I have a function of two variables and I need to maximise it for given constraints. The function: F(x) = x1 / (x2 * constant) subject to: 20000 <= x1 <= 50000, 1 <= x2 <= 5
Kindly guide me how to do this using MATLAB.
Regards Abubakr
MATLAB: I want to maximize a non linear function
non-linear optimizationoptimizationOptimization Toolbox
Related Solutions
%{
x1+x2+x3+x4+x5 =1000;x1^2-4x2+5x3^3+x4^4-3.5x5^2 = 300%}
Notice that x2 is the only variable that appears linearly in the second equation. So rewrite the first equation as
%{x2 = 1000 - x1 - x3 - x4 - x5%}Now substitute that into the second equation
%{x1^2-4*(1000 - x1 - x3 - x4 - x5)+5x3^3+x4^4-3.5x5^2 = 300%}This is a quadratic in x1 (or x5), so solve it for x1
syms x1 x2 x3 x4 x5eqn = x1^2-4*(1000 - x1 - x3 - x4 - x5)+5*x3^3+x4^4-3.5*x5^2 == 300
X1 = solve(eqn, x1)
Now you run two different PSO runs, one substituting 1000 - x1 - x3 - x4 - x5 for x2 and the first of those X1 values for x1; the other run substituting 1000 - x1 - x3 - x4 - x5 for x2 and the second of those X1 values for x1. These runs will not require equality or inequality constraints (unless there are more constraints you did not tell us about.)
The runs you would do would be over 3 variables only, x3, x4, x5, with you having substituted for x1 and x2 in your objective function.
You don’t need matlab to find the maximum value of this function. The subtraction by 398 does not affect maximization, nor does multiplication by 725.2 or addition by 1. Therefore the problem is equivalent to finding x1 and x2 which maximize x1/x2. Since both are restricted to positive values, the maximum clearly occurs at maximum x1 and minimum x2, namely x1 = 5 and x2 = 40. All done without firing up matlab.
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