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intfminunc

Solves an unconstrainted multi-variable mixed integer non linear programming optimization problem

Calling Sequence

xopt = intfminunc(f,x0)
xopt = intfminunc(f,x0,intcon)
xopt = intfminunc(f,x0,intcon,options)
[xopt,fopt] = intfminunc(.....)
[xopt,fopt,exitflag]= intfminunc(.....)
[xopt,fopt,exitflag,gradient,hessian]= intfminunc(.....)

Input Parameters

f :

A function, representing the objective function of the problem.

x0 :

A vector of doubles, containing the starting values of variables of size (1 X n) or (n X 1) where 'n' is the number of Variables.

intcon :

A vector of integers, representing the variables that are constrained to be integers.

options :

A list, containing the option for user to specify. See below for details.

Outputs

xopt :

A vector of doubles, containing the computed solution of the optimization problem.

fopt :

A double, containing the the function value at x.

exitflag :

An integer, containing the flag which denotes the reason for termination of algorithm. See below for details.

gradient :

A vector of doubles, containing the objective's gradient of the solution.

hessian :

A matrix of doubles, containing the Lagrangian's hessian of the solution.

Description

Search the minimum of a multi-variable mixed integer non linear programming unconstrained optimization problem specified by : Find the minimum of f(x) such that

intfminunc calls Bonmin, which is an optimization library written in C++, to solve the bound optimization problem.

Options

The options allow the user to set various parameters of the Optimization problem. The syntax for the options is given by:

options= list("IntegerTolerance", [---], "MaxNodes",[---], "MaxIter", [---], "AllowableGap",[---] "CpuTime", [---],"gradobj", "off", "hessian", "off" );

The default values for the various items are given as:

options = list('integertolerance',1d-06,'maxnodes',2147483647,'cputime',1d10,'allowablegap',0,'maxiter',2147483647,'gradobj',"off",'hessian',"off")

The exitflag allows to know the status of the optimization which is given back by Ipopt.

For more details on exitflag, see the Bonmin documentation which can be found on http://www.coin-or.org/Bonmin

A few examples displaying the various functionalities of intfminunc have been provided below. You will find a series of problems and the appropriate code snippets to solve them.

Example

We begin with the minimization of a simple non-linear function.

Find x in R^2 such that it minimizes:

//Example 1:
//Objective function to be minimised
function y=f(x)
y= x(1)^2 + x(2)^2;
endfunction
//Starting point
x0=[2,1];
intcon = [1];
[xopt,fopt]=intfminunc(f,x0,intcon)
// Press ENTER to continue

Example

We now look at the Rosenbrock function, a non-convex performance test problem for optimization routines. We use this example to illustrate how we can enhance the functionality of intfminunc by setting input options. We can pre-define the gradient of the objective function and/or the hessian of the lagrange function and thereby improve the speed of computation. This is elaborated on in example 2. We also set solver parameters using the options.

///Example 2:
//Objective function to be minimised
function y=f(x)
y= 100*(x(2) - x(1)^2)^2 + (1-x(1))^2;
endfunction
//Starting point
x0=[-1,2];
intcon = [2]
//Options
options=list("MaxIter", [1500], "CpuTime", [500]);
//Calling
[xopt,fopt,exitflag,gradient,hessian]=intfminunc(f,x0,intcon,options)
// Press ENTER to continue

Example

Unbounded Problems: Find x in R^2 such that it minimizes:

//The below problem is an unbounded problem:
//Find x in R^2 such that the below function is minimum
//f = - x1^2 - x2^2
//Objective function to be minimised
function [y, g, h]=f(x)
y = -x(1)^2 - x(2)^2;
g = [-2*x(1),-2*x(2)];
h = [-2,0;0,-2];
endfunction
//Starting point
x0=[2,1];
intcon = [1]
options = list("gradobj","ON","hessian","on");
[xopt,fopt,exitflag,gradient,hessian]=intfminunc(f,x0,intcon,options)

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