A stochastic algorithm for extremum search, optimal in one step

Abstract

CONSTRUCTION of a one-step optimal algorithm of random search for the global maximum of a function of one varible, satisfying a Lipschitz condition, is reduced to the solution of a game in the unit square. The solution of this game is in turn reduced to the solution of a matrix game. The optimal strategies for the matrix games are found in explicit form, thus enabling a computer-realizable algorithm of global optimization to be constructed.