Optimization with symbolic math

I want to find the values of c0, c1, c2 maximizing

 f = sym('-((c1-a)*ln(c1-a)-(c1-a))/3+(c1*lnc1-c1)/3-((c2-b)*ln(c2-b)-(c2-b))/6+(c2*lnc2-c2)/6+(1+h10+h20)*lnc0

subject to the following constraints

 g = sym('c0(1+h10+h20)+h11c1+h22c2=3*h11+6*h22')
 h10 = 1 - (c1-c0)/3
 h11 = (c1-c0)/3 
 h20 = 1 - (c2-c0)/6
 h22 = (c2 - c0)/6

All values of C is between 1 and 6.

How do I do this in MatLab?

Answer 1

[Sean de Wolski]

Do you need to solve this symbolically or would using one of the numerical solvers like fmincon or patternsearch work for you?

doc fmincon
doc patternsearch

[Marianne]

I want to solve it numerically, but knowing nothing about matlab I have no idea how to do it. Tried to search in tutorials, but didn't really know what to look for. Will look up fmincon and patternsearch, thank you=)