lsqnonlin Solves a non linear data fitting problems. xopt = lsqnonlin(fun,x0) xopt = lsqnonlin(fun,x0,lb,ub) xopt = lsqnonlin(fun,x0,lb,ub,options) [xopt,resnorm] = lsqnonlin( ... ) [xopt,resnorm,residual] = lsqnonlin( ... ) [xopt,resnorm,residual,exitflag] = lsqnonlin( ... ) [xopt,resnorm,residual,exitflag,output,lambda,gradient] = lsqnonlin( ... ) fun : a function, representing the objective function and gradient (if given) of the problem x0 : a vector of double, contains initial guess of variables. lb : a vector of double, contains lower bounds of the variables. ub : a vector of double, contains upper bounds of the variables. options : a list containing the parameters to be set. xopt : a vector of double, the computed solution of the optimization problem. resnorm : a double, objective value returned as the scalar value i.e. sum(fun(x).^2). residual : a vector of double, solution of objective function i.e. fun(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. gradient : a vector of doubles, containing the Objective's gradient of the solution. Search the minimum of a constrained non-linear least square problem specified by : \begin{eqnarray} &\mbox{min}_{x} & (f_1(x)^2 + f_2(x)^2 + ... + f_n(x)^2) \\ & lb \leq x \leq ub \\ \end{eqnarray} The routine calls fmincon which calls Ipopt for solving the non-linear least square 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", [---],"GradObj", "on"); 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. GradObj : a string, representing the gradient function is on or off. Default Values : options = list("MaxIter", [3000], "CpuTime", [600], "GradObj", "off"); 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.constrviolation: The max-norm of the constraint violation. 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. Harpreet Singh