BLMVM

The NEOS Server offers BLMVM for the solution of nonlinear optimization problems with simple bounds on the variables.

This solver is a limited memory, variable metric method. It assumes that the variable bounds are fixed and the gradient of the objective function can be computed. This solver creates a quadratic model function in the full space of variables using projected gradients. This gradient information is stored in such a way that the storage required is linear in number of variables. Since the algorithm does not require second derivatives, the method can be applied when the Hessian is not available or not practical to compute.

If it is desired, BLMVM can solve the minimization problem without requiring the user to provide any gradient evaluations. This is accomplished through the automatic differentiation tools ADIC and ADIFOR.

To use BLMVM with AMPL files, try the BLMVM (AMPL input) page.

BLMVM was developed by Steve Benson and Jorge Moré. The algorithm can be found in the Toolkit for Advanced Optimization.

Using the NEOS Server for BLMVM

To solve a bound constrained minimization problem, the user must submit to the server:

The number of variables
A subroutine that defines the starting point (optional)
A subroutine that defines the bounds on the variables
A subroutine that evaluates the objective function and gradient or a subroutine that evaluates only the objective function (using automatic differentiation).

How many variables are in your problem
Number of dimensions:

Are you providing a subroutine that calculates both function and gradient evaluations or a subroutine that only provides function evaluations. The second choice will invoke Automatic Differentiation using ADIC.
Derivative Method:

If your function is in partially separable form, then enter the number of function elements
Number of function elements:

In what file is the function to evaluate function and gradient? If you are using the function/gradient option, then your function must be called 'fcn' and have this prototype:

C:
void fcn(int *ndim, double x[], double *f, double g[])

int *ndim -- # of dimensions in the problem
double x[] -- vector to evaluate the function at

double *f -- address of a double to store function value
double g[] -- array to store gradient

If you are using the function/automatic differentiation option, then your function must be called 'fcn' and have this prototype.

void fcn(int *ndim, double x[], double *f)

Evaluate function/gradient(local file):

In what file is the function to set the variable bounds? The default values are +,- infinity, insert only the boundary values that are not at infinity. If you do not want any variable bounds, then you can leave this entry blank. Otherwise, the function must be called 'xbound' and have this prototype:

void xbound(int *ndim, double l[], double u[])

int *ndim -- # of dimensions in the problem

double l[] -- array of lower bounds
double u[] -- array of upper bounds

Set variable bounds (local file):

In what file is the function to set the initial vector? The function must be called 'initpt' and have this prototype:

void initpt(int *ndim, double x[])

int *ndim -- # of dimensions in the problem
double x[] -- the initial vector

Initial Value Function:

Enter optional command-line arguments. Below are selected options. See TAO User Manual for details and a complete listing.

-tao_fatol (0.0001): Stop if solution is within
-tao_frtol (0.0001): Stop if relative solution is within
-tao_gatol (0.0): Stop if norm of gradient is less than
-tao_grtol (0.0): Stop if norm of gradient divided by function value is less than
-tao_gttol (0.0): Stop if the norm of the gradient is less than the norm of the initial gradient times this value
-tao_max_it (10000): Maximum number of iterations
-tao_max_funcs (10000): Maximum number of function evaluations
-tao_fmin (-1e30): Stop if function less than
-tao_lmvm_lm (5): Number of vectors to retain for hessian approximation
-tao_monitor : Display information at every iteration

Enter any (optional) TAO options:

Comments:

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e-mail address:

Please do not click the 'Submit to NEOS' button more than once.

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