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# Global optimization

Global optimization is a branch of applied mathematics and numerical analysis that deals with the global optimization of a function or a set of functions according to some criteria. [1]

67 relations: Algorithm, Anatoly Zhigljavsky, Ant colony optimization algorithms, Applied mathematics, Bayesian optimization, Bayesian statistics, Best, worst and average case, Chemical engineering, Combinatorial optimization, Computational phylogenetics, Convex optimization, Curve fitting, Differential evolution, Discrete optimization, Evolution strategy, Evolutionary algorithm, Feasible region, Function (mathematics), Genetic algorithm, Gibbs free energy, Giorgio Parisi, Graduated optimization, Integer, IOSO, Iterative method, Kepler conjecture, Linear programming, Local search (optimization), Markov chain Monte Carlo, Mathematical optimization, Maxima and minima, Memetic algorithm, Metaheuristic, Molecular dynamics, Monte Carlo method, Multi-objective optimization, Multi-swarm optimization, Multidisciplinary design optimization, Non-linear least squares, Numerical analysis, Observational error, Ordered field, Ordered ring, Panos M. Pardalos, Particle swarm optimization, Polynomial SOS, Positive polynomial, Protein structure prediction, Radio propagation model, Ralph E. Gomory, ... Expand index (17 more) »

## Algorithm

In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems.

## Anatoly Zhigljavsky

Anatoly Aleksandrovich Zhigljavsky (born 19 November 1953) is a professor of statistics in the school of mathematics at Cardiff University.

## Ant colony optimization algorithms

In computer science and operations research, the ant colony optimization algorithm (ACO) is a probabilistic technique for solving computational problems which can be reduced to finding good paths through graphs.

## Applied mathematics

Applied mathematics is the application of mathematical methods by different fields such as science, engineering, business, computer science, and industry.

## Bayesian optimization

Bayesian optimization is a sequential design strategy for global optimization of black-box functions that doesn't require derivatives.

## Bayesian statistics

Bayesian statistics, named for Thomas Bayes (1701–1761), is a theory in the field of statistics in which the evidence about the true state of the world is expressed in terms of degrees of belief known as Bayesian probabilities.

## Best, worst and average case

In computer science, best, worst, and average cases of a given algorithm express what the resource usage is at least, at most and on average, respectively.

## Chemical engineering

Chemical engineering is a branch of engineering that uses principles of chemistry, physics, mathematics and economics to efficiently use, produce, transform, and transport chemicals, materials and energy.

## Combinatorial optimization

In applied mathematics and theoretical computer science, combinatorial optimization is a topic that consists of finding an optimal object from a finite set of objects.

## Computational phylogenetics

Computational phylogenetics is the application of computational algorithms, methods, and programs to phylogenetic analyses.

## Convex optimization

Convex optimization is a subfield of optimization that studies the problem of minimizing convex functions over convex sets.

## Curve fitting

Curve fitting is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, possibly subject to constraints.

## Differential evolution

In evolutionary computation, differential evolution (DE) is a method that optimizes a problem by iteratively trying to improve a candidate solution with regard to a given measure of quality.

## Discrete optimization

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

## Evolution strategy

In computer science, an evolution strategy (ES) is an optimization technique based on ideas of evolution.

## Evolutionary algorithm

In artificial intelligence, an evolutionary algorithm (EA) is a subset of evolutionary computation, a generic population-based metaheuristic optimization algorithm.

## Feasible region

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.

## Function (mathematics)

In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.

## Genetic algorithm

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).

## Gibbs free energy

In thermodynamics, the Gibbs free energy (IUPAC recommended name: Gibbs energy or Gibbs function; also known as free enthalpy to distinguish it from Helmholtz free energy) is a thermodynamic potential that can be used to calculate the maximum of reversible work that may be performed by a thermodynamic system at a constant temperature and pressure (isothermal, isobaric).

## Giorgio Parisi

Giorgio Parisi (born 4 August 1948) is an Italian theoretical physicist, whose research has focused on quantum field theory, statistical mechanics and complex systems.

