{"ID":2836895,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.20178","arxiv_id":"2511.20178","title":"Stochastic Sequential Quadratic Programming for Optimization with Functional Constraints","abstract":"Stochastic convex optimization problems with nonlinear functional constraints are ubiquitous in signal processing applications including constrained least-squares, set-membership adaptive filtering, and trajectory optimization under uncertain fields. The presence of nonlinear functional constraints renders traditional projected stochastic gradient descent and related projection-based methods inefficient, and motivates the use of first-order methods. However, existing first-order methods, including primal and primal-dual algorithms, typically rely on a bounded (sub-)gradient assumption, which may be too restrictive in high-dimensional settings. We propose a stochastic sequential quadratic programming (SSQP) algorithm that works entirely in the primal domain, avoids projecting onto the feasible region, obviates the need for bounded gradients, and achieves state-of-the-art oracle complexity under standard smoothness and convexity assumptions. A faster version, namely SSQP-Skip, is also proposed, where the quadratic sub-problems can be skipped in most iterations. Finally, we develop an accelerated variance-reduced version of SSQP (VARAS), whose oracle complexity bounds match those for solving unconstrained finite-sum convex optimization problems. The superior performance of the proposed algorithms is demonstrated via numerical experiments on real datasets.","short_abstract":"Stochastic convex optimization problems with nonlinear functional constraints are ubiquitous in signal processing applications including constrained least-squares, set-membership adaptive filtering, and trajectory optimization under uncertain fields. The presence of nonlinear functional constraints renders traditional...","url_abs":"https://arxiv.org/abs/2511.20178","url_pdf":"https://arxiv.org/pdf/2511.20178v2","authors":"[\"Panchajanya Sanyal\",\"Srujan Teja Thomdapu\",\"Ketan Rajawat\"]","published":"2025-11-25T11:00:22Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}