AI & ML
RALES: A Risk-Averse Augmented Lagrangian Equality-Constrained SQP Method
arXiv cs.NA0 views
arXiv:2611.13201v1 Announce Type: cross Abstract: This paper develops RALES, an augmented Lagrangian method for risk-averse optimization in function spaces with nonsmooth risk measures, nonlinear equality constraints, and convex geometric constraints. The method combines safeguarded risk and constraint multiplier updates with efficient sequential quadratic programming based on inexact subproblem solves. The analysis establishes asymptotic stationarity for nonconvex problems and gives conditions for feasibility of weak primal accumulation points. Under additional assumptions on subproblem accuracy, duality, and boundedness, it provides global primal optimality guarantees and weak convergence of the full stored and candidate multiplier sequences to a common dual maximizer. Dual convergence is strong when all penalty parameters remain bounded. Numerical experiments for a finitely sampled semilinear PDE control problem, with the Conditional Value-at-Risk and the Mean-Plus-Semideviation risk measures, illustrate the method's performance as the spatial mesh is refined and as the number of samples increases.
Source:https://arxiv.org/abs/2611.13201PreviousA constrained mixed variational formulation with Legendre-dual defects for incremental irreversible thermodynamicsNextFP64 Performance and the Limits of Ozaki Emulation on HPC Systems
Related posts
I wanted one screen that said whether a kids' app was worth installing
0dev.to

Before I Could Build GPT, I Had to Teach a Machine to Learn
0dev.to
Cogent and OpenAI build cyber defense factories for enterprises
0OpenAI Blog
ChatGPT Plus for veterans and servicemembers
0OpenAI Blog
Hitting 200 Strokes: What the Signature Maker Does at Its Stroke Limit
0dev.to
A Lightweight, Open-Source Network Digital Twin Blueprint for IoT-Edge Environments
0arXiv cs.NI