linear programming , quadratic programming, nonlinear programming and integer programming

The example of this section has three important properties.
• Its variables (the amounts of ice cream and butter to produce) are continuous variables. They can take on any real value, subject to satisfying the bounds and constraints.
• All constraints and bounds involve linear functions of the variables. That is, each term of the sum is either a constant or else a constant multiple of one of the variables.
• The objective function—profit, in this case—is also a linear function of the variables.
Problems with these three essential properties are known aslinear programmingproblems or linear programs. Most of our book is devoted to algorithms for solving this classof problems. Linear programming can be extended in various ways to give broader classesof optimization problems. For instance, if we allow the objective function to be a quadratic function of the variables (but still require the constraint to be linear and the variables to be continuous), we obtain quadratic programming problems, which we study in Chapter 7. If we allow both constraints and objective to be nonlinear functions (but still require continuous variables), the problem becomes a nonlinear program. If we restrict some of the variables to take on integer values, the problem becomes an integer program. We give several references for nonlinear and integer programming in the Notes and References at the end of this chapter