lsqnonneg

Parameters

-

C : -: a matrix of double, represents the multiplier of the solution x in the expression C⋅x - d. Number of columns in C is equal to the number of elements in x.
d : -: a vector of double, represents the additive constant term in the expression C⋅x - d. Number of elements in d is equal to the number of rows in C matrix.
xopt : -: a vector of double, the computed solution of the optimization problem.
resnorm : -: a double, objective value returned as the scalar value norm(C⋅x-d)^2.
residual : -: a vector of double, solution residuals returned as the vector d-C⋅x.
exitflag : -: The exit status. See below for details.
output : -: The structure consist of statistics about the optimization. See below for details.
lambda : -: The structure consist of the Lagrange multipliers at the solution of problem. See below for details.

Description

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Solves nonnegative least-squares curve fitting problems specified by :

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The routine calls Ipopt for solving the nonnegative least-squares curve fitting problems, Ipopt is a library written in C++.

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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", [---]);
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.
Default Values : options = list("MaxIter", [3000], "CpuTime", [600]);

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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.

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

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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.constrviolation: The max-norm of the constraint violation.

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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.

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Examples

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// A basic lsqnonneg problem
-C = [1 1 1;
-1 1 0;
-0 1 1;
-1 0 0;
-0 0 1]
-d = [89;
-67;
-53;
-35;
-20;]
-[xopt,resnorm,residual,exitflag,output,lambda] = lsqnonneg(C,d)

Authors

-

Harpreet Singh

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lsqnonneg

Calling Sequence

Parameters

Description

Examples

Authors