What Is Optimization Toolbox?

4 Large-Scale AlgorithmsBox ConstraintsThe box constrained problem is of the form(4-7)where l is a vector of lower bounds, and u is a vector of upper bounds. Some(orall)ofthecomponents of can be equal to and some (or all) of thecomponents of can beequalto The method generates a sequence ofstrictly feasible points. Two techniques are used to maintain feasibility whileachieving robust convergence behavior. First, a scaled modified Newtonstep replaces the unconstrained Newton step (to define the two-dimensionalsubspace ). Second, reflections are used to increase the stepsize.The scaled modified Newton step arises from examining the Kuhn-Tuckernecessary conditions for Equation 4-7,where(4-8)and the vector is defined below, for each :• If and then• If and then• If and then• If and thenThe nonlinear system Equation 4-8 is not differentiable everywhere.Nondifferentiability occurs when Youcanavoidsuchpointsbymaintaining strict feasibility, i.e., restricting .4-10