[MINIMUM,FVAL,EXITFLAG,OUTPUT] = fminbfgs(FUN,PARS,[OPTIONS],[CONSTRAINTS], ....) BFGS search This minimization method uses the steepest descent/ Broyden-Fletcher-Goldfarb-Shanno method with polynomial line search. Calling: fminbfgs(fun, pars) asks to minimize the 'fun' objective function with starting parameters 'pars' (vector) fminbfgs(fun, pars, options) same as above, with customized options (optimset) fminbfgs(fun, pars, options, fixed) is used to fix some of the parameters. The 'fixed' vector is then 0 for free parameters, and 1 otherwise. fminbfgs(fun, pars, options, lb, ub) is used to set the minimal and maximal parameter bounds, as vectors. fminbfgs(fun, pars, options, constraints) where constraints is a structure (see below). fminbfgs(problem) where problem is a structure with fields problem.objective: function to minimize problem.x0: starting parameter values problem.options: optimizer options (see below) problem.constraints: optimization constraints fminbfgs(..., args, ...) sends additional arguments to the objective function criteria = FUN(pars, args, ...) Example: banana = @(x)100*(x(2)-x(1)^2)^2+(1-x(1))^2; [x,fval] = fminbfgs(banana,[-1.2, 1]) Input: FUN is the function to minimize (handle or string): criteria = FUN(PARS) It needs to return a single value or vector. PARS is a vector with initial guess parameters. You must input an initial guess. PARS can also be given as a single-level structure. OPTIONS is a structure with settings for the optimizer, compliant with optimset. Default options may be obtained with o=fminbfgs('defaults') options.MinFunEvals sets the minimum number of function evaluations to reach An empty OPTIONS sets the default configuration. CONSTRAINTS may be specified as a structure constraints.min= vector of minimal values for parameters constraints.max= vector of maximal values for parameters constraints.fixed= vector having 0 where parameters are free, 1 otherwise constraints.step= vector of maximal parameter changes per iteration constraints.eval= expression making use of 'p', 'constraints', and 'options' and returning modified 'p' or function handle email@example.com(p) An empty CONSTRAINTS sets no constraints. Additional arguments are sent to the objective function. Output: MINIMUM is the solution which generated the smallest encountered value when input into FUN. FVAL is the value of the FUN function evaluated at MINIMUM. EXITFLAG return state of the optimizer OUTPUT additional information returned as a structure. Reference: Broyden, C. G., J. of the Inst of Math and Its Appl 1970, 6, 76-90 Fletcher, R., Computer Journal 1970, 13, 317-322 Goldfarb, D., Mathematics of Computation 1970, 24, 23-26 Shanno, D. F.,Mathematics of Computation 1970, 24, 647-656 Contrib: C. T. Kelley, 1998, Iterative Methods for Optimization [bfgswopt] Version: Aug. 22, 2017 See also: fminsearch, optimset (c) E.Farhi, ILL. License: EUPL.