What Is Optimization Toolbox?

lsqcurvefitNote that at the time that lsqcurvefit is called, xdata and ydataare assumed to exist and are vectors of the same size. They must bethesamesizebecausethevalueF returned by fun must be the samesize as ydata.After 27 function evaluations, this example gives the solutionx =498.8309 -0.1013resnorm =9.5049There may be slight variation in the number of iterations and the valueof the returned x that is dependent upon the platform and release.AlgorithmLarge-Scale OptimizationBy default lsqcurvefit chooses the large-scale algorithm. Thisalgorithm is a subspace trust region method and is based on theinterior-reflective Newton method described in [1] and[2]. Eachiteration involves the approximate solution of a large linear systemusing the method of preconditioned conjugate gradients (PCG). See“Trust-Region Methods for Nonlinear Minimization” on page 4-3 and“Preconditioned Conjugate Gradients” on page 4-7.Medium-Scale Optimizationlsqcurvefit, withtheLargeScale option set to 'off' withoptimset, uses the Levenberg-Marquardt method with line-search[4], [5], and [6]. Alternatively, a Gauss-Newton method [3] withline-search may be selected. You can choose the algorithm bysetting the LevenbergMarquardt option with optimset. SettingLevenbergMarquardt to 'off' (and LargeScale to 'off') selects theGauss-Newton method, which is generally faster when the residualis small.The default line search algorithm, i.e., LineSearchType option set to'quadcubic', is a safeguarded mixed quadratic and cubic polynomialinterpolation and extrapolation method. You can select a safeguarded8-151