Solving Constrained Convex Optimization Problems Using Gradient Descent

The paper only says that the optimal value can be obtained by the gradient descent method. I downloaded some code about gradient descent on MATLAB, and the objective functions are relatively simple, such as f = x^2 + y^2 + 5, and the optimization problems are all unconstrained. How can I solve the following problem using gradient descent? Is there an example to refer to?

[Torsten]

Try fmincon.

[Li Qing]

Thanks!

Answer 1

[Alan Weiss]

That problem does not look unconstrained to me: you have two sets of constraints listed.

But the main point is twofold: there is no built-in code for gradient descent in Optimization Toolbox™, but there are several solvers (such as fmincon, which Torsten mentioned) that can address constrained nonlinear optimization problems.

You might find the Problem-Based Optimization Workflow to be the most natural way to formulate and solve your problem.

Good luck,

Alan Weiss

MATLAB mathematical toolbox documentation