Penalty Functions and Duality in Stochastic Programming Via ϕ-Divergence Functionals

The paper considers stochastically constrained nonlinear programming problems. A penalty function is constructed in terms of a “distance” between random variables, defined in terms of the ϕ-divergence functional (a generalization of the relative entropy). A duality theory is developed in which a general relation between ϕ-divergence and utility functions is revealed, via the conjugate transform, and a new type of certainty equivalent concept emerges.