How to solve (code) the following optimization problem into matlab optimization toolbox?

I'm very novice in optimization and have a convex optimization shown in the attached photo. Could someone help me in coding this optimization problem into matlab and solve it using the optimization toolbox?

Answer 1

[Alan Weiss]

Perhaps you could help yourself by looking at an introductory example of constrained optimization. Then look at the documentation on writing objective functions and constraints, if the example isn't detailed enough.

Alan Weiss

MATLAB mathematical toolbox documentation

[Hessam]

Could you tell me which solver is the best to be used for this optimization? Besides, I don't have an initial matrix (point), X0, to start from. What should I do?

[Alan Weiss]

To choose an appropriate solver, consult the Optimization Decision Table.

Initial points are tough. Perhaps you could take a random point within your bounds:

 x0 = lb + rand(size(lb)).*(ub - lb);

Good luck,

Alan Weiss

MATLAB mathematical toolbox documentation