This example shows how to use two nonlinear optimization solvers and how to set options. The nonlinear solvers that we use in this example are fminunc and fmincon. All the principles outlined in this example apply to the other nonlinear solvers, such as fgoalattain, fminimax, lsqnonlin, lsqcurvefit, and fsolve. Sis To Sisx & Jar Converter Full there. The example starts with minimizing an objective function, then proceeds to minimize the same function with additional parameters. After that, the example shows how to minimize the objective function when there is a constraint, and finally shows how to get a more efficient and/or accurate solution by providing gradients or Hessian, or by changing some options.

Function [x,fval] = nestedbowlpeak(a,b,c,x0,options)%NESTEDBOWLPEAK Nested function for parameter passing in TUTDEMO.% Copyright 2008 The MathWorks, Inc. [x,fval] = fminunc(@nestedfun,x0,options); function y = nestedfun(x) y = (x(1)-a).*exp(-((x(1)-a).^2+(x(2)-b).^2))+((x(1)-a).^2+(x(2)-b).^2)/c; end end In this method, the parameters (a,b,c) are visible to the nested objective function called nestedfun. The outer function, nestedbowlpeak, calls fminunc and passes the objective function, nestedfun.

Define the parameters, initial guess, and options. Fgradevals = 14 Constrained Optimization Example with User-Supplied Hessian If you give not only a gradient, but also a Hessian, solvers are even more accurate and efficient. Fmincon's interior-point solver takes a Hessian matrix as a separate function (not part of the objective function).

Optimization Toolbox™ 4 User’s Guide. How to Contact The MathWorks www.mathworks.com Web comp.soft-sys.matlab Newsgroup. Exporting to the MATLAB Workspace. Learn about the Optimization Toolbox key features, which can help you solve linear, quadratic, integer, and nonlinear optimization problems.

The Hessian function H(x,lambda) should evaluate the Hessian of the Lagrangian; see the User's Guide for the definition of this term. Solvers calculate the values lambda.ineqnonlin and lambda.eqlin; your Hessian function tells solvers how to use these values. In this problem we have but one inequality constraint, so the Hessian is. First-order Norm of Iter F-count f(x) Feasibility optimality step 0 1 2.365241e-01 0.000e+00 1.972e-01 1 3 5.821325e-02 0.000e+00 1.443e-01 8.728e-01 2 5 -1.218829e-01 0.000e+00 1.007e-01 4.927e-01 3 6 -1.421167e-01 0.000e+00 8.486e-02 5.165e-02 4 7 -2.261916e-01 0.000e+00 1.989e-02 1.667e-01 5 8 -2.433609e-01 0.000e+00 1.537e-03 3.486e-02 6 9 -2.446875e-01 0.000e+00 2.057e-04 2.727e-03 7 10 -2.448911e-01 0.000e+00 2.068e-06 4.191e-04 8 11 -2.448931e-01 0.000e+00 2.001e-08 4.218e-06 Local minimum found that satisfies the constraints. Optimization completed because the objective function is non-decreasing in feasible directions, to within the default value of the optimality tolerance, and constraints are satisfied to within the default value of the constraint tolerance.

There were fewer, and different iterations this time. The solution to this problem has been found.