 

Problem 3. Brown  BartholomewBiggs, ODE vs SQP methods for constrained optimisation, Technical Report No.179, June 1987. The Hatfield Polytechnic, UK. (Fortran 77) 

Problem 4. Brown  BartholomewBiggs, ODE vs SQP methods for constrained optimisation, Technical Report No.179, June 1987. The Hatfield Polytechnic, UK. (Fortran 77) 

Problem 5. Brown  BartholomewBiggs, ODE vs SQP methods for constrained optimisation, Technical Report No.179, June 1987. The Hatfield Polytechnic, UK. (Fortran 77) 

Problem 6. Brown  BartholomewBiggs, ODE vs SQP methods for constrained optimisation, Technical Report No.179, June 1987. The Hatfield Polytechnic, UK. (Fortran 77) 

Problem 7. Brown  BartholomewBiggs, ODE vs SQP methods for constrained optimisation, Technical Report No.179, June 1987. The Hatfield Polytechnic, UK. (Fortran 77) 

Problem 8. Brown  BartholomewBiggs, ODE vs SQP methods for constrained optimisation, Technical Report No.179, June 1987. The Hatfield Polytechnic, UK. (Fortran 77) 

Problem 9. Brown  BartholomewBiggs, ODE vs SQP methods for constrained optimisation, Technical Report No.179, June 1987. The Hatfield Polytechnic, UK. (Fortran 77) 

Problem 10. Brown  BartholomewBiggs, ODE vs SQP methods for constrained optimisation, Technical Report No.179, June 1987. The Hatfield Polytechnic, UK. (Fortran 77) 

Problem 11."Witch of Agnesi". Brown  BartholomewBiggs, ODE vs SQP methods for constrained optimisation, Technical Report No.179, June 1987. The Hatfield Polytechnic, UK. (Fortran 77) 

Problem 12. Brown  BartholomewBiggs, ODE vs SQP methods for constrained optimisation, Technical Report No.179, June 1987. The Hatfield Polytechnic, UK. (Fortran 77) 

Problem 13."FourLeaved Rose". Brown  BartholomewBiggs, ODE vs SQP methods for constrained optimisation, Technical Report No.179, June 1987. The Hatfield Polytechnic, UK. (Fortran 77) 

Problem 14. Brown  BartholomewBiggs, ODE vs SQP methods for constrained optimisation, Technical Report No.179, June 1987. The Hatfield Polytechnic, UK. (Fortran 77) 

Problem 16. Brown  BartholomewBiggs, ODE vs SQP methods for constrained optimisation, Technical Report No.179, June 1987. The Hatfield Polytechnic, UK. (Fortran 77) 

A. BenIsrael, A. BenTal, S. Zlobec, Optimality in nonlinear programming: A feasible directions approach. John Wiley & Sons, New York, 1981. Example from pp.68 (paragraph 6.5) (Fortran 77) 

A. BenIsrael, A. BenTal, S. Zlobec, Optimality in nonlinear programming: A feasible directions approach. John Wiley & Sons, New York, 1981. Example from pp.75 (paragraph 7.2) (Fortran 77) 

Shape optimization of a cam. M. Anitescu,
R. Serban, A sparse superlinearly
convergent SQP with applications to twodimensional shape optimization. Preprint
ANL/MCSP7060198, Argonne National Laboratory, Argonne, Illinoiss,
1998. 

Hiebert's 3rd Chemical Equilibrium Problem. Mordechai Shacham, Numerical solution of constrained nonlinear algebraic equations. International Journal for Numerical Methods in Engineering, Vol.23, 1986, pp.14551481. Problem 1, pp.1463. (Fortran 77) 

Distribution of electrons on a sphere. R. Vanderbei, Nonlinear optimization models.
http://www.sor.princeton.edu/~rvdb/ampl/nlmodels 

C.A., Floudas, P.M., Pardalos, A collection of test problems for constrained global optimization algorithms. SpringerVerlag, Berlin, 1990. Lecture Notes in Computer Science, vol.455. (Problem 3.3.1, pp.2324. Minimization of a concave quadratic function subject to linear and quadratic constraints) (Fortran 77) 

