What Is Optimization Toolbox?

3 Standard AlgorithmsLine Search and Merit FunctionThe solution to the QP subproblem produces a vectorform a new iterate, which is used to(3-40)The step length parameter is determined in order to produce a sufficientdecrease in a merit function. The merit function used by Han [24] andPowell [35] of the following form is used in this implementation.Powell recommends setting the penalty parameter(3-41)This allows positive contribution from constraints that are inactive in theQP solution but were recently active. In this implementation, the penaltyparameter is initially set to(3-42)(3-43)whererepresents the Euclidean norm.This ensures larger contributions to the penalty parameter from constraintswith smaller gradients, which would be the case for active constraints atthe solution point.3-38