Laptin Y.P. – Institute of Cybernetics of National Academy of Sciences of Ukraine, laptin_yu_p@mail.ru,

Zhurbenko N.G. – Institute of Cybernetics of National Academy of Sciences of Ukraine, zhurbnick@yandex.ru,

Likhovid A.P.Institute of Cybernetics of National Academy of Sciences of Ukraine,  o.lykhovyd@gmail.com

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)