C.A., Floudas, P.M., Pardalos, A collection of test problems for constrained global optimization algorithms. SpringerVerlag, Berlin, 1990. Lecture Notes in Computer Science, vol.455. (Problem 5.2.1, pp.3739. Test problem 1: Propane, Isobutane, nButane Nonsharp Separation.) (Fortran 77) 

C.A., Floudas, P.M., Pardalos, A collection of test problems for constrained global optimization algorithms. SpringerVerlag, Berlin, 1990. Lecture Notes in Computer Science, vol.455. (Problem 5.3.1, pp.4146. Test problem 2: Propane, Isobutane, nButane, Isopentane Separation.) (Fortran 77) 

C.A., Floudas, P.M., Pardalos, A collection of test problems for constrained global optimization algorithms. SpringerVerlag, Berlin, 1990. Lecture Notes in Computer Science, vol.455. (Problem 5.4.1, pp.4749. Test problem 3: Blending/Pooling/Separation.) (Fortran 77) 

C.A., Floudas, P.M., Pardalos, A collection of test problems for constrained global optimization algorithms. SpringerVerlag, Berlin, 1990. Lecture Notes in Computer Science, vol.455. (Problem 6.2.1, pp.59. Test problem 1: Haverly's Pooling Problem  Case I.) (Fortran 77) 

C.A., Floudas, P.M., Pardalos, A collection of test problems for constrained global optimization algorithms. SpringerVerlag, Berlin, 1990. Lecture Notes in Computer Science, vol.455. (Problem 6.4.1, pp.61. Test problem 3: Haverly's Pooling Problem  Case III.) (Fortran 77) 

C.A., Floudas, P.M., Pardalos, A collection of test problems for constrained global optimization algorithms. SpringerVerlag, Berlin, 1990. Lecture Notes in Computer Science, vol.455. (Problem 6.4.1, pp.61. Test problem 3: Haverly's Pooling Problem  Case IV. A new variant with another objective function.) (Fortran 77) 

C.A., Floudas, V. Visweswaran, Quadratic Optimization, In Handbook of Global Optimization. R. Horst and P.M. Pardalos (Eds.) Kluwer Academic Publishers, 1994, pp. 217270. (IC circuit layout and compaction, pages 4041) (Fortran 77) 

C.A., Floudas, V. Visweswaran, Quadratic Optimization, In Handbook of Global Optimization. R. Horst and P.M. Pardalos (Eds.) Kluwer Academic Publishers, 1994, pp. 217270. (Robust stability of linear systems, pages 4143) (Fortran 77) 

Hanging Chain. A.S. Bondarenko, D.M., Bortz and J.J., More, COPS: Large scale nonlinearly constrained optimization problems, Preprint ANL/MCSTM237, Argonne National Laboratory, September 1998, (October 1999 revision) pp.1011.(Robust stability of linear systems, pages 4143) (Problem suggested by H. Mittelmann.) (Fortran 77) 

The Human Heart Dipole. B.M., Averick, R.G., Carter, J.J., Moré, The MINPACK2 test problem collection. Technical Memorandum No.150, Argonne National Laboratory, Argonne, Illinois, May 1991, pp.7. (Fortran 77) 

Problem 80, Page 100. W. Hock and K. Schittkowski, Test Examples for Nonlinear Programming Codes. SpringerVerlag, 1981. Lecture Notes in Economics and Mathematical Systems, vol. 187. (Fortran 77) 

Problem 81, Page 101. W. Hock and K. Schittkowski, Test Examples for Nonlinear Programming Codes. SpringerVerlag, 1981. Lecture Notes in Economics and Mathematical Systems, vol. 187. (Fortran 77) 

Problem 83, Page 102. W. Hock and K. Schittkowski, Test Examples for Nonlinear Programming Codes. SpringerVerlag, 1981. Lecture Notes in Economics and Mathematical Systems, vol. 187. (Fortran 77) 

