Matlab code to find optimal values for x and y

Question

Frey Okee 2015-4-1

编辑： Walter Roberson 2021-6-25

Can someone help me with Matlab code to find numerical solutions for optimal values of x and y which satisfy the following optimization problem?

where

and

Answer 1

Walter Roberson 2021-6-25

编辑：Walter Roberson 2021-6-25

min() cannot be differentiated, and most of the minimizers require (implicit) differentiation. So you need to take one of the following approaches:

use ga() from the Global Optimization Toolbox
use surrogate optimization
use patternsearch()
use fminmax() https://www.mathworks.com/help/optim/ug/fminimax.html
break the problem into pieces that do not individually use min(), use a normal optimizer such as fmincon() on the pieces, and then merge the pieces together