Linear and Nonlinear Programming Problems

The most common method of categorizing optimization problems is as either a linear programming problem or a nonlinear programming problem. In addition to constraints on the value of f(x), whether an optimization problem is linear or nonlinear influences the selection of the algorithm you use to solve the problem.

Note   In the context of optimization, the term programming does not refer to computer programming. Programming also refers to scheduling or planning. Linear and nonlinear programming are subsets of mathematical programming. The objective of mathematical programming is the same as optimization—maximizing or minimizing f(x).

Linear programming problems are discrete optimization problems. A finite solution set X and a combinatorial nature characterize discrete optimization problems. A combinatorial nature refers to the fact that several solutions to the problem exist. Each solution to the problem consists of a different combination of parameters. However, at least one optimal solution exists. Planning a route to several destinations so you travel the minimum distance typifies a combinatorial optimization problem.

Nonlinear programming problems are continuous optimization problems. An infinite and continuous set X characterizes continuous optimization problems.