Abstracts

Lightweight Constrained Stochastic Optimization

Ketan Rajawat,  IIT Kanpur

Many problems in signal processing, wireless communications, and robotics require solving stochastic nonconvex optimization problems with nonlinear functional constraints. Although stochastic first-order methods are scalable, nonlinear constraints make projection-based approaches computationally expensive, since each projection may require solving a difficult constrained problem. This talk presents a unified class of lightweight prox-linear algorithms that handle such constraints through an exact-penalty reformulation followed by local linearization of the penalized constraints. The resulting methods generate simple convex updates while avoiding projections, nonlinear constrained subproblems, and explicit dual updates, requiring only stochastic gradients and first-order constraint information. A central theoretical component is a proximity-based equivalence result showing that, under suitable nondegeneracy conditions, near-stationarity of the penalized problem implies proximity-based near-optimality/KKT stationarity of the original constrained problem. Building on this principle, we discuss several algorithms, including SCAMPL, D-SMPL, and D-SCAMPL, covering both centralized and decentralized settings. These algorithms achieve the state-of-the-art O(ϵ^−3/2) stochastic first-order oracle complexity and provide efficient solutions for constrained optimization in communications and robotics.