Benders Decomposition  Algorithm for NLP, MILP and MINLP that relies on decomposition in which variables are partitioned into complicating and noncomplicating 

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  Logicbased 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 

KarushKuhnTucker 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 

Mixedinteger Linear Programming (MILP)  Extension of linear programming that allows some of the variables to take on discrete values (mostly 01) 

Mixedinteger Nonlinear Programming (MINLP)  Extension of nonlinear programming that allows some of the variables to take on discrete values (mostly 01) 

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 

NPCompleteness  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 
