What Is ILOG CPLEX?

ILOG CPLEX is a tool for solving linear optimization problems, commonly referred to as Linear Programming (LP) problems, of the form:

Maximize (or Minimize)	c1x1 + c2x2 +...+ cnxn
subject to	a11x1 + a12x2 +...+ a1nxn ~ b1 a21x1 + a22x2 +...+ a2nxn ~ b2 ... am1x1 + am2x2 +...+ amnxn ~ bm
with these bounds	l1 x1 u1 ... ln xn un

where ~ can be , , or =, and the upper bounds ui and lower bounds li may be positive infinity, negative infinity, or any real number.

The elements of data you provide as input for this LP are:

Objective function coefficients	c1, c2, ... , cn
Constraint coefficients	a11, a21, ... , an1 ... am1, am2, ..., amn
Righthand sides	b1, b2, ... , bm
Upper and lower bounds	u1, u2, ... , un and l1, l2, ... , ln

The optimal solution that ILOG CPLEX computes and returns is:

ILOG CPLEX also can solve several extensions to LP: