fminbnd

Parameters

f : +: a function, representing the objective function of the problem
x1 : +: a vector, containing the lower bound of the variables of size (1 X n) or (n X 1) where 'n' is the number of Variables, where n is number of Variables
x2 : +: 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 x2 is empty it means upper bound is +infinity
options : +: a list, containing the option for user to specify. See below for details.
xopt : +: a vector of doubles, containing the the computed solution of the optimization problem.
fopt : +: a scalar of double, containing the the function value at x.
exitflag : +: a scalar of integer, containing the flag which denotes the reason for termination of algorithm. See below for details.
output : +: a structure, containing the information about the optimization. See below for details.
lambda : +: a structure, containing the Lagrange multipliers of lower bound and upper bound at the optimized point. See below for details.

Description

Search the minimum of a multi-variable function on bounded interval specified by : +Find the minimum of f(x) such that

The routine calls Ipopt for solving the Bounded Optimization problem, Ipopt is a library written in C++.

The options allows the user to set various parameters of the Optimization problem. +It should be defined as type "list" and contains the following fields. +

Syntax : options= list("MaxIter", [---], "CpuTime", [---], TolX, [----]);
MaxIter : a Scalar, containing the Maximum Number of Iteration that the solver should take.
CpuTime : a Scalar, containing the Maximum amount of CPU Time that the solver should take.
TolX : a Scalar, containing the Tolerance value that the solver should take.
Default Values : options = list("MaxIter", [3000], "CpuTime", [600], TolX, [1e-4]);

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

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

For more details on exitflag see the ipopt documentation, go to http://www.coin-or.org/Ipopt/documentation/

The output data structure contains detailed informations about the optimization process. +It has type "struct" and contains the following fields. +

output.Iterations: The number of iterations performed during the search
output.Cpu_Time: The total cpu-time spend during the search
output.Objective_Evaluation: The number of Objective Evaluations performed during the search
output.Dual_Infeasibility: The Dual Infeasiblity of the final soution

The lambda data structure contains the Lagrange multipliers at the end +of optimization. In the current version the values are returned only when the the solution is optimal. +It has type "struct" and contains the following fields. +

lambda.lower: The Lagrange multipliers for the lower bound constraints.
lambda.upper: The Lagrange multipliers for the upper bound constraints.

Examples

//Find x in R^6 such that it minimizes:
+//f(x)= sin(x1) + sin(x2) + sin(x3) + sin(x4) + sin(x5) + sin(x6)
+//-2 <= x1,x2,x3,x4,x5,x6 <= 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];
+//Options
+options=list("MaxIter",[1500],"CpuTime", [100],"TolX",[1e-6])
+//Calling Ipopt
+[x,fval] =fminbnd(f, x1, x2, options)

Examples

//Find x in R such that it minimizes:
+//f(x)= 1/x^2
+//0 <= x <= 1000
+//Objective function to be minimised
+function y=f(x)
+y=1/x^2
+endfunction
+//Variable bounds
+x1 = [0];
+x2 = [1000];
+//Calling Ipopt
+[x,fval,exitflag,output,lambda] =fminbnd(f, x1, x2)

Examples

//The below problem is an unbounded problem:
+//Find x in R^2 such that it minimizes:
+//f(x)= -[(x1-1)^2 + (x2-1)^2]
+//-inf <= x1,x2 <= inf
+//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 = [];
+//Options
+options=list("MaxIter",[1500],"CpuTime", [100],"TolX",[1e-6])
+//Calling Ipopt
+[x,fval,exitflag,output,lambda] =fminbnd(f, x1, x2, options)

Authors

R.Vidyadhar , Vignesh Kannan

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fminbnd

Calling Sequence

Parameters

Description

Examples

Examples

Examples

Authors