                              For extensive glossary on optimization see Mathematical Programming Glossary

 Benders Decomposition - Algorithm for NLP, MILP and MINLP that relies on decomposition in which variables are partitioned into complicating and non-complicating Bilinear Function - Function given by the sum of products of two variables Branch and Bound - Algorithm for MILP and MINLP that relies on enumeration and bounding of a tree search to find the optimum integer solution Constraint Programming - Logic-based optimization technique that is based on implicit enumeration and constraint propagation Constraints - Equations and/or inequalities that constrain the values of the variables in an optimization model Convex Function - Function coincides or underestimates all linear interpolations between any two arbitrary points (e.g. all linear functions are convex) Convex Region - Region in which any linear combination obtained from two arbitrary points yields a new point belonging to that region Cutting Planes - Additional constraints that are added to MILP problems to improve their LP approximation when all variables are treated as continuous variables Disjunctive Programming - Optimization problem with an objective function and constraints expressed in logic form with disjunctions ( OR operators), and propositional logic. Feasible Region - Region given by set of values of variables that satisfy constraints. Global Optimization - Methods that guarantee findingb the global optimum in nonlinear optimization problems Global Optimum - Optimum solution to model (1) such that any feasible variable values different to that produce a worsening in the objective function value Karush-Kuhn-Tucker Conditions - Generalization of the zero derivative optimality condition to problems with constraints Local Optimum - Optimum solution to a model such that small perturbations around that point lead to a worsening of the objective function value Linear Programming - Optimization problems with linear objective function and constraints involving only continuous variables Mixed-integer Linear Programming (MILP) - Extension of linear programming that allows some of the variables to take on discrete values (mostly 0-1) Mixed-integer Nonlinear Programming (MINLP) - Extension of nonlinear programming that allows some of the variables to take on discrete values (mostly 0-1) Multiobjective Optimization - Optimization problems with more than one objective function Multiperiod Optimization - Optimization problems in which constraints are specified over several time periods or a set of scenarios Nonlinear Programming - Optimization problems with nonlinear objective function and constraints involving only continuous variables Nonconvexity - Condition of a function or region that does not satisfy convexity conditions NP-Completeness - Theoretical characterization of worst case for computational requirements that increase exponentially with problem size Optimum Solution - Variable values that correspond to the solution to a mathematical optimization model with a single objective function and constraints. Outer Approximation - Algorithm for MINLP that relies on accumulation of linearizations to bound the objective function and feasible region Penalty Function - Redefined objective function which involves the original objective plus a weighted violation of the constraints Stochastic Optimization - Optimization problems in which some of the input data are random or subject to fluctuations