Graduated optimization is a global optimization technique that attempts to solve a difficult optimization problem by initially solving a greatly simplified problem, and progressively transforming that problem (while optimizing) until it is equivalent to the difficult optimization problem.

## Integer

An integer (from the Latin ''integer'' meaning "whole")Integer&#x2009;'s first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").

## IOSO

IOSO (Indirect Optimization on the basis of Self-Organization) is a multiobjective, multidimensional nonlinear optimization technology.

## Iterative method

In computational mathematics, an iterative method is a mathematical procedure that uses an initial guess to generate a sequence of improving approximate solutions for a class of problems, in which the n-th approximation is derived from the previous ones.

## Kepler conjecture

The Kepler conjecture, named after the 17th-century mathematician and astronomer Johannes Kepler, is a mathematical theorem about sphere packing in three-dimensional Euclidean space.

## Linear programming

Linear programming (LP, also called linear optimization) is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships.

## Local search (optimization)

In computer science, local search is a heuristic method for solving computationally hard optimization problems.

## Markov chain Monte Carlo

In statistics, Markov chain Monte Carlo (MCMC) methods comprise a class of algorithms for sampling from a probability distribution.

## Mathematical optimization

In mathematics, computer science and operations research, mathematical optimization or mathematical programming, alternatively spelled optimisation, is the selection of a best element (with regard to some criterion) from some set of available alternatives.

## Maxima and minima

In mathematical analysis, the maxima and minima (the respective plurals of maximum and minimum) of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given range (the local or relative extrema) or on the entire domain of a function (the global or absolute extrema).

## Memetic algorithm

Memetic algorithms (MAs) represent one of the recent growing areas of research in evolutionary computation.

## Metaheuristic

In computer science and mathematical optimization, a metaheuristic is a higher-level procedure or heuristic designed to find, generate, or select a heuristic (partial search algorithm) that may provide a sufficiently good solution to an optimization problem, especially with incomplete or imperfect information or limited computation capacity.

## Molecular dynamics

Molecular dynamics (MD) is a computer simulation method for studying the physical movements of atoms and molecules.

## Monte Carlo method

Monte Carlo methods (or Monte Carlo experiments) are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results.

## Multi-objective optimization

Multi-objective optimization (also known as multi-objective programming, vector optimization, multicriteria optimization, multiattribute optimization or Pareto optimization) is an area of multiple criteria decision making, that is concerned with mathematical optimization problems involving more than one objective function to be optimized simultaneously.

## Multi-swarm optimization

Multi-swarm optimization is a variant of particle swarm optimization (PSO) based on the use of multiple sub-swarms instead of one (standard) swarm.

## Multidisciplinary design optimization

Multi-disciplinary design optimization (MDO) is a field of engineering that uses optimization methods to solve design problems incorporating a number of disciplines.

## Non-linear least squares

Non-linear least squares is the form of least squares analysis used to fit a set of m observations with a model that is non-linear in n unknown parameters (m > n).

## Numerical analysis

Numerical analysis is the study of algorithms that use numerical approximation (as opposed to general symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics).

## Observational error

Observational error (or measurement error) is the difference between a measured value of a quantity and its true value.

## Ordered field

In mathematics, an ordered field is a field together with a total ordering of its elements that is compatible with the field operations.

## Ordered ring

In abstract algebra, an ordered ring is a (usually commutative) ring R with a total order ≤ such that for all a, b, and c in R.

## Panos M. Pardalos

Panos M. Pardalos is a Greek scientist and engineer, currently a Distinguished Professor and the Paul and Heidi Brown Preeminent Professor in Industrial and Systems Engineering at University of Florida.

## Particle swarm optimization

In computer science, particle swarm optimization (PSO) is a computational method that optimizes a problem by iteratively trying to improve a candidate solution with regard to a given measure of quality.

## Polynomial SOS

In mathematics, a form (i.e. a homogeneous polynomial) h(x) of degree 2m in the real n-dimensional vector x is sum of squares of forms (SOS) if and only if there exist forms g_1(x),\ldots,g_k(x) of degree m such that h(x).

## Positive polynomial

In mathematics, a positive polynomial on a particular set is a polynomial whose values are positive on that set.

## Protein structure prediction

Protein structure prediction is the inference of the three-dimensional structure of a protein from its amino acid sequence—that is, the prediction of its folding and its secondary and tertiary structure from its primary structure.

A radio propagation model, also known as the Radio Wave Propagation Model or the Radio Frequency Propagation Model, is an empirical mathematical formulation for the characterization of radio wave propagation as a function of frequency, distance and other conditions.

## Ralph E. Gomory

Ralph Edward Gomory (born 7 May 1929) is an American applied mathematician and executive.

## Real closed field

In mathematics, a real closed field is a field F that has the same first-order properties as the field of real numbers.

## Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

## Roberto Battiti

Roberto Battiti (born 1961) is an Italian computer scientist, Professor of computer science at the University of Trento, director of the LIONlab (Learning and Intelligent Optimization), and deputy director of the DISI Department (Electrical Engineering and Computer Science) and delegate for technology transfer.

## Round-off error

A round-off error, also called rounding error, is the difference between the calculated approximation of a number and its exact mathematical value due to rounding.

## Safety engineering

Safety engineering is an engineering discipline which assures that engineered systems provide acceptable levels of safety.

## Sampling (signal processing)

In signal processing, sampling is the reduction of a continuous-time signal to a discrete-time signal.

## Set (mathematics)

In mathematics, a set is a collection of distinct objects, considered as an object in its own right.

## Simulated annealing

Simulated annealing (SA) is a probabilistic technique for approximating the global optimum of a given function.

## Simulation

Simulation is the imitation of the operation of a real-world process or system.

## Social cognitive optimization

Social cognitive optimization (SCO) is a population-based metaheuristic optimization algorithm which was developed in 2002.

## Spin glass

A spin glass is a disordered magnet, where the magnetic spins of the component atoms (the orientation of the north and south magnetic poles in three-dimensional space) are not aligned in a regular pattern. The term "glass" comes from an analogy between the magnetic disorder in a spin glass and the positional disorder of a conventional, chemical glass, e.g., a window glass. In window glass or any amorphous solid the atomic bond structure is highly irregular; in contrast, a crystal has a uniform pattern of atomic bonds. In ferromagnetic solid, magnetic spins all align in the same direction; this would be analogous to a crystal. The individual atomic bonds in a spin glass are a mixture of roughly equal numbers of ferromagnetic bonds (where neighbors have the same orientation) and antiferromagnetic bonds (where neighbors have exactly the opposite orientation: north and south poles are flipped 180 degrees). These patterns of aligned and misaligned atomic magnets create what are known as frustrated interactions - distortions in the geometry of atomic bonds compared to what would be seen in a regular, fully aligned solid. They may also create situations where more than one geometric arrangement of atoms is stable. Spin glasses and the complex internal structures that arise within them are termed "metastable" because they are "stuck" in stable configurations other than the lowest-energy configuration (which would be aligned and ferromagnetic). The mathematical complexity of these structures is difficult but fruitful to study experimentally or in simulations, with applications to artificial neural networks in computer science, in addition to physics, chemistry, and materials science.

## State space search

State space search is a process used in the field of computer science, including artificial intelligence (AI), in which successive configurations or states of an instance are considered, with the intention of finding a goal state with a desired property.

## Swarm intelligence

Swarm intelligence (SI) is the collective behavior of decentralized, self-organized systems, natural or artificial.

## Tabu search

Tabu search, created by Fred W. Glover in 1986 and formalized in 1989, is a metaheuristic search method employing local search methods used for mathematical optimization.

## Travelling salesman problem

The travelling salesman problem (TSP) asks the following question: "Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city and returns to the origin city?" It is an NP-hard problem in combinatorial optimization, important in operations research and theoretical computer science.

## Tree (graph theory)

In mathematics, and more specifically in graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one path.

## Václav Chvátal

Václav (Vašek) Chvátal (is a Professor Emeritus in the Department of Computer Science and Software Engineering at Concordia University in Montreal, Canada. He has published extensively on topics in graph theory, combinatorics, and combinatorial optimization.

## References

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