fminsearchbnd

Bound constrained optimization using fminsearch.

Description

Fminsearch does not admit bound constraints.
However simple transformation methods exist to
convert a bound constrained problem into an
unconstrained problem.

Fminsearchbnd is used exactly like fminsearch,
except that bounds are applied to the variables.
The bounds are applied internally, using a
transformation of the variables. (Quadratic for
single bounds, sin(x) for dual bounds.)

The bounds are inclusive inequalities, which admit
the boundary values themselves, but will not permit
ANY function evaluations outside the bounds.

Note that fminsearchbnd allows the user to exactly fix a variable at some given value, by setting both bounds to the exact same value.

Example usage:
rosen = @(x) (1-x(1)).^2 + 105*(x(2)-x(1).^2).^2;

% unconstrained fminsearch solution
fminsearch(rosen,[3 3])
ans =
    1.0000 1.0000

% Lower bounds, no upper bounds
fminsearchbnd(rosen,[2.5 2.5],[2 2],[])
ans =
    2.0000 4.0000

Lower bounds on both vars, upper bound on x(2)
fminsearchbnd(rosen,[2.5 2.5],[2 2],[inf 3])
ans =
    2.0000 3.0000

• Acknowledgements: This submission has inspired the following:; Fminspleas, Zfit, fminsearchbnd new, Fminsearchcon, optimize
• MATLAB release: MATLAB 7.0.1 (R14SP1)
• Other requirements: This code should work on any release of matlab which allows the use of sub-functions.
• Published M Files: fminsearchbnd_demo
• Other Files: fminsearchbnd/.DS_Store, ; fminsearchbnd/demo/.DS_Store, ; fminsearchbnd/demo/fminsearchbnd_demo.m, ; fminsearchbnd/doc/.DS_Store, ; fminsearchbnd/doc/Understanding_fminsearchbnd.rtf, ; fminsearchbnd/fminsearchbnd.m, ; fminsearchbnd/test/.DS_Store, ; fminsearchbnd/test/test_main.m, ; license.txt

[Ken Campbell]

Nice trick solving a common problem

[Vijit Nair]

This is a great funcn. Thanks John.

[Evan Palmer]

Works really well and is very handy! Nice job!

[Kaushik b]

Thanks a lot. It really useful and works beautifully.

[Rui Miguel]

I was really needing it! thanks a lot.
Has worked flawlessly for me.

[cedric penard]

Works very well, exellent ! Thanks.

[G.H. Rao]

excellent program. on these lines I applied bounds successfully to the genetic algorithm program 'ga' of Matlab release 14

[CC Gomez]

Nicely written.

[Yes its Good]

works very well!

[Umberto .]

 

[Dmitrey Kroshko]

I connected John D'Errico file to the OpenOpt project
http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=13115&objectType=file
& informed him (I hope my letter passed antispam filter OK)
if any pretensions will be received, I promise to exclude the one
btw now default inner solver is Shor ralg with AST, which is better than current implementation of fminsearch, at least, for those task I tried with. Also, it can handle (sub)gradient info provided by user, and corresponding changes in John code were made.

[Natis Angarita]

 

[jimmy tsai]

It's great. I couldn't solve my problem with fmincon but did it with this file. I really appreciate it.

[Eli Tom]

Nice indeed.

[Lauren Cooney]

thank you for this great program! it saved me a lot of time and frustration!

[Yang Zhang]

I like this program and do you think it is possible to expand it to deal with linear constraints?

[John D'Errico]

See fminsearchcon for linear and nonlinear inequality constraints. Equality constraints are more difficult to implement when coupled with bound constraints as implemented using transformations - John.

[Alex Chirokov]

I really like this code: it is very well written and useful.

[Yossef Ehrlichman]

It's really working. Helped alot! Matlab should incoprate it into its libraries.

[Mert Sabuncu]

excellent code - gets the job done!

[Ken Purchase]

Notice: I have submitted a slightly modified version that includes output and plot functions as well as slightly improved handling of varargin. Search for fminsearch.

The original is excellent and very useful- I hope the changes didn't break anything.

[M. P.]

Worked beautifully for my own optimization problem. Thanks John.

[M. P.]

 

[Chirackel Yoonus]

Very useful

[leo nidas]

Thanks John!

[Umesh Rudrapatna]

Thanks a lot! Helped me a lot.

[Chris Men]

the beauty is yours.

[Srinivasa Chemudupati]

Cannot Thank you enough John!!

[Will]

Excellent modification to create a very useful algorithm. Thanks!

[Ryan Webb]

 Great Function. Used it mane times.

However, now I have a trickier problem where one of the boundaries is a function of one of the variables. Making UB a function of xtrans is possible, but how would fminsearchbnd determine this intent given that the cases for transformation (k) are determined solely by the initial numerical values of the constraints? Thoughts?

[John D'Errico]

Ryan,

This is really not a bound constrained problem. Your constraint is a general one, either a linear or a nonlinear inequality constraint.

The simple solution is to use a code that allows explicit linear or nonlinear constraints. There are a few on the FEX. In fact my fminsearchcon on the FEX does that, by applying a penalty to the problem when a constraint is violated. You might also look at optimize, by Rody Oldenhuis. This code allows explicit constraints of all forms.

However, there is a simple way to solve this class of problem with fminsearchbnd. Use another class of transformation. For example, suppose one wishes to minimize the function f(x,y), subject to the "bound" constraint that x <= erf(y).

Transform your problem such that

u = x + erf(y)
v = x - erf(y)

Clearly, v must be bounded above by 0. So use fminsearchbnd to optimize over the two dimensional domain (u,v). Inside your objective function, for any value of (u,v) you will compute the parameters (x,y) as

x = (u + v)/2;
y = erfinv(u - x);

Now you can finish evaluating the function f(x,y).

The only problem here happens if you also had other fixed bounds on x and y. But many other transformations would also have worked. For example, this transformation:

u = x
v = x - erf(y)

will still allow simple bound constraints on the parameter x, as well as allowing the nonlinear constraint x <= erf(y) as a bound constraint.

John