Inequality Constrained Stochastic Nonlinear Optimization via Active-Set Sequential Quadratic Programming

Abstract

We study nonlinear optimization problems with 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, using a differentiable exact augmented Lagrangian as the merit function. The algorithm adaptively selects the penalty parameters of augmented Lagrangian and performs stochastic line search to decide the stepsize. The global convergence is established: for any initialization, the “liminf” of the KKT residuals converges to zero almost surely. Our algorithm and analysis further develop the prior work Na et al. (2021) by allowing nonlinear inequality constraints. We demonstrate the performance of the algorithm on a subset of nonlinear problems collected in the CUTEst test set.

Sen Na

PhD (2016-2021)

Sen Na was a PhD student in the Department of Statistics at The University of Chicago. Prior to graduate school, he obtained BS in mathematics at Nanjing University, China. His research interests lie in nonlinear and nonconvex optimization, dynamic programming, high-dimensional statistics and their interface.

Mladen Kolar

Associate Professor of Econometrics and Statistics

Mladen Kolar is an Associate Professor of Econometrics and Statistics at the University of Chicago Booth School of Business. His research is focused on high-dimensional statistical methods, graphical models, varying-coefficient models and data mining, driven by the need to uncover interesting and scientifically meaningful structures from observational data.