OVERVIEW OF TOOLBOX
Successfully installed toolbox must showing you, Global Optimization Toolbox name in 'Scilab Help' as well as in 'Scilab Demonstration' list.
For toolbox's execution use following command OR Under 'Scilab Demonstration' list click 'Univariate Example with GUI Facility':
exec('Toolbox_Directory_Path\demos\Multivariate.sce'); // Use semicolon at end of the command. [e.g. exec('D:\Global_Optimization_toolbox\demos\Multivariate.sce');]
The same example with GUI messages explained below:
1) First step, it will asking for 'Enter Polynomial in the simplified format'.Followed by clicking 'Ok' button.
e.g. Here default polynomial given is, x+2*y+10. Click 'Ok'.
Note: Use alphbetes between f to z and signs +,-,/,* and ^
For Example: x+y*z-2*x^2+9999/9999
If polynomial is not in said format then, message will come 'Re-Enter Correct Polynomial','x+y*z-2*x^2+9999/9999'. Hence polynomial should be in said format.
2) Enter number of variable used in the polynomial. Followed by clicking 'Ok' button.
e.g. Here default value given is, 2. Click 'Ok'.
Number must be positive nonzero, therwise message will come 'Re-Enter Correct Number of Variables ?'.
3) Enter number of iteration to get an answer i.e. Global Minimum (zcap)
e.g. Here default value given is, 250. Click 'Ok'.
Note: Recommended that, start with the current value 250.
This count varies and it depends on entered polynomial and entered bounds.
For some cases: If 250 iterations completed and till program not getting or calculating answer Global minimum (zcap) with given tolerences on global minimum and minimizer then, program again asking with message, 'You have exceeds given No. of Iterations. Press OK with new entry or put 0(zero) to stop ?'
If you put '0', you may get global minimum,zcap with less accuracy.
4) Enter Bounds to respective variables: Lower Bound | Upper Bound
e.g. Here default value given is;
[0,0; 0,0].
Don't click 'Ok' here, because bound's(Lower or Upper) number both should not be zero,otherwise message will come 'Re-Enter Correct Bounds to respective //variables'.
For this example, take as follows; [0,1;
0,1].
then, Click 'Ok'.
Note: One row shows, bounds for that (one) variable used in the polynomial. Here, First row showing bounds on 'x' variable. and second row showing bounds on 'y' variable.
Means, number of rows equal to number of variable, bounds on each element.
5) Enter Tolerance on Global minimizers/bounds i.e. Lsol
e.g. Here default value given is, 0.000001. Click 'Ok'.
6) Enter Tolerance on Global minimum i.e. zcap
e.g. Here default value given is, 0.000001. Click 'Ok'.
7) If 250 iteration completed and till program not calculating answer Global minimum (zcap) with given tolerences on global minimum and minimizer then, program again asking with message, 'You have exceeds given No. of Iterations.Press OK with new entry or put 0(zero) to stop ?'
e.g. Here for this example, this message not comes.
That's all about execution of your polynomial, into this toolbox.
ABOUT ANSWER:
For this example, on scilab console window you will get
zcap =
10.
Lsol =
0 0
0 0 . ans = 18.12 .
Here, 'ans' is nothing but the time required for execution of a program.
1. Shashwati Ray, P.S.V. Nataraj. An efficient algorithm for range computation of polynomials using the Bernstein form. Journal of Global Optimization, 45: 403-426,2009;
2. G. T. Cargo and O. Shisha. The Bernstein form of a polynomial. Jl. of research of NBS,70B:79-81,1966.
3. S. Ray, A new approach to range computation of polynomial problems using the Bernstein form. PhD thesis, Systems and Control Engineering, IIT Bombay, India, 2007.