quadprog for constrained maximisation

I am trying to rewrite the following maximisation problem in quadprog format.

max{w} (w'.M - r) / (w S w)^-0.5 subject to w'. 1 = 1 and all w >=1

How can such problem be reformulated to suite Matlab optimisation solvers like quadprog (https://uk.mathworks.com/help/optim/ug/quadprog.html)?

Answer 1

[Alan Weiss]

I don't know how that problem can be formulated for quadprog. However, it is simple to formulate it for fmincon. For help, check the documentation:

• Write scalar objective function
• Maximize instead of minimize
• Linear constraints
• Lower bound constraints

Alan Weiss

MATLAB mathematical toolbox documentation