Matlab code to find optimal values for x and y

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 and

Answer 1

[Walter Roberson]

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