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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

 

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