Stochastic optimization techniques for finding optimal submeasures

In this paper, the author looks at some quite general optimization problems on the space of probabilistic measures. These problems originated in mathematical statistics but have applications in several other areas of mathematical analysis. The author extends previous work by considering a more general form of the constraints, and develops numerical methods (based on stochastic quasigradient techniques) and some duality relations for problems of this type. This paper is a contribution to research on stochastic optimization currently underway within the Adaptation and Optimization Project.