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(Unspecified stopping criteria are disabled i.e., they have innocuous defaults.) The various stopping criteria can be specified via the following fields of your structure. (If they are not specified, the tolerances default to zero.) Stopping criteriaĪs explained in the C API Reference and the Introduction), you have multiple options for different stopping criteria that you can specify. Tolerances are specified as fields opt.fc_tol and opt.h_tol, which (if they are set) should be vectors (not cell arrays) of tolerances, of the same lengths as opt.fc and opt.h, respectively. Optionally, you can specify a tolerance in judging feasibility for the purposes of stopping the optimization, as in C. Recall that a cell array is specified via. Just as for nonlinear constraints in C, you can specify nonlinear inequality and equality constraints by setting opt.fc and opt.h to be cell arrays of function handles (of the same form as the objective function above) for the inequality and equality constraints, respectively. To specify an unbounded dimension, you can use ± inf in Matlab to specify ±∞. The bound constraints can be specified by setting opt.lower_bounds and/or opt.upper_bounds to vectors of length n (the same as the length of the initial guess passed to nlopt_optimize). If your objective function returns NaN ( nan in Matlab), that will force the optimization to terminate, equivalent to calling nlopt_force_stop in C. Not all of the optimization algorithms (below) use the gradient information: for algorithms listed as "derivative-free," the nargout will always be 1 and the gradient need never be computed. That is, grad(i) should upon return contain the partial derivative, for. In addition, if the caller requests two return values ( nargout > 1), then the second return value gradient should be a vector (row or column) of length n that is the gradient of the function with respect to the optimization parameters at x. (Whether x is a row or column vector depends on whether the initial guess you pass to nlopt_optimize is a row or column vector, respectively.) The first return value should be the value of the function at the point x, where x row or column vector of the n of the n optimization parameters (the same length as the initial guess passed to nlopt_optimize). The function f should be of the form: function = myfunc(x) The objective function is specified setting either the opt.min_objective or opt.max_objective field to a function handle for the objective function f, depending on whether one wishes to minimize or maximize f, respectively. you set opt.lower_bounds to be a different length). An error will occur if you use vectors of inconsistent lengths (e.g. The dimension n of the problem (the number of optimization parameters) is determined implicitly by the length of the vector you pass to nlopt_optimize as the initial guess. You need not set all the fields of the structure any fields that are not specified take on innocuous default values (the same as if you did not specify those parameters in the C interface). Just as in C, algorithms are specified by predefined constants of the form NLOPT_MMA, NLOPT_COBYLA, etcetera. Given an algorithm (see NLopt Algorithms for possible values) and the dimensionality of the problem ( n, the number of optimization parameters). Every opt structure should specify the algorithm, via:
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All of the parameters of the optimization are specified (dimensions, algorithm, stopping criteria, constraints, objective function, etcetera) simply by assigning fields to this structure, and then one finally calls the nlopt_optimize(opt) function in order to perform the optimization. The NLopt API revolves around an Matlab structure, analogous to the nlopt_opt object in C and similar objects in NLopt's interfaces for other languages. m files (mostly implementing constants and documentation) from the src/octave directory of the NLopt release and put it into the same directory as the MEX file. Using this or your own compiled version, you can then download nlopt-optimize-mex.c file, rename it to nlopt-optimize.c, and compile it into a MEX file callable from Matlab - the result must be put into your Matlab path or your working directory. On Windows, we provide a precompiled the NLopt library, which includes a matlab directory. On Unix, the Matlab and Octave interfaces should automatically be installed in places where they will be found at runtime, assuming you have Matlab and Octave correctly installed on your machine, as documented in the Installation manual. The main purpose of this section is to document the syntax and unique features of the Matlab API for more detail on the underlying features, please refer to the C documentation in the NLopt Reference. The NLopt includes interfaces callable from the Matlab and GNU Octave (a free-software Matlab-like program), using identical syntax.