Originally posted by: PARIKSHIT SHARMA

helllo everyone i have to minimize a linear objective function and my constraints are Non Linear, Non Quadratic, Mixed Integer meaning integer as well as real and number of constraints will be around 3 to 6 so is this feasible or possible to use CPLEX to solve my optimization problem. Please reply It will be really helpful for me, Thanking you in advance! 

CPLEX cannot handle non-linear, non-quadratic constraints. How do your constraints look exactly? Maybe there is way to translate or linearize them.

Originally posted by: PARIKSHIT SHARMA

Thanks for the reply

My Constraints are Sums of products of various terms often involving factorials. 

Hi,

let me share a tiny example with factorial:

using CP;

int n=8;

int fact8=prod(i in 1..n) i;

execute
{
writeln("8! = ",fact8);
}

// Find the max factorial that is less than 1000
dvar int x in 1..n;
dvar int f in 1..100000;
maximize f;

subject to
{
f<=1000;
f==prod(i in 1..n) ((i<=x)*i+(i>=x+1));
}

execute
{
writeln("x","! = ",f);
}

that gives

8! = 40320
// solution with objective 720
x! = 720

regards

Originally posted by: PARIKSHIT SHARMA

My problem is like this as will be written in LaTeX :

\documentclass[fleqn,a4paper,12pt]{article}

\begin{document}

Minimize \quad $z$\\

Subject to:

\[P_{C_{k},k}\leq{z}\hspace{3.7cm}\forall k\in\{1,2.....m\}\]

\[P_{C_{k,k}} = \frac{\frac{1}{(C_k)!}.{(\frac{\lambda_k}{\mu_k})}^{C_k}}{{\sum\limits_{n=0}^{n=C_k}\frac{1}{n!}.(\frac{\lambda_k}{\mu_k})^n}}\quad\quad\quad\quad \forall k\in\{1.....m\}\]

$C_k$ are variables for different $k$ and $C_k$ belongs to integer.

\end{document}

Is there any possibility to solve this optimization problem in CPLEX ?

[I am attaching the LaTeX model as PDF]

So you not only need factorial of decision variables, you also have decision variables in the denominator of quotients and in exponents. At first glance this looks beyond CPLEX's capabilities.