Inequality Constrained Stochastic Nonlinear Optimization via Active-Set Sequential Quadratic Programming. (arXiv:2109.11502v2 [math.OC] UPDATED)

We study nonlinear optimization problems with a stochastic objective and
deterministic equality and inequality constraints, which emerge in numerous
applications including finance, manufacturing, power systems and, recently,
deep neural networks. We propose an active-set stochastic sequential quadratic
programming algorithm that uses a differentiable exact augmented Lagrangian as
the merit function. The algorithm adaptively selects the penalty parameters of
the augmented Lagrangian, and performs stochastic line search to decide the
stepsize. The global convergence is established: for any initialization, the
"liminf" …

arxiv inequality math optimization programming stochastic