What Is Optimization Toolbox?

quadprogAlgorithmLarge-Scale OptimizationThe large-scale algorithm is a subspace trust-region method based onthe interior-reflective Newton method described in [1]. Each iterationinvolves the approximate solution of a large linear system using themethod of preconditioned conjugate gradients (PCG). See “Trust-RegionMethods for Nonlinear Minimization” on page 4-3 and “PreconditionedConjugate Gradients” on page 4-7.Medium-Scale Optimizationquadprog uses an active set method, which is also a projection method,similar to that described in [2]. It finds an initial feasible solution byfirst solving a linear programming problem. This method is discussedin 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), thenquadprog gives this error:Equal upper and lower bounds not permittedin this large-scale method.Use equality constraints and the medium-scalemethod instead.If you only have equality constraints you can still use the large-scalemethod. But if you have both equalities and bounds, you must use themedium-scale method.Medium-Scale OptimizationWhen the problem is infeasible, quadprog gives this warning:Warning: The constraints are overly stringent;there is no feasible solution.In this case, quadprog produces a result that minimizes the worst caseconstraint violation.8-200