Maxmin subject to marginal constraints (Q1905227)

A nonsmooth semi-infinite programming problem is investigated where a minimum-function is maximized. (Note that this is equivalent to an ordinary semi-infinite programming problem if the additional variable is maximized subject to infinite constraints: to be not more than the minimized function for every value of minimizing variable.) The minimum-function is assumed to be strictly concave and the constraint functions are also concave with respect to the maximizing variable. The constraints are assumed to have nonempty interior. Some speculative examples of such problems are considered. In order to solve the problem numerically, an algorithm of stochastic quasi-gradient method with infinitesimal stepsize is suggested. The algorithm is proved to converge with probability equal 1.