In this paper, a robust sequential quadratic programming method of Burke and Han (Math Programming, 1989) for constrained optimization is generalized to problem with stochastic objective function, deterministic equality and inequality constraints. A stochastic line search scheme in Paquette and Scheinberg (SIOPT, 2020) is employed to globalize the steps.
We show that in the case where the algorithm fails to terminate in finite number of iterations, the sequence of iterates will converge almost surely to a Karush-Kuhn-Tucker point under the assumption of extended Mangasarian-Fromowitz constraint qualification.We also show that, with a specific sampling method, the probability of the penalty parameter approaching infinity is 0. Encouraging numerical results are reported.
View A Sequential Quadratic Programming Method for Optimization with Stochastic Objective Functions, Deterministic Inequality Constraints and Robust Subproblems