What Is Optimization Toolbox?

lsqlinNotesFor problems with no constraints, use \ (matrix left division). Forexample, x= A\b.Because the problem being solved is always convex, lsqlin will find aglobal, although not necessarily unique, solution.Better numerical results are likely if you specify equalities explicitly,using Aeq and beq, instead of implicitly, using lb and ub.Large-Scale OptimizationIf x0 is not strictly feasible, lsqlin chooses a new strictly feasible(centered) starting point.If components of x have no upper (or lower) bounds, set thecorresponding components of ub (or lb) toInf (or -Inf for lb) asopposed to an arbitrary but very large positive (or negative in the caseof lower bounds) number.AlgorithmLarge-Scale OptimizationWhen the problem given to lsqlin has only upper and lower bounds;i.e., no linear inequalities or equalities are specified, and the matrixC has at least as many rows as columns, the default algorithm is thelarge-scale method. This method is a subspace trust region methodbased on the interior-reflective Newton method described in [1]. 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 Optimizationlsqlin, withtheLargeScale option set to 'off' with optimset, orwhen linear inequalities or equalities are given, is based on quadprog,which uses an active set method similar to that described in [2]. Itfinds an initial feasible solution by first solving a linear programmingproblem. See “Quadratic Programming” on page 4-13.8-163