minimax

(redirected from Minmax)
Also found in: Dictionary.

minimax

[′min·ə‚maks]
(mathematics)
The minimum of a set of maxima.
In the theory of games, the smallest of a set of maximum possible losses, each representing the most unfavorable outcome of a particular strategy.

Minimax

 

in mathematics, the value of the expression

of a real function f(x,y) of two variables. The concept of maximin equal to maxy minxf(x, y) is related to the concept of minimax. In the theory of zero-sum games, the fundamental optimality principle is the minimax principle, which consists in the attempt of a player to minimize his loss, assuming that his opponent’s strategy takes the most unfavorable form.

minimax

(games)
An algorithm for choosing the next move in a two player game. A player moves so as to maximise the minimum value of his opponent's possible following moves. If it is my turn to move, I give a value to each legal move I might make. If the result of a move is an immediate win for me I give it positive infinity and, if it is an immediate win for you, negative infinity. The value to me of any other move is the minimum of the values resulting from each of your possible replies.

The above algorithm will give every move a value of positive or negative infinity since the value of every move will be the value of some final winning or losing move. This can be extended if we can supply a heuristic evaluation function which gives values to non-final game states without considering all possible following complete sequences. We can then limit the minimax algorithm to look only a certain number of moves ahead. This number is called the "look-ahead" or "ply".

See also alpha/beta pruning.

References in periodicals archive ?
Interpolating in these points will yield good polynomial approximants for the geometry, compared to the minmax polynomial approximant.
Zalmai and Qinghong Zhang: Optimality conditions and duality in minmax fractional programming, part I: necessary and sufficient optimality conditions, J.
This is the so-called minmax D-optimal design (Gaylor and Sweeny 1978), here referred to as D1.
Minmax industrial-grade nylon 6 and 6,6 resin comes in either black or a wide range of neutral colors.
Company sources say new Minmax resins are not based on recycled materials but do contain some off-spec resin.
Zalmai: Generalized ([eta], [rho])-invex functions and parametric duality models for discrete minmax fractional programming problems containing arbitrary norms, Southeast Asian Bull.
Sylvester [19], and several different proofs can be found in textbooks [3, 6, 11, 13, 15], one of which is based on the minmax characterization of eigenvalues of Hermitian matrices.
The minmax setup and solution of the problem of optimal load scheduling in the hydro-thermal power system under uncertain information are described in [9].
0: -- Dozens of new accelerated effects, including unique ICE-developed filters such as ICE'd Unsharp Mask, ICE'd MinMax, ICE'd Channel Blur, and more - and popular ICE'd Final Effects Complete filters for such treatments as explosions, distortions and transition effects.
The second and more sophisticated approach is to solve a minmax problem to determine local operators that optimize the convergence speed over the full range of admissible frequencies [[[omega].
In this paper, we present a set of necessary optimality conditions and a multitude of global parametric sufficient optimality results under a variety of generalized (F, b, [phi], [rho], [theta])univexity conditions for the following continuous minmax fractional programming problem involving nondifferentiable functions:
The first eight filters to be made available to users are Gaussian Blur, Unconstrained Gaussian Blur, Dolly Blur, Pan Blur, Lens flare, Twirl, MinMax, 3D depth of field