Linear and Nonlinear Programming

Linear programs (LPs) and nonlinear programs (NLPs) are mathematical problems in which data are used to find the values of variables that minimize or maximize an objective function while simultaneously satisfying several imposed constraints on the values of the variables. Such problems arise frequently in computer science, mathematics, business, economics, statistics, engineering, operations research, and the sciences. An overview of the similarities and differences between LPs and NLPs is presented here. For example, although the art of building LP and NLP models involves identifying the variables, objective function, and constraints, methods for solving such problems differ greatly. A finite procedure has been developed to solve all LPs; however, no such procedure is available for solving NLPs. Keywords: linear programming; nonlinear programming; optimization; linear optimization; nonlinear optimization; mathematical models; operations research