Nonlinear Programming

Abstract

AbstractAs we discussed in Chapter 4, in linear programming (LP) applications, our purpose is to optimize (i.e., maximize or minimize) a linear objective function subject to linear constraints. Although a large number of practical decision problems can be accurately modeled as linear programs, it should be emphasized that in some cases using LP to formulate an inherently nonlinear decision problem (i.e., forcing the world to fit the model) may not provide an accurate representation of reality. In many OR problems due to economies/diseconomies of scale (e.g., quantity discounts), interaction among decision variables (e.g., variance of a portfolio) or transformations that result in nonlinearities (e.g., a linear stochastic programming formulation transformed into an equivalent nonlinear deterministic one), an LP formulation becomes impossible to use. In these cases, we would need to utilize the techniques of nonlinear programming (NLP) that can deal with both nonlinear objective functions and nonlinear constraints.KeywordsDecision VariableUnconstrained OptimizationPositive SemidefiniteConstraint QualificationNonlinear Programming ProblemThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.