INTSOLVER: An interval based solver for Global Optimization

Interval based functions to solve small global optimization problems with guaranteed bounds.

Description

We present a set of functions based on interval arithmetic to solve small size global optimization problems with guaranteed bounds on solutions. Interval analysis can be used to bound ALL solutions of nonlinear optimization problem, equality constrained or not as well to bound ALL solutions of a nonlinear system of equation. Our functions can deal with these problems using an implementation of the interval Newton method with a bissection scheme. The capabilities of our functions can be showed through the analysis of some important global optimization examples that we provide with the main functions.

• MATLAB release: MATLAB 7.7 (R2008b)
• Other requirements: INTLAB available at http://www.ti3.tu-harburg.de/~rump/intlab/

[sebastian]

Excuse me,I've Intlab and insolver in my machine, I've a problems with Insolver, I want to solve a nolinear system of equations with intksolve.m, and intksolve.m, because the result isn't an interval, it's solution of real numers not intervals. see this:

>> x0 = [infsup(-10,10), infsup(-10,10), infsup(-10,10), infsup(-10,10)];
f = @(x) [-2*(x(1)+x(2)-x(3)-1)-2*(x(1)+x(2))-10*x(1)+2*x(4),-2*(x(1)+x(2)-x(3)-1)-2*(x(1)+x(2)),2*(x(1)+x(2)-x(3)-1)+x(4), 2*x(1)+x(3)]
x = intksolve(f, x0)
f =
    @(x) [-2*(x(1)+x(2)-x(3)-1)-2*(x(1)+x(2))-10*x(1)+2*x(4),-2*(x(1)+x(2)-x(3)-1)-2*(x(1)+x(2)),2*(x(1)+x(2)-x(3)-1)+x(4), 2*x(1)+x(3)]
intval x =
    0.1428 0.2142 -0.2857 0.7142

I need to obtain the interval solution of x(1),x(2)... x(4)
What I have to do?
I need the article of hansen& greenberg for information about your implementation (intsolve) for free thanks

[Dmitrey Kroshko]

free (even for commercial usage) solver interalg (http://openopt.org/interalg) seems to work tens-hundreds-thousands times faster and is more stable, the bench is provided there.

[Tiago Montanher]

Dear Dmitrey,

Thank you for use my intsolver and point some issues on it. I observed that you found some problems which make Intsolver works improperly. I will work on that and post a correction as soon as possible.

Sincerely
Tiago