Optimization with multiple unknowns, multi-constraints, and 2 objectives

I want to run an efficient frontier with available details in different scenarios. However, my measure of y axis (used to be return) and x axis (used to be standard deviation of return) are changed into some nonlinear thing. And the weight on different investments sum to 1 and never to below 0.

So I have multiple unknowns(different weight for different investments), multiple constraints (weight constraints) and 2 optimal objectives (self defined).

Is there any tool in Matlab can help with that?

Answer 1

[Alan Weiss]

Take a look at gamultiobj from Global Optimization Toolbox, and this example from Optimization Toolbox.

Alan Weiss

MATLAB mathematical toolbox documentation