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Optimization problem

Index Optimization problem

In mathematics and computer science, an optimization problem is the problem of finding the best solution from all feasible solutions. [1]

48 relations: Additive inverse, Approximation algorithm, Bounded set, Canonical form, Clique problem, Combinatorial optimization, Computational problem, Computer science, Constraint (mathematics), Continuous or discrete variable, Countable set, Counting problem (complexity), Decision problem, Design Optimization, Discrete mathematics, Discrete optimization, Feasible region, Finite set, Function problem, Glove problem, Graph (discrete mathematics), Integer, Juraj Hromkovič, Knapsack problem, L-reduction, List of continuity-related mathematical topics, Loss function, Makespan, Mathematics, Maximum satisfiability problem, Measure (mathematics), NP (complexity), Operations research, Permutation, Polynomial, Polynomial-time approximation scheme, Polynomial-time reduction, Real number, Recursive language, Search problem, Semi-infinite programming, Set (mathematics), Set cover problem, Sign (mathematics), Time complexity, Travelling salesman problem, Turing reduction, Variable (mathematics).

Additive inverse

In mathematics, the additive inverse of a number is the number that, when added to, yields zero.

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Approximation algorithm

In computer science and operations research, approximation algorithms are efficient algorithms that find approximate solutions to NP-hard optimization problems with provable guarantees on the distance of the returned solution to the optimal one.

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Bounded set

In mathematical analysis and related areas of mathematics, a set is called bounded, if it is, in a certain sense, of finite size.

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Canonical form

In mathematics and computer science, a canonical, normal, or standard form of a mathematical object is a standard way of presenting that object as a mathematical expression.

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Clique problem

In computer science, the clique problem is the computational problem of finding cliques (subsets of vertices, all adjacent to each other, also called complete subgraphs) in a graph.

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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.

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Computational problem

In theoretical computer science, a computational problem is a mathematical object representing a collection of questions that computers might be able to solve.

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Computer science

Computer science deals with the theoretical foundations of information and computation, together with practical techniques for the implementation and application of these foundations.

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Constraint (mathematics)

In mathematics, a constraint is a condition of an optimization problem that the solution must satisfy.

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Continuous or discrete variable

In mathematics, a variable may be continuous or discrete.

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Countable set

In mathematics, a countable set is a set with the same cardinality (number of elements) as some subset of the set of natural numbers.

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Counting problem (complexity)

In computational complexity theory and computability theory, a counting problem is a type of computational problem.

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Decision problem

In computability theory and computational complexity theory, a decision problem is a problem that can be posed as a yes-no question of the input values.

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Design Optimization

Design optimization is an engineering design methodology using a mathematical formulation of a design problem to support selection of the optimal design among many alternatives.

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Discrete mathematics

Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous.

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Discrete optimization

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

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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.

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Finite set

In mathematics, a finite set is a set that has a finite number of elements.

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Function problem

In computational complexity theory, a function problem is a computational problem where a single output (of a total function) is expected for every input, but the output is more complex than that of a decision problem.

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Glove problem

In operations research, the glove problem (also known as the condom problem) is an optimization problem used as an example that the cheapest capital cost often leads to dramatic increase in operational time, but that the shortest operational time need not be given by the most expensive capital cost.

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Graph (discrete mathematics)

In mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related".

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Integer

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

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Juraj Hromkovič

Juraj Hromkovič (born 1958) is a Slovak Computer Scientist and Professor at ETH Zürich.

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Knapsack problem

The knapsack problem or rucksack problem is a problem in combinatorial optimization: Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible.

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L-reduction

In computer science, particularly the study of approximation algorithms, an L-reduction ("linear reduction") is a transformation of optimization problems which linearly preserves approximability features; it is one type of approximation-preserving reduction.

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List of continuity-related mathematical topics

In mathematics, the terms continuity, continuous, and continuum are used in a variety of related ways.

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Loss function

In mathematical optimization, statistics, econometrics, decision theory, machine learning and computational neuroscience, a loss function or cost function is a function that maps an event or values of one or more variables onto a real number intuitively representing some "cost" associated with the event.

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Makespan

In operations research, the makespan of a project is the total time that elapses from the beginning to the end.

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Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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Maximum satisfiability problem

In computational complexity theory, the maximum satisfiability problem (MAX-SAT) is the problem of determining the maximum number of clauses, of a given Boolean formula in conjunctive normal form, that can be made true by an assignment of truth values to the variables of the formula.

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Measure (mathematics)

In mathematical analysis, a measure on a set is a systematic way to assign a number to each suitable subset of that set, intuitively interpreted as its size.

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NP (complexity)

In computational complexity theory, NP (for nondeterministic polynomial time) is a complexity class used to describe certain types of decision problems.

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Operations research

Operations research, or operational research in British usage, is a discipline that deals with the application of advanced analytical methods to help make better decisions.

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Permutation

In mathematics, the notion of permutation relates to the act of arranging all the members of a set into some sequence or order, or if the set is already ordered, rearranging (reordering) its elements, a process called permuting.

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Polynomial

In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.

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Polynomial-time approximation scheme

In computer science, a polynomial-time approximation scheme (PTAS) is a type of approximation algorithm for optimization problems (most often, NP-hard optimization problems).

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Polynomial-time reduction

In computational complexity theory, a polynomial-time reduction is a method of solving one problem by means of a hypothetical subroutine for solving a different problem (that is, a reduction), that uses polynomial time excluding the time within the subroutine.

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Real number

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

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Recursive language

In mathematics, logic and computer science, a formal language (a set of finite sequences of symbols taken from a fixed alphabet) is called recursive if it is a recursive subset of the set of all possible finite sequences over the alphabet of the language.

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Search problem

In computational complexity theory and computability theory, a search problem is a type of computational problem represented by a binary relation.

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Semi-infinite programming

In optimization theory, semi-infinite programming (SIP) is an optimization problem with a finite number of variables and an infinite number of constraints, or an infinite number of variables and a finite number of constraints.

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Set (mathematics)

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

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Set cover problem

The set cover problem is a classical question in combinatorics, computer science and complexity theory.

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Sign (mathematics)

In mathematics, the concept of sign originates from the property of every non-zero real number of being positive or negative.

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Time complexity

In computer science, the time complexity is the computational complexity that describes the amount of time it takes to run an algorithm.

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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.

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Turing reduction

In computability theory, a Turing reduction from a problem A to a problem B, is a reduction which solves A, assuming the solution to B is already known (Rogers 1967, Soare 1987).

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Variable (mathematics)

In elementary mathematics, a variable is a symbol, commonly an alphabetic character, that represents a number, called the value of the variable, which is either arbitrary, not fully specified, or unknown.

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Redirects here:

NP optimization problem, Optimal solution, Optimal value.

References

[1] https://en.wikipedia.org/wiki/Optimization_problem

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