What Is Optimization Toolbox?

Optimization Tool ExamplesOptimization Tool Examples• “Optimization Tool with the fmincon Solver” on page 5-47• “Optimization Tool with the lsqlin Solver” on page 5-51Optimization Tool with the fmincon SolverThisexampleshowshowtousetheOptimizationToolwiththefminconsolver to minimize a quadratic subject to linear and nonlinear constraintsand bounds.Consider the problem of finding [x 1, x 2]thatsolvesmin ( )x f x = x + x1 2 2 2subject to the constraints05 . ≤ x− x − x + 1≤01 21 2 2 2− x − x + 1≤0−9x− x + 9≤01 2 2 2− x − x ≤ 01 2 2− x + x ≤ 02 2 11The starting guess for this problem is x 1=3andx 2=1.Step 1: Write an M-file objfun.m for the objective function.function f = objfun(x)f = x(1)^2 + x(2)^2;Step 2: Write an M-file nonlconstr.m for the constraints.function [c,ceq] = nonlconstr(x)c = [-x(1)^2 - x(2)^2 + 15-47