What Is Optimization Toolbox?

2 Tutorial3.7081Sharing Variables Using Nested FunctionsThe preceding example uses an existing function ellipj that has morearguments than would be passed by fsolve. If you are writing your ownfunction, you can use the technique above, or you might find it moreconvenient to use a nested function. Nested functions have the additionaladvantage that you can share variables between them. For example, supposeyou want to minimize an objective function, subject to an additional nonlinearconstraint that the objective function should never exceed a certain value.To avoid having to recompute the objective function value in the constraintfunction, you can use a nested function.You can see an example of sharing variables via nested functions in “SimulinkExample Using fminimax” on page 2-33.Nonlinear Equations with Analytic JacobianThis example demonstrates the use of the default medium-scale fsolvealgorithm. It is intended for problems where• The system of nonlinear equations is square, i.e., the number of equationsequals the number of unknowns.• There exists a solution such that .The example uses fsolve to obtain the minimum of the banana (orRosenbrock) function by deriving and then solving an equivalent system ofnonlinear equations. The Rosenbrock function, which has a minimum at, is a common test problem in optimization. It has a high degree ofnonlinearity and converges extremely slowly if you try to use steepest descenttype methods. It is given byFirst generalize this function to an n-dimensional function, for any positive,even value of n:2-22