MATLAB: Optimization function based on different domain of optimized variables

optimizationOptimization Toolbox

Hello,

I have an linear objective function f(x1,x2,x3.. ) which is defined for a fixed domain of x1 say x1< (constant k). Also the objective function changes to g(x1,x2,x3 … ) if x1> (constant k). The objective function in both the cases is linear. x1,x2,x3 are the optimization variables. There are set of other equality and inquality constraints on the other variables.

I was trying to solve this optimization problem using linprog .

How can I switch the optimization function based on the domain of x1? Can I iterate over the current value of x1 and check if it is less than that constant in 'linprog' solver and accordingly select the optimization function f or g?

Best Answer

Solve the problem twice, once with the constraint x1<=k and once with x1>=k, imposing the appropriate objective function in each case. Whichever of the solutions gives the best objective function value wins.

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MATLAB: GA algorithm toolbox (define constraint)

This kind of system can be programmed by introducing up to 4 new integer variables, with the logical conditions

x1 == x6 * x4
x1 == x7 * x5
x2 == x8 * x4
x2 == x9 * x5

You would then follow that by reducing the original equations, replacing each x1 by x6 * x4 and each x2 by x8 * x4 everywhere the equations,

Then you would add the nonlinear equality constraints

x6 * x4 - x7 * x5
x8 * x4 - x9 * x5

The list of variables would be x3, x4, x5, x6, x7, x8, x9 with x4 through x9 all integer variables (so x3 is the only non-integer variable.)

I know your original list did not require x5 to be integer, but your integer constraints on the other variables require that x5 be integer, I figure.

MATLAB: Optimization

A linear function is twice differentiable - the second derivative is zero! So go ahead and use fmincon.

Best Answer

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MATLAB: GA algorithm toolbox (define constraint)

MATLAB: Optimization

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