A Stochastic Algorithm for Finding Points Satisfying Infinitely Many Inequality Constraints

Abstract

An optimization algorithm for finding a point satisfying infinitely many inequality constraints is presented. The algorithm approximates the maximum of an infinite number of inequalities at a point by performing a set of random experiments, resulting in a finite number of inequalities, over which the maximum is taken. It uses a constraint-dropping scheme, by which it eliminates points from a constraint-set at hand, which are felt to be irrelevant. At each point the algorithm constructs, it evaluates a measure of optimality, which indicates how close the point is to satisfying all of the constraints. It uses this measure to determine the number of random experiments performed. The number of such experiments tends to be small initially, when the point at hand is far from satisfying all of the constraints, and it increases gradually as a solution point is approached.