Look up minimax in Wiktionary, the free dictionary.
Minimax is a strategy in decision theory and related disciplines.
Minimax, minmax, or min-max can also refer to:
Minimax is a strategy in decision theory and related disciplines.
Minimax, minmax, or min-max can also refer to:
In graph theory, an expander graph is a sparse graph that has strong connectivity properties, quantified using vertex, edge or spectral expansion. Expander constructions have spawned research in pure and applied mathematics, with several applications to complexity theory, design of robust computer networks, and the theory of error-correcting codes.
Minmax is a decision rule used in artificial intelligence, decision theory, game theory, statistics, and philosophy for minimizing the possible loss for a worst case scenario. When dealing with gains, it is referred to as "maximin" – to maximize the minimum gain. Originally formulated for several-player zero-sum game theory, covering both the cases where players take alternate moves and those where they make simultaneous moves, it has also been extended to more complex games and to general decision-making in the presence of uncertainty.
In mathematics, a Hermitian matrix is a complex square matrix that is equal to its own conjugate transpose—that is, the element in the i-th row and j-th column is equal to the complex conjugate of the element in the j-th row and i-th column, for all indices i and j:
In voting systems, the Smith set, named after John H. Smith, but also known as the top cycle, or as Generalized Top-Choice Assumption (GETCHA), is the smallest non-empty set of candidates in a particular election such that each member defeats every candidate outside the set in a pairwise election. The Smith set provides one standard of optimal choice for an election outcome. Voting systems that always elect a candidate from the Smith set pass the Smith criterion and are said to be 'Smith-efficient' or to satisfy the Smith criterion.
In mathematics, spectral graph theory is the study of the properties of a graph in relationship to the characteristic polynomial, eigenvalues, and eigenvectors of matrices associated with the graph, such as its adjacency matrix or Laplacian matrix.
In mathematics, a saddle point or minimax point is a point on the surface of the graph of a function where the slopes (derivatives) in orthogonal directions are all zero, but which is not a local extremum of the function. An example of a saddle point is when there is a critical point with a relative minimum along one axial direction and at a relative maximum along the crossing axis. However, a saddle point need not be in this form. For example, the function has a critical point at that is a saddle point since it is neither a relative maximum nor relative minimum, but it does not have a relative maximum or relative minimum in the -direction.
In the mathematical area of game theory, a minimax theorem is a theorem providing conditions that guarantee that the max–min inequality is also an equality. The first theorem in this sense is von Neumann's minimax theorem about zero-sum games published in 1928, which was considered the starting point of game theory. Von Neumann is quoted as saying "As far as I can see, there could be no theory of games ... without that theorem ... I thought there was nothing worth publishing until the Minimax Theorem was proved".
In linear algebra and functional analysis, the min-max theorem, or variational theorem, or Courant–Fischer–Weyl min-max principle, is a result that gives a variational characterization of eigenvalues of compact Hermitian operators on Hilbert spaces. It can be viewed as the starting point of many results of similar nature.
In matrix theory, the Perron–Frobenius theorem, proved by Oskar Perron (1907) and Georg Frobenius (1912), asserts that a real square matrix with positive entries has a unique eigenvalue of largest magnitude and that eigenvalue is real. The corresponding eigenvector can be chosen to have strictly positive components, and also asserts a similar statement for certain classes of nonnegative matrices. This theorem has important applications to probability theory ; to the theory of dynamical systems ; to economics ; to demography ; to social networks ; to Internet search engines (PageRank); and even to ranking of American football teams. The first to discuss the ordering of players within tournaments using Perron–Frobenius eigenvectors is Edmund Landau.
In computational complexity theory, Yao's principle is a way to prove lower bounds on the worst-case performance of randomized algorithms, by comparing them to deterministic (non-random) algorithms. It states that, for any randomized algorithm, there exists a probability distribution on inputs to the algorithm, so that the expected cost of the randomized algorithm on its worst-case input is at least as large as the cost of the best deterministic algorithm on a random input from this distribution. Thus, to establish a lower bound on the performance of randomized algorithms, it suffices to find an appropriate distribution of difficult inputs, and to prove that no deterministic algorithm can perform well against that distribution. This principle is named after Andrew Yao, who first proposed it.
In mathematics, comparison theorems are theorems whose statement involves comparisons between various mathematical objects of the same type, and often occur in fields such as calculus, differential equations and Riemannian geometry.
Minimax is a European pay television channel aimed at children, headquartered in Hungary, and broadcasting to 11 Central European countries. The channel was also broadcast in Spain from 1994 to 1998 and Poland from 1999 to 2004. Minimax's policy goals include edutainment and non-violent programs.
In mathematics, the Courant minimax principle gives the eigenvalues of a real symmetric matrix. It is named after Richard Courant.
In statistical decision theory, where we are faced with the problem of estimating a deterministic parameter (vector) from observations an estimator is called minimax if its maximal risk is minimal among all estimators of . In a sense this means that is an estimator which performs best in the worst possible case allowed in the problem.
Teletoon+ is a Polish television channel owned and operated by the Canal+ Group through Canal+ Polska SA, available on Platforma Canal+. The channel aims at young people in the age group of 7–17 years, carrying various animated films and television series.
Alan Jerome Hoffman was an American mathematician and IBM Fellow emeritus, T. J. Watson Research Center, IBM, in Yorktown Heights, New York. He was the founding editor of the journal Linear Algebra and its Applications, and held several patents. He contributed to combinatorial optimization and the eigenvalue theory of graphs. Hoffman and Robert Singleton constructed the Hoffman–Singleton graph, which is the unique Moore graph of degree 7 and diameter 2.
Randomized algorithms are algorithms that employ a degree of randomness as part of their logic. These algorithms can be used to give good average-case results (complexity-wise) to problems which are hard to solve deterministically, or display poor worst-case complexity. An algorithmic game theoretic approach can help explain why in the average case randomized algorithms may work better than deterministic algorithms.
The term ranked voting, also known as preferential voting or ranked choice voting, pertains to any voting system where voters use a rank to order candidates or options—in a sequence from first, second, third, and onwards—on their ballots. Ranked voting systems vary based on the ballot marking process, how preferences are tabulated and counted, the number of seats available for election, and whether voters are allowed to rank candidates equally. An electoral system that utilizes ranked voting employs one of numerous counting methods to determine the winning candidate or candidates. Additionally, in some ranked voting systems, officials mandate voters to rank a specific number of candidates, sometimes all; while in others, voters may rank as many candidates as they desire.