Question

PLEASE MAKE UP ANY 3 NONLINEAR PROGRAMMING PROBLEMs BY YOUR OWN AND SOLVE IT in either EXCEL, matlab or lingo.

Answer 1

Answer:-

solving nonlinear programming problems by using matlab:-

You can include nonlinear constraints by writing a function that computes both equality and inequality constraint values. A nonlinear constraint function has the syntax

[c,ceq] = nonlinconstr(x)

The function c(x) represents the constraint c(x) <= 0. The function ceq(x) represents the constraint ceq(x) = 0.

Note:   You must have the nonlinear constraint function return both c(x) and ceq(x), even if you have only one type of nonlinear constraint. If a constraint does not exist, have the function return [] for that constraint.

For example, if you have the nonlinear equality constraint x1^2+x2=1 and the nonlinear inequality constraint x1x2 ≥ –10, rewrite them as

x1^2+x2−1=0,

−x1x2−10≤0,

and then solve the problem using the following steps.

For this example, solve the problem

minf(x)=e^x1(4x1^2+2(x2)^2+4x1x2+2x2+1).

Step 1: Write a file objfun.m.

Step 2: Write a file confuneq.m for the nonlinear constraints.

Step 3: Invoke constrained optimization routine.

Output when j.m in the above photo is run:-

Note that ceq is equal to 0 within the default tolerance on the constraints of 1.0e^-006 and that c is less than or equal to 0, as desired.

Note:- you can do the same procedure for different functions using different equality and inequality constraints