AI RESEARCH
High Probability Complexity Bounds of Trust-Region Stochastic Sequential Quadratic Programming with Heavy-Tailed Noise
arXiv CS.LG
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ArXi:2503.19091v3 Announce Type: replace-cross In this paper, we consider nonlinear optimization problems with a stochastic objective and deterministic equality constraints. We propose a Trust-Region Stochastic Sequential Quadratic Programming (TR-SSQP) method and establish its high-probability iteration complexity bounds for identifying first- and second-order $\epsilon$-stationary points. In our algorithm, we assume that exact objective values, gradients, and Hessians are not directly accessible but can be estