minimaxn.adj.

Brit.

/ˈmɪnɪmaks/, U.S.

/ˈmɪniˌmæks/

Origin: Perhaps of multiple origins. A borrowing from French. Perhaps also partly formed within English, by compounding. Etymon: French minimax.

Etymology: In sense A. 1 < French minimax (H. Poincaré Méthodes Nouvelles de la Mécanique Céleste (1899) III. xxviii. 246: see below) < mini- (in minimum adj.) + max- (in maximum adj.). In subsequent senses perhaps re-formed independently in English. With sense B. 3 compare earlier min-max adj. and n.Poincaré says that he uses the word ‘à l'exemple des Anglais’, but earlier use has not been traced.

Chiefly Mathematics.

A. n.

1. A point in a topological space at which a function defined on the space is stationary (i.e. its first derivatives in all directions vanish at the point), and which has a local maximum in one direction and a local minimum in another. Also: the behaviour of a function at such a point. Cf. maximum n. 2, minimum n. 1. Now rare.For a function on a plane (i.e. one defining a surface in three-dimensional space) such a point is called a saddle point.

ΚΠ

1917 Trans. Amer. Math. Soc. 18 240 If J₀ is the value of J at a point P₀ and if the inequality J < J₀ − ε where ε is small and positive defines more than one region near the point P₀, then P₀ will be called a point of minimax.

1931 Amer. Jrnl. Math. 53 169 It has been proved..that Ω(x,y) possesses a minimax at each of the libration points L₁, L₂ and L₃ and it accordingly follows that Ω(x,y) must have an absolute minimum at L₄ and L₅.

2. The smallest of a set of maxima. Also: a minimax strategy (see sense B. 3).

ΚΠ

1958 Engineering 21 Mar. 369/2 Player B, on the other hand, will determine the largest value in each column, and the smallest of these, the ‘minimax’.

1962 Sci. Amer. Dec. 114/2 Both firms were guided by the principle of the minimax, choosing the best of the worst outcomes.

1968 Brit. Med. Bull. 24 232/2 This would be the Bayesian Strategy of decision theory.., but other strategies, such as minimax or restricted Bayes, could also be used.

1970 G. S. G. Beveridge & R. S. Schechter Optimization xii. 656 The value of P (and L) lies between the row maxi-min and the column mini-max.

1996 Economist 30 Mar. 96/2 At the other extreme, a hypercautious government would prefer ‘minimax’—the minimum of maximums.

B. adj.

1. Designating or relating to a point in a space at which a function is stationary and has a local maximum in one direction and a local minimum in another. Now rare.

ΘΚΠ

the world > relative properties > number > mathematics > [adjective] > relating to mathematical property

simple1570

dissevered1605

periodicala1690

irreductible1753

analytical1799

analytic1800

compound1806

well-conditioned1843

one-valued1884

non-empty1905

well-behaved1912

minimax1917

irredundant1925

non-linear1930

constructive1938

extremal1939

max-min1949

meta-analytic1968

meta-analytic1978

1917 G. D. Birkhoff in Proc. National Acad. Sci. U.S.A. 3 315 Another method may be employed to find a large class of stable periodic orbits which I call of minimax type.

1935 Amer. Jrnl. Math. 57 930 The minimum and minimax methods..establish immediately the existence of an infinite number of closed periodic orbits.

1940 Ann. Math. 41 419 The critical limits, such as absolute minima, relative minima, minimax values, etc., are in general infinite in number.

a. Designating or resulting in the smallest of a set of maxima.

ΚΠ

1938 Amer. Jrnl. Math. 60 831 Let r be any integer such that H(r + 1) assumes the maximum of H(m). The R(n)-block [r + 1, r + R(n)] will then be termed a minimax n-covering in (a).

1940 Amer. Jrnl. Math. 62 237 Let s_n denote a value of s for which the maximum diameter of the sets G_s[t_e(n)] is a minimum,..and let this minimax diameter be d(n).

1951 Ann. Math. Statistics 22 466 The minimax risk is ½(1 − a).

1990 Glasgow Math. Jrnl. 32 267 If G is a finitely generated soluble-by-finite group of finite rank, then G is a finite extension of a soluble minimax group.

b. Used predicatively.

ΚΠ

1952 Ann. Math. Statistics 23 587 For such weight functions the supremum of the risk over all θ ε Ω is infinite for every decision function, so that every decision function is minimax.

1970 R. B. Ash Basic Probability Theory viii. 250 It is immediate from the definition of admissibility that an admissible test with constant risk (i.e., α = β) is minimax.

3. Designating or relating to a strategy that minimizes the greatest loss or risk to which a participant in a game or other situation of conflict will be liable. Also: designating the theorem which states that for a finite zero-sum game with two players, the smallest maximum loss that a player can choose to risk by a suitable choice of strategy is equal to the greatest minimum guaranteed gain. Cf. maximin adj. and n.

ΘΚΠ

the world > action or operation > prosperity > success > mastery or superiority > [adjective] > specific advantage

minimax1947

maximin1949

zero-sum1965

1947 A. Wald in Econometrica 15 283 An element a₀ in A is said to be a minimax strategy of player 1 if Inf_b K(a, b) takes its maximum value with respect to a for a = a₀.

1949 Econometrica 17 230 Often Nature's strategy is completely unknown. In that case Wald suggests that the statistician play a minimax strategy: that is, the statistician should select that decision procedure which minimizes the maximum risk.

1957 R. D. Luce & H. Raiffa Games & Decisions i. 2 Although Borel gave a clear statement of an important class of game theoretic problems and introduced the concepts of pure and mixed strategies, von Neumann points out that he did not obtain one crucial result—the minimax theorem—without which no theory of games can be said to exist.

1978 M. Jevons Murder at Margin xiv. 138 If two people are charged with a crime and are separated by the police with no chance of their communicating, there are certain circumstances in which it would be rational for them to confess—even if they did not commit the crime. In economics this is called a minimax strategy.

1993 Personal Computer World July 539/1 Many of the best cognitive games programs have a mini-max algorithm lurking somewhere or other in their innards.

This entry has been updated (OED Third Edition, March 2002; most recently modified version published online March 2022).

