Stochastic Control With Affine Dynamics and Extended Quadratic Costs

An extended quadratic function is a quadratic function plus the indicator function of an affine set, i.e., a quadratic function with embedded linear equality constraints. In this article, we show that, under some technical conditions, random convex extended quadratic functions are closed under addition, composition with an affine function, expectation, and partial minimization, i.e., minimizing ov...