intfminbnd

Input Parameters

f : +: A function, representing the objective function of the problem.
: +: A vector, containing the lower bound of the variables of size (1 X n) or (n X 1) where n is number of variables. If it is empty it means that the lower bound is .
: +: A vector, containing the upper bound of the variables of size (1 X n) or (n X 1) or (0 X 0) where n is the number of variables. If it is empty it means that the upper bound is .
intcon : +: A vector of integers, representing the variables that are constrained to be integers.
options : +: A list, containing the options 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 function on bounded interval specified by : +Find the minimum of f(x) such that

intfminbnd 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" ); +

IntegerTolerance : A Scalar, a number with that value of an integer is considered integer.
MaxNodes : A Scalar, containing the maximum number of nodes that the solver should search.
CpuTime : A scalar, specifying the maximum amount of CPU Time in seconds that the solver should take.
AllowableGap : A scalar, that specifies the gap between the computed solution and the the objective value of the best known solution stop, at which the tree search can be stopped.
MaxIter : A scalar, specifying the maximum number of iterations that the solver should take.
gradobj : A string, to turn on or off the user supplied objective gradient.
hessian : A scalar, to turn on or off the user supplied objective hessian.

+ 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 the user to know the status of the optimization which is returned by Bonmin. The values it can take and what they indicate is described below: +

0 : Optimal Solution Found
1 : Maximum Number of Iterations Exceeded. Output may not be optimal.
2 : Maximum amount of CPU Time exceeded. Output may not be optimal.
3 : Stop at Tiny Step.
4 : Solved To Acceptable Level.
5 : Converged to a point of local infeasibility.

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 intfminbnd have been provided below. You will find a series of problems and the appropriate code snippets to solve them.

Example

We start with a simple objective function. Find x in R^6 such that it minimizes:

//Example 1:
+//Objective function to be minimised
+function y=f(x)
+y=0
+for i =1:6
+y=y+sin(x(i));
+end
+endfunction
+//Variable bounds
+x1 = [-2, -2, -2, -2, -2, -2];
+x2 = [2, 2, 2, 2, 2, 2];
+intcon = [2 3 4]
+[x,fval] =intfminbnd(f ,intcon, x1, x2)
+// Press ENTER to continue

Example

+ Here we solve a bounded objective function in R^6. We use this function to illustrate how we can further enhance the functionality of fminbnd 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=0
+for i =1:6
+y=y+sin(x(i));
+end
+endfunction
+//Variable bounds
+x1 = [-2, -2, -2, -2, -2, -2];
+x2 = [2, 2, 2, 2, 2, 2];
+intcon = [2 3 4]
+//Options
+options=list("MaxIter",[1500],"CpuTime", [100])
+[x,fval] =intfminbnd(f ,intcon, x1, x2, options)
+// Press ENTER to continue

Example

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

///Example 3: Unbounded problem:
+//Objective function to be minimised
+function y=f(x)
+y=-((x(1)-1)^2+(x(2)-1)^2);
+endfunction
+//Variable bounds
+x1 = [-%inf , -%inf];
+x2 = [ %inf , %inf];
+//Options
+options=list("MaxIter",[1500],"CpuTime", [100]);
+intcon = [1 2];
+[x,fval,exitflag,output,lambda] =intfminbnd(f,intcon, x1, x2, options)

Report an issue
+ << fminunc + +	+ FOSSEE Optimization Toolbox + +	+ intfmincon >> + +

intfminbnd

Calling Sequence

Input Parameters

Outputs

Description

Options

Example

Example

Example

Authors