Flashcards: Mathematical optimization

A Bellman equation, named after its discoverer, Richard Bellman, also known as a dynamic programming equation, is a necessary condition for optimality associated with the mathematical optimization method known as dynamic programming.

The P versus NP problem is a major unsolved problem in computer science.

In mathematical optimization, the Karush–Kuhn–Tucker (KKT) conditions (also known as the Kuhn–Tucker conditions) are first order necessary conditions for a solution in nonlinear programming to be optimal, provided that some are satisfied.

Discrete optimization is a branch of optimization in applied mathematics and computer science.

In the field of mathematical optimization, stochastic programming is a framework for modeling optimization problems that involve uncertainty.

Pareto efficiency, or Pareto optimality, is a state of allocation of resources in which it is impossible to make any one individual better off without making at least one individual worse off.

In computer science and operations research, a genetic algorithm (GA) is a metaheuristic inspired by the process of natural selection that belongs to the larger class of evolutionary algorithms (EA).

A Mathematical Programming Language (AMPL) is an algebraic modeling language to describe and solve high-complexity problems for large-scale mathematical computing (i.e., large-scale optimization and scheduling-type problems).

The International Society for Structural and Multidisciplinary Optimization is a learned society in the field of multidisciplinary design optimization that was founded in October 1991.

APOPT (for Advanced Process OPTimizer) is a software package for solving large-scale optimization problems of any of these forms: * Linear programming (LP) * Quadratic programming (QP) * Quadratically constrained quadratic program (QCQP) * Nonlinear programming (NLP) * Mixed integer programming (MIP) * Mixed integer linear programming (MILP) * Mixed integer nonlinear programming (MINLP)

In mathematical optimization, a feasible region, feasible set, search space, or solution space is the set of all possible points (sets of values of the choice variables) of an optimization problem that satisfy the problem's constraints, potentially including inequalities, equalities, and integer constraints.

A Walrasian auction, introduced by Léon Walras, is a type of simultaneous auction where each agent calculates its demand for the good at every possible price and submits this to an auctioneer.

Analytica is a visual software package developed by Lumina Decision Systems for creating, analyzing and communicating quantitative decision models.

The geometric median of a discrete set of sample points in a Euclidean space is the point minimizing the sum of distances to the sample points.

In the design of experiments, optimal designs (or optimum designs) are a class of experimental designs that are optimal with respect to some statistical criterion.

In mathematical optimization, ordinal optimization is the maximization of functions taking values in a partially ordered set ("poset").

SAMPL, which stands for "Stochastic AMPL", is an algebraic modeling language resulting by expanding the well-known language AMPL with extended syntax and keywords.

The MOEA Framework is an open-source evolutionary computation library for Java that specializes in multi-objective optimization.

Quadratic programming (QP) is a special type of mathematical optimization problem—specifically, the problem of optimizing (minimizing or maximizing) a quadratic function of several variables subject to linear constraints on these variables.

In statistics, response surface methodology (RSM) explores the relationships between several explanatory variables and one or more response variables.

ParadisEO is a white-box object-oriented framework dedicated to the flexible design of metaheuristics.

Mathematics of Operations Research is a peer-reviewed scientific journal first published in February 1976.

AIMMS (an acronym for "Advanced Interactive Multidimensional Modeling System") is a software system designed for modeling and solving large-scale optimization and scheduling-type problems.

Advanced process monitor (APMonitor), is a modeling language for differential algebraic (DAE) equations.

Job shop scheduling (or job-shop problem) is an optimization problem in computer science and operations research in which ideal jobs are assigned to resources at particular times.