What Is Optimization Toolbox?

quadprogNotesIn general quadprog locates a local solution unless the problem isstrictly convex.Better numerical results are likely if you specify equalities explicitly,using Aeq and beq, instead of implicitly, using lb and ub.If the components of x have no upper (or lower) bounds, then quadprogprefers that the corresponding components of ub (or lb) besettoInf(or -Inf for lb) as opposed to an arbitrary but very large positive (ornegative in the case of lower bounds) number.Large-Scale OptimizationBy default, quadprog uses the large-scale algorithm if you specify thefeasible region using, but not both, of the following types of constraints:• Upper and lower bounds constraints• Linear equality constraints, in which the columns of the constraintmatrix Aeq are linearly independent. Aeq is typically sparse.You cannot use inequality constraints with the large-scale algorithm.If the preceding conditions are not met, quadprog reverts to themedium-scale algorithm.If you do not supply x0, orx0 is not strictly feasible, quadprog chooses anew strictly feasible (centered) starting point.If an equality constrained problem is posed and quadprog detectsnegative curvature, the optimization terminates because the constraintsare not restrictive enough. In this case, exitflag is returned with thevalue -1, amessageisdisplayed(unlesstheoptions Display option is'off'), and the x returned is not a solution but a direction of negativecurvature with respect to H.For problems with simple lower and upper bounds (lb, ub), quadprogexits based on the value of TolFun. For problems with only equalityconstraints (Aeq, beq), the exit is based on TolPCG. AdjustTolFun andTolPCG to affect your results. TolX is used by both types of problems.8-199