What Is Optimization Toolbox?

lsqnonlinGauss-Newton method, which is generally faster when the residualis small.The default line search algorithm, i.e., the LineSearchType optionset to 'quadcubic', is a safeguarded mixed quadratic and cubicpolynomial interpolation and extrapolation method. You can select asafeguarded cubic polynomial method by setting the LineSearchTypeoption to 'cubicpoly'. This method generally requires fewer functionevaluations but more gradient evaluations. Thus, if gradients are beingsupplied and can be calculated inexpensively, the cubic polynomial linesearch method is preferable. The algorithms used are described fully inChapter 3, “Standard Algorithms”.DiagnosticsLarge-Scale OptimizationThe large-scale method does not allow equal upper and lower bounds.For example, iflb(2)==ub(2), lsqlin gives the errorEqual upper and lower bounds not permitted.(lsqnonlin does not handle equality constraints, which is another wayto formulate equal bounds. If equality constraints are present, usefmincon, fminimax, orfgoalattain for alternative formulations whereequality constraints can be included.)LimitationsThe function to be minimized must be continuous. lsqnonlin mightonly give local solutions.lsqnonlin only handles real variables. When x has complex variables,the variables must be split into real and imaginary parts.Large-Scale OptimizationThe large-scale method for lsqnonlin does not solve underdeterminedsystems; it requires that the number of equations (i.e., the number ofelements of F) be at least as great as the number of variables. In theunderdetermined case, the medium-scale algorithm is used instead.(If bound constraints exist, a warning is issued and the problem issolved with the bounds ignored.) See Large-Scale Problem Coverage8-176