How to find optimal values to a function using KKT Conditions (Karush Kuhn Tucker Conditions)?

It's really simple verify the KKT (Karush-Kuhn-Tucker) conditions, but I'm stuck in doing this by a MatLab code.

Has anyone got a MatLab program/code or any suggestion for finding the optimal value of a function with constrains using KKT conditions?

The implementation need to be done 'manually', without use fmincon, solve or other MatLab function that give only the optimal results.

I need to solve: max f(x,y)=a1*x^5 + a2*y^4 + a3*x^3 + a4*y^2 + x*y + a5; s.t. 5*x + 3*y <= b1; 3*x + 5*y <= b2;

Has anyone got a MatLab program/code or any suggestion for finding the optimal value of a function with constrains using KKT conditions?

[Vinh Nguyen]

Not entirely sure what you want. But to solve "manually", you can implement KKT conditions. You will get a system of equations (there should be 4 equations with 4 variables). Then I think you can solve the system of equations "manually" or use some simple code to help you with that.

[king]

hello jose Souza, i was wondering if you've gotten a solution to this. i am working on something similar and i am having the same problem.

[Prashasti Srivastava]

Hi Jose Souza, please share if you have got solution to this. It'll be very kind. Thanks

[Qingyang Xiao]

Hi Jose, you can first apply KKT conditions for this problem (of course you need first prove it's a convex optimization problem), then, hard code by multiple equations for all four KKT conditions (i.e. stationary, primal & dual feasibility and complementary slackness ) in matlab. It should work.