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Here, a Las Vegas algorithm is a randomized algorithm whose runtime may vary, but for which the result is always correct. [7] [8] For example, this form of Yao's principle has been used to prove the optimality of certain Monte Carlo tree search algorithms for the exact evaluation of game trees. [8]
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It is always true that the left-hand side is at most the right-hand side (max–min inequality) but equality only holds under certain conditions identified by minimax theorems. The first theorem in this sense is von Neumann 's minimax theorem about two-player zero-sum games published in 1928, [ 2 ] which is considered the starting point of game ...
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.
Minimax approximation algorithm, algorithms to approximate a function; The Courant minimax principle, a characterization of the eigenvalues of a real symmetric matrix; Minimax theorem, one of a number of theorems relating to the max-min inequality; The Min-max theorem, a characterization of eigenvalues of compact Hermitian operators on Hilbert ...
Local and global maxima and minima for cos(3πx)/x, 0.1≤ x ≤1.1. In mathematical analysis, the maximum and minimum [a] of a function are, respectively, the greatest and least value taken by the function.
The MM algorithm is an iterative optimization method which exploits the convexity of a function in order to find its maxima or minima. The MM stands for “Majorize-Minimization” or “Minorize-Maximization”, depending on whether the desired optimization is a minimization or a maximization.
Quickselect was presented without analysis by Tony Hoare in 1965, [41] and first analyzed in a 1971 technical report by Donald Knuth. [11] The first known linear time deterministic selection algorithm is the median of medians method, published in 1973 by Manuel Blum, Robert W. Floyd, Vaughan Pratt, Ron Rivest, and Robert Tarjan. [5]