non-linear optimization with complex constrains

hi，my friends

i have a problem need your help

My problem as following:

min f(x)=s(1)+s(2)+s(3)

s.t.

s(1)=0.5x(1)^2+w
s(2)=-4x(2)+7
s(3)=-3x(3)^3+6x^2
x(1)+x(2)+x(3)=100
0<x(1)<x(2)<x(3)

where x(1)<20 then w=100,

else w =500

Do you know how to convert constrains to standard form ,g(x) >= 0

which function can solve the question above, thank you

Answer 1

[Alan Weiss]

I think that you need to solve two different problems, one assuming w =100, one assuming w = 500. Your objective is discontinuous at x(1) = 20, and Optimization Toolbox solvers cannot handle a discontinuous objective.

You could try a solver from Global Optimization Toolbox such as patternsearch.

Alan Weiss

MATLAB mathematical toolbox documentation

[bo peng]

this is a good answer, i think you are right