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Programming language: Rust

## rustimization

A rust optimization library which includes L-BFGS-B and Conjugate Gradient algorithm.

## Documentation

The simplest way to use these optimization algorithm is to use the Funcmin class.

``````extern crate rustimization;
use rustimization::minimizer::Funcmin;
fn test(){
let f = |x: &Vec<f64>| { (x+4.0).powf(2.0)};
let g = |x: &Vec<f64>| {vec![2.0*(x+4.0)]};
let mut x = vec![40.0f64];
{
//you must create a mutable object
let mut fmin = Funcmin::new(&mut x,&f,&g,"cg");
fmin.minimize();
}
println!("{:?}",x);
}
``````

Output

``````[-4.000000000000021]
``````

here Funcmin constructor takes four parameters first one is initial estimation x second and third one is the function f and the derivative g of the function respectively and forth one is the algorithm you want to use. Currently two algorithms available "cg" and "lbfgsb" if you want more parameter tuning you can use the classes of the algorithm such as for Lbbfgsb_minimizer class

### Example

``````let f = |x:&Vec<f64>|{ (x+4.0).powf(2.0)};
let g = |x:&Vec<f64>|{vec![2.0*(x+4.0)]};
let mut x = vec![40.0f64];
{
//creating lbfgsb object. here it takes three parameter
let mut fmin = Lbfgsb::new(&mut x,&f,&g);
//seting upper and lower bound first parameter is the index and second one is value
fmin.set_upper_bound(0,100.0);
fmin.set_lower_bound(0,10.0);
//set verbosity. higher value is more verbosity. the value is -1<= to <=101
fmin.set_verbosity(101);
//start the algorithm
fmin.minimize();
}
println!("{:?}",x);
``````

Output

``````RUNNING THE L-BFGS-B CODE

* * *

Machine precision = 2.220D-16
N =            1     M =            5

L =  1.0000D+01

X0 =  4.0000D+01

U =  1.0000D+02

At X0         0 variables are exactly at the bounds

At iterate    0    f=  1.93600D+03    |proj g|=  3.00000D+01

ITERATION     1

---------------- CAUCHY entered-------------------
There are            1   breakpoints

Piece      1 --f1, f2 at start point  -7.7440D+03  7.7440D+03
Distance to the next break point =   3.4091D-01
Distance to the stationary point =   1.0000D+00
Variable             1   is fixed.
Cauchy X =
1.0000D+01

---------------- exit CAUCHY----------------------

0  variables are free at GCP            1
LINE SEARCH           0  times; norm of step =    30.000000000000000

At iterate    1    f=  1.96000D+02    |proj g|=  0.00000D+00

X =  1.0000D+01

G =  2.8000D+01

* * *

Tit   = total number of iterations
Tnf   = total number of function evaluations
Tnint = total number of segments explored during Cauchy searches
Skip  = number of BFGS updates skipped
Nact  = number of active bounds at final generalized Cauchy point
Projg = norm of the final projected gradient
F     = final function value

* * *

N    Tit     Tnf  Tnint  Skip  Nact     Projg        F
1      1      2      1     0     1   0.000D+00   1.960D+02

X =  1.0000D+01
F =   196.00000000000000

Cauchy                time 1.570E-04 seconds.
Subspace minimization time 0.000E+00 seconds.
Line search           time 1.800E-05 seconds.

Total User time 9.330E-04 seconds.

convergence!
``````

## Requirements

To use this library you must have gfortran installed in your pc

• for windows use fortran compiler provided by mingw or TDM-GCC
• for linux you can use the package manager to install gfortran
• for Mac os you can install it form here or here

The orginal L-BFGS-B fortran subroutine is distributed under BSD-3 license. To know more about the condition to use this fortran routine please go here.

To know more about the condition to use the Conjugate Gradient Fortran routine please go here

## References

1. R. H. Byrd, P. Lu and J. Nocedal. A Limited Memory Algorithm for Bound Constrained Optimization, (1995), SIAM Journal on Scientific and Statistical Computing , 16, 5, pp. 1190-1208.
2. C. Zhu, R. H. Byrd and J. Nocedal. L-BFGS-B: Algorithm 778: L-BFGS-B, FORTRAN routines for large scale bound constrained optimization (1997), ACM Transactions on Mathematical Software, Vol 23, Num. 4, pp. 550 - 560.
3. J.L. Morales and J. Nocedal. L-BFGS-B: Remark on Algorithm 778: L-BFGS-B, FORTRAN routines for large scale bound constrained optimization (2011), to appear in ACM Transactions on Mathematical Software.
4. J. C. Gilbert and J. Nocedal. Global Convergence Properties of Conjugate Gradient Methods for Optimization, (1992) SIAM J. on Optimization, 2, 1.

*Note that all licence references and agreements mentioned in the rustimization README section above are relevant to that project's source code only.