Problem 95, Page 109. W. Hock and K. Schittkowski, Test Examples for Nonlinear Programming Codes.SpringerVerlag, 1981. Lecture Notes in Economics and Mathematical Systems, vol. 187. (Fortran 77) 

Problem 96, Page 109. W. Hock and K. Schittkowski, Test Examples for Nonlinear Programming Codes. SpringerVerlag, 1981. Lecture Notes in Economics and Mathematical Systems, vol. 187. (Fortran 77) 

Problem 97, Page 109. W. Hock and K. Schittkowski, Test Examples for Nonlinear Programming Codes. SpringerVerlag, 1981. Lecture Notes in Economics and Mathematical Systems, vol. 187. (Fortran 77) 

Problem 98, Page 109. W. Hock and K. Schittkowski, Test Examples for Nonlinear Programming Codes.SpringerVerlag, 1981. Lecture Notes in Economics and Mathematical Systems, vol. 187. (Fortran 77) 

Problem 100, Page 111. W. Hock and K. Schittkowski, Test Examples for Nonlinear Programming Codes.SpringerVerlag, 1981. Lecture Notes in Economics and Mathematical Systems, vol. 187. (Fortran 77) 

Problem 106, Page 115. Heat exchanger design. W. Hock and K. Schittkowski, Test Examples for Nonlinear Programming Codes. SpringerVerlag, 1981. Lecture Notes in Economics and Mathematical Systems, vol. 187. (Fortran 77) 

Problem 108, Page 117. W. Hock and K. Schittkowski, Test Examples for Nonlinear Programming Codes. SpringerVerlag, 1981. Lecture Notes in Economics and Mathematical Systems, vol. 187. (Fortran 77) 

Problem 112, Page 121. Chemical Equlibrium problem. W. Hock and K. Schittkowski, Test Examples for Nonlinear Programming Codes. SpringerVerlag, 1981. Lecture Notes in Economics and Mathematical Systems, vol. 187. (Fortran 77) 

Problem 113, Page 122. Chemical Equlibrium problem. W. Hock and K. Schittkowski, Test Examples for Nonlinear Programming Codes. SpringerVerlag, 1981. Lecture Notes in Economics and Mathematical Systems, vol. 187. (Fortran 77) 

Design of an electrical circuit. M. Lowe, Nonlinear Programming: Augmented Lagrangian Techniques for Constrained Minimization. Ph. D. Thesis, Montana Univ. (Fortran 77) 

Problem 116, Page 124. 3stage membrane separation. W.
Hock and K. Schittkowski, Test Examples for
Nonlinear Programming Codes. SpringerVerlag,
1981. Lecture Notes in Economics and Mathematical Systems, vol. 187. (Fortran
77) 

5stage membrane separation. Ron S. Dembo, A set of geometric programming test problems and their solutions. Mathematical Programming, vol. 10, 1976, pp.208211. (Fortran 77) 

Problem P1. L. Pibouleau, P., Floquet, S., Domenech, Optimisation de procedes chimiques par une methode de gradient reduit. Partie II. Exemples d'illustration. Comparaison avec d'autres methodes. RAIRO Recherche Operationnelle, vol.19, no.4, 1985, pp.325 (Fortran 77) 

Largest small polygon. A.S. Bondarenko, D.M., Bortz and J.J., More, COPS: Large scale nonlinearly constrained optimization problems, Preprint ANL/MCSTM237, Argonne National Laboratory, September 1998, (October, 1999 revision) pp.34. (Fortran 77) 

Andrei's Pooling Problem. A pooling problem. This problem
has been created during my visit to Bonner & Moore Associated GmbH, Wiesbaden,
Germany, as a result of a technical discussion with Dr. Ronald Coxhead. (December, 1996) (Fortran 77) 

Hansen Problem. Chemical Mixing Problem. (Fortran 77) 

Combustion of Propane. B.M., Averick, R.G., Carter, J.J., Moré, The MINPACK2 test problem collection. Technical Memorandum No.150, Argonne National Laboratory, Argonne, Illinois, May 1991, pp.8. (Fortran 77) 

Combustion of Propane. A least squares approach. B.M., Averick, R.G., Carter, J.J., Moré,
The MINPACK2 test problem collection. Technical Memorandum No.150,
Argonne National Laboratory, Argonne, Illinois, May 1991, pp.8. (Fortran 77) 

Combustion of Propane. Reduced Formulation. B.M., Averick, R.G., Carter, J.J., Moré, The MINPACK2 test problem collection. Technical Memorandum No.150, Argonne National Laboratory, Argonne, Illinois, May 1991, pp.9. (Fortran 77) 

Combustion of Propane. Reduced Formulation. A least squares
approach. B.M., Averick, R.G., Carter,
J.J., Moré, The MINPACK2 test problem
collection. Technical Memorandum No.150, Argonne National Laboratory,
Argonne, Illinois, May 1991, pp.9. (Fortran 77) 

Problem 230, Page 54. K. Schittkowski, More test examples for nonlinear programming codes. Springer Verlag, 1987. Lecture Notes in Economics and Mathematical Systems, vol. 282. (Fortran 77) 

Problem 329, Page 150. K. Schittkowski, More test examples for nonlinear programming codes. Springer Verlag, 1987. Lecture Notes in Economics and Mathematical Systems, vol. 282. (Fortran 77) 

Problem 338, Page 159. K. Schittkowski, More test examples for nonlinear programming codes. Springer Verlag, 1987. Lecture Notes in Economics and Mathematical Systems, vol. 282. (Fortran 77) 

Problem 346, Page 167. Design of a disc flywheel. K. Schittkowski, More test examples for nonlinear programming codes. Springer Verlag, 1987. Lecture Notes in Economics and Mathematical Systems, vol. 282. (Fortran 77) 

Problem 376, Page 195. Optimization of a multispindle automatic lathe. K. Schittkowski, More test examples for nonlinear programming codes. Springer Verlag, 1987. Lecture Notes in Economics and Mathematical Systems, vol. 282. (Fortran 77) 

Problem 107, Page 116. Static Power Scheduling . W. Hock and K. Schittkowski, Test Examples for Nonlinear Programming Codes.SpringerVerlag, 1981. Lecture Notes in Economics and Mathematical Systems, vol. 187 (Fortran 77) 

Problem 93, Page 108. Design of an electric transformer. W. Hock and K. Schittkowski, Test Examples for Nonlinear Programming Codes.SpringerVerlag, 1981. Lecture Notes in Economics and Mathematical Systems, vol. 187 (Fortran 77) 
Fortran subroutines for PFI with a preassigned
pivot procedure computation: 

Input file with some examples. 
Solving linear algebraic systems by LU factorization of sparse matrices. (Fortran 77) 

Technical Report No. 2/1995. 

A tridiagonal system (n=100) 

Another tridiagonal system (n=100) 

Wilkinson example. Data for this system are in sys.txt 

Linear algebraic system with Hilbert matrix 

Random generated matrix (n=100 and n=1000) 

Penthadiagonal system 

Random generated matrix (n=1000) 

HB/lund_b system (n=147, nz=1294). Data for this system are in mm1.txt 

HB/1138_bus system (n=1138, nz=2596). Data for this system are in hb1138bus.txt 

GH1484 system. University of Florida Sparse Matrix Collection (n=1484, nz=6110) . Data for this system are in gh1484.txt 
Block Triangularization of a largescale sparse matrix. (Fortran 77) 
Fibonacci method for onedimensional function minimization. (Fortran 77) 

Technical Report on Fibonacci method for onedimensional function minimization. 
Powell direct search method. (Fortran 77) 

Technical Report on Powell direct search method. 
A simple algorithm for computing of a zero of a nonlinear function of a variable in a given interval [a,b]. 

A simple algorithm for computing all zeros of a nonlinear function of a variable in a given interval [a,b]. 