How do I use fsolve

Consider the following unconstrained optimization problem: minimize f(x1,x2,…xn)=x1^3+x1^2+2x2^2+3x3^2+x1x2+x2x3-8x1-16x2-32x3+110

Solve it using Matlab’s built-in function: fsolve.

Answer 1

[Walter Roberson]

You cannot directly use fsolve() for that.

However, you can manually find the partial derivatives by doing minor calculus yourself, and then use fsolve() to find where the partial derivatives are all 0.

Partial derivatives of all 0 will be either a minima or a maxima or a saddle point. It happens that that equation has a minima and a maxima, so you will need to be careful.

[Barry Ellis]

Thank you Walter. I am new to MATLAB and I guess I didn't ask the question right. I was asked to solve this using MATLAB functions fsolve and fminunc. I was told to first solve it using the analytical method and verify that the found solution is a minimum rather than a maximum, or inflection point. Then I'm supposed to solve it using fsolve, and then solve it using fminunc.

I'm completely lost on this.

[Barry Ellis]

I found that x(1) can either be 1.0604 or -1.6401. I can do this by hand, but MATLAB has me stumped.