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- W2014760774 abstract "A METHOD possessing quadratic convergence is described, for minimizing a maximum function on a set specified by a system of inequalities. The method is effective in the neighbourhood of a stationary point, and can therefore be recommended for the final stage of computations. Its “sphere of efficiency” may be reached by using any method which converges to the stationary point. The various methods now available for finding the minima of a maximum function are all essentially of the first order (they utilize the first directional derivatives in order to discover the direction of descent). Like all first-order methods, they converge slowly in the vicinity of the minimum. When minimizing in En a continuously differentiable function, some rapidly convergent method, possessing quadratic convergence (e.g. Newton's method), is used at the final stage. The present paper aims at developing a method with quadratic convergence, representing an extension of the method of maxima equalization [1], for minimizing a maximum function on a set specified by a system of inequalities. The method is effective in the neighbourhood of a stationary point and may there-fore be recommended for the final stage of computations. Its “sphere of effectiveness” may be reached by using any method converging to the stationary point." @default.
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- W2014760774 date "1972-01-01" @default.
- W2014760774 modified "2023-09-27" @default.
- W2014760774 title "Acceleration of convergence when solving minimax problems" @default.
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- W2014760774 doi "https://doi.org/10.1016/0041-5553(72)90065-1" @default.
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