单词	minimax
释义	minimaxn.adj. Brit. /ˈmɪnɪmaks/, U.S. /ˈmɪniˌmæks/ Origin: Perhaps of multiple origins. A borrowing from French. Perhaps also partly formed within English, by compounding. Etymon: French minimax. Etymology: In sense A. 1 < French minimax (H. Poincaré Méthodes Nouvelles de la Mécanique Céleste (1899) III. xxviii. 246: see below) < mini- (in minimum adj.) + max- (in maximum adj.). In subsequent senses perhaps re-formed independently in English. With sense B. 3 compare earlier min-max adj. and n.Poincaré says that he uses the word ‘à l'exemple des Anglais’, but earlier use has not been traced. Chiefly Mathematics. A. n. 1. A point in a topological space at which a function defined on the space is stationary (i.e. its first derivatives in all directions vanish at the point), and which has a local maximum in one direction and a local minimum in another. Also: the behaviour of a function at such a point. Cf. maximum n. 2, minimum n. 1. Now rare.For a function on a plane (i.e. one defining a surface in three-dimensional space) such a point is called a saddle point. ΚΠ 1917 Trans. Amer. Math. Soc. 18 240 If J₀ is the value of J at a point P₀ and if the inequality J < J₀ − ε where ε is small and positive defines more than one region near the point P₀, then P₀ will be called a point of minimax. 1931 Amer. Jrnl. Math. 53 169 It has been proved..that Ω(x,y) possesses a minimax at each of the libration points L₁, L₂ and L₃ and it accordingly follows that Ω(x,y) must have an absolute minimum at L₄ and L₅. 2. The smallest of a set of maxima. Also: a minimax strategy (see sense B. 3). ΚΠ 1958 Engineering 21 Mar. 369/2 Player B, on the other hand, will determine the largest value in each column, and the smallest of these, the ‘minimax’. 1962 Sci. Amer. Dec. 114/2 Both firms were guided by the principle of the minimax, choosing the best of the worst outcomes. 1968 Brit. Med. Bull. 24 232/2 This would be the Bayesian Strategy of decision theory.., but other strategies, such as minimax or restricted Bayes, could also be used. 1970 G. S. G. Beveridge & R. S. Schechter Optimization xii. 656 The value of P (and L) lies between the row maxi-min and the column mini-max. 1996 Economist 30 Mar. 96/2 At the other extreme, a hypercautious government would prefer ‘minimax’—the minimum of maximums. B. adj. 1. Designating or relating to a point in a space at which a function is stationary and has a local maximum in one direction and a local minimum in another. Now rare. ΘΚΠ the world > relative properties > number > mathematics > [adjective] > relating to mathematical property simple1570 dissevered1605 periodicala1690 irreductible1753 analytical1799 analytic1800 compound1806 well-conditioned1843 one-valued1884 non-empty1905 well-behaved1912 minimax1917 irredundant1925 non-linear1930 constructive1938 extremal1939 max-min1949 meta-analytic1968 meta-analytic1978 1917 G. D. Birkhoff in Proc. National Acad. Sci. U.S.A. 3 315 Another method may be employed to find a large class of stable periodic orbits which I call of minimax type. 1935 Amer. Jrnl. Math. 57 930 The minimum and minimax methods..establish immediately the existence of an infinite number of closed periodic orbits. 1940 Ann. Math. 41 419 The critical limits, such as absolute minima, relative minima, minimax values, etc., are in general infinite in number. 2. a. Designating or resulting in the smallest of a set of maxima. ΚΠ 1938 Amer. Jrnl. Math. 60 831 Let r be any integer such that H(r + 1) assumes the maximum of H(m). The R(n)-block [r + 1, r + R(n)] will then be termed a minimax n-covering in (a). 1940 Amer. Jrnl. Math. 62 237 Let s_n denote a value of s for which the maximum diameter of the sets G_s[t_e(n)] is a minimum,..and let this minimax diameter be d(n). 1951 Ann. Math. Statistics 22 466 The minimax risk is ½(1 − a). 1990 Glasgow Math. Jrnl. 32 267 If G is a finitely generated soluble-by-finite group of finite rank, then G is a finite extension of a soluble minimax group. b. Used predicatively. ΚΠ 1952 Ann. Math. Statistics 23 587 For such weight functions the supremum of the risk over all θ ε Ω is infinite for every decision function, so that every decision function is minimax. 1970 R. B. Ash Basic Probability Theory viii. 250 It is immediate from the definition of admissibility that an admissible test with constant risk (i.e., α = β) is minimax. 3. Designating or relating to a strategy that minimizes the greatest loss or risk to which a participant in a game or other situation of conflict will be liable. Also: designating the theorem which states that for a finite zero-sum game with two players, the smallest maximum loss that a player can choose to risk by a suitable choice of strategy is equal to the greatest minimum guaranteed gain. Cf. maximin adj. and n. ΘΚΠ the world > action or operation > prosperity > success > mastery or superiority > [adjective] > specific advantage minimax1947 maximin1949 zero-sum1965 1947 A. Wald in Econometrica 15 283 An element a₀ in A is said to be a minimax strategy of player 1 if Inf_b K(a, b) takes its maximum value with respect to a for a = a₀. 1949 Econometrica 17 230 Often Nature's strategy is completely unknown. In that case Wald suggests that the statistician play a minimax strategy: that is, the statistician should select that decision procedure which minimizes the maximum risk. 1957 R. D. Luce & H. Raiffa Games & Decisions i. 2 Although Borel gave a clear statement of an important class of game theoretic problems and introduced the concepts of pure and mixed strategies, von Neumann points out that he did not obtain one crucial result—the minimax theorem—without which no theory of games can be said to exist. 1978 M. Jevons Murder at Margin xiv. 138 If two people are charged with a crime and are separated by the police with no chance of their communicating, there are certain circumstances in which it would be rational for them to confess—even if they did not commit the crime. In economics this is called a minimax strategy. 1993 Personal Computer World July 539/1 Many of the best cognitive games programs have a mini-max algorithm lurking somewhere or other in their innards. This entry has been updated (OED Third Edition, March 2002; most recently modified version published online March 2022). minimaxv. Brit. /ˈmɪnɪmaks/, U.S. /ˈmɪnɪˌmæks/ Origin: Formed within English, by conversion. Etymon: minimax n. Etymology: < minimax n. Chiefly Mathematics. transitive. To make equal to a minimax value. Also intransitive: to adopt a minimax strategy. ΚΠ 1957 Jrnl. Soc. Industr. & Appl. Math. 5 109 Our formulation of the problem includes the possibility of minimaxing some measure of inaccuracy. 1957 Jrnl. Soc. Industr. & Appl. Math. 5 121 The loss L which is to be minimaxed is the number of observations required before stopping. 1964 J. Gould & W. L. Kolb Dict. Social Sci. 573/2 The goal may be assumed to take the form of maximizing (or, in game theory, minimaxing) the expected value, over some time interval, of a utility function. 1985 Ann. Statistics 13 1094 The statistical problem of minimaxing V(ψ,f) over Ψ_r × ℱ is meaningless unless the least informative member F₀ has positive information. This entry has been updated (OED Third Edition, March 2002; most recently modified version published online March 2022). < n.adj.1917v.1957
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minimaxn.adj.

minimaxv.