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
