What Is Optimization Toolbox?

Linearly Constrained ProblemsThe scaled modified Newton step for the nonlinear system of equationsgiven by Equation 4-8 is defined as the solution to the linear system(4-9)at the kth iteration, whereand(4-10)(4-11)Here plays the role of the Jacobian of Each diagonal component of thediagonal matrix equals 0, -1, or 1. If all the components of l and u are finite,At a point where , might not be differentiable.is defined at such a point. Nondifferentiability of this type is not acause for concern because, for such a component, it is not significant whichvalue takes. Further, will still be discontinuous at this point, but thefunction is continuous.Second, reflections are used to increase the stepsize. A (single) reflectionstep is defined as follows. Given a step that intersects a bound constraint,consider the first bound constraint crossed by p; assume it is the ith boundconstraint (either the ith upper or ith lower bound). Then the reflection stepexcept in the ith component, where .4-11