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arXiv · 2304.04380

A sequential quadratic programming method for nonsmooth stochastic optimization with upper-C^2 objective

J. Wang·I. Aravena·C. G. Petra
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Abstract

We propose a sequential quadratic programming (SQP) method that can incorporate adaptive sampling for stochastic nonsmooth nonconvex optimization problems with upper-C^2 objectives. Upper-$\Ctwo$ functions can be viewed as difference-of-convex (DC) functions with smooth convex parts. They are common among certain classes of solutions to parametric optimization problems, e.g., recourse of stochastic programming and closest-point projection onto closed sets. Our proposed algorithm is a stochastic SQP with line search and bounded algorithmic parameters and is shown to achieve subsequential convergence in expectation for nonsmooth problems with upper-C^2 objectives. We discuss various sampling strategies, including an adaptive sampling one, that can potentially improve algorithm efficiency. The capabilities of our algorithm are demonstrated by solving a joint production, pricing and shipment problem, as well as a realistic optimal power flow problem as used in current power grid industry practice.

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J. Wang, I. Aravena, C. G. Petra. 2023-04-10. A sequential quadratic programming method for nonsmooth stochastic optimization with upper-C^2 objective. https://arxiv.org/abs/2304.04380

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