** Laptin Y.P. **– Institute of Cybernetics of
National Academy of Sciences of

** Zhurbenko N.G. – **Institute of Cybernetics of National
Academy of Sciences of

** Likhovid A.P.** –

*Software implementation of the method of convex
conical extensions *

algorithm
description | download
software tool (Windows) | download
software tool (Linux)

Software implementation of
the method of conical extensions** **[1] is designed for solving optimization
problems with constraints in AMPL software environment (http://www.ampl.com/index.html).
The objective function may not be defined outside the feasible
region. The method is effective in solving ill-conditioned and badly scaled
problems. To solve the transformed unconstrained optimization problem
Shor's r-algorithm is used [2]. Without constraints the program's
behavior is identical to AmplRalg.
Description of the
mathematical model of optimization problem and input data must be in accordance
with the requirements of AMPL. The prepared description of the mathematical
model can be used to solve the problem by any solver, providing an interface
with AMPL. The initial value of problem variables is used to define a basic point from which a
conical extension of the objective function is formed. This point should
be an interior point of the feasible set of the problem.

Executable module ConExp.exe must run in AMPL
environment by commands of AMPL, as well
as other solvers. For this a student or a full
version of AMPL software is required on computer (http://www.ampl.com/DOWNLOADS/index.htmll). ConExp.exe module must be in the same directory
where the other solvers AMPL are located. Below example of run of
module ConExp.exe is presented.

ampl: *reset;*

ampl: *model**mathmod**.mod; # model
description*

ampl: *data**mathmod**.dat; # data
description*

ampl: *option solver ConExp**;*

ampl: *solve;*

In
the same directory file RALG.OPT of parameters of r-algorithm should be
located. RALG.OPT file contains the following data (you can change the numeric
values only)

Limit_of_iterations |
10000 |
(by_default__1000) |

Argument_accuracy |
1.00E-006 |
(by_default_1.e-6) |

Gradient_accuracy |
1.00E-006 |
(by_default_1.e-6) |

Output_interval |
100 |
(by_default____10) |

Initial_step |
1 |
(by_default____1.) |

Q1_parameter |
0.95 |
(by_default__0.95) |

Q2_parameter |
1.2 |
(by_default__1.20) |

Alpha_parameter |
2 |
(by_default___2.0) |

Penalty_parameter |
1000 |
(by_default_1000.) |

A
description of parameters of r-algorithm is given in the description of AmplRalg
software module. (**Penalty_parameter** value is not used.)

Requirements
for software and hardware environment:

· PC of standard configuration;

·
32-bit operating system -
Windows XP/ 2003/Vista or later, Linux;

·
Student or full version of
AMPL software environment

1.
*Laptin
Y.P, Likhovid A.P The*
use of convex continuations of functions for solving nonlinear optimization
problems / / Control systems and machines. - 2010. - №. - P. (in
Russian)

2. *N.Z Shor, N.G Zhurbenko *Minimization
method using operation of space dilation in the direction of the difference of
two successive gradients // Kibernetika. - 1971. - № 3. - P. 51-59. (in
Russian)