fminunc Solves a multi-variable unconstrainted optimization problem xopt = fminunc(f,x0) xopt = fminunc(f,x0,options) [xopt,fopt] = fminunc(.....) [xopt,fopt,exitflag]= fminunc(.....) [xopt,fopt,exitflag,output]= fminunc(.....) [xopt,fopt,exitflag,output,gradient]=fminunc(.....) [xopt,fopt,exitflag,output,gradient,hessian]=fminunc(.....) f : a function, representing the objective function of the problem x0 : a vector of doubles, containing the starting of variables. options: a list, containing the option for user to specify. See below for details. xopt : a vector of doubles, the computed solution of the optimization problem. fopt : a scalar of double, 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. gradient : a vector of doubles, containing the the gradient of the solution. hessian : a matrix of doubles, containing the the hessian of the solution. Search the minimum of an unconstrained optimization problem specified by : Find the minimum of f(x) such that \begin{eqnarray} &\mbox{min}_{x} & f(x)\\ \end{eqnarray} The routine calls Ipopt for solving the Un-constrained 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", [---], "Gradient", ---, "Hessian", ---); 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. Gradient : a function, representing the gradient function of the Objective in Vector Form. Hessian : a function, representing the hessian function of the Objective in Symmetric Matrix Form. Default Values : options = list("MaxIter", [3000], "CpuTime", [600]); 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 output.Message: The output message for the problem R.Vidyadhar , Vignesh Kannan