What Is Optimization Toolbox?

lsqcurvefitcubic polynomial method by setting LineSearchType to 'cubicpoly'.This method generally requires fewer function evaluations but moregradient evaluations. Thus, if gradients are being supplied and canbe calculated inexpensively, the cubic polynomial line search methodis preferable. The algorithms used are described fully in Chapter 3,“Standard Algorithms”.DiagnosticsLarge-Scale OptimizationThe large-scale method does not allow equal upper and lower bounds.For example, if lb(2)==ub(2), lsqlin gives the errorEqual upper and lower bounds not permitted.(lsqcurvefit does not handle equality constraints, which is anotherway to 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. lsqcurvefit mightonly give local solutions.lsqcurvefit only handles real variables (the user-defined functionmust only return real values). When x has complex variables, thevariables must be split into real and imaginary parts.Large-Scale OptimizationThe large-scale algorithm for lsqcurvefit does not solveunderdetermined systems; it requires that the number of equations, i.e.,the row dimension of F, be at least as great as the number of variables.In the underdetermined case, the medium-scale algorithm is usedinstead. See Large-Scale Problem Coverage and Requirements on page2-42 for more information on what problem formulations are coveredand what information must be provided.The preconditioner computation used in the preconditioned conjugategradient part of the large-scale method forms JTJ (where J is theJacobian matrix) before computing the preconditioner; therefore, a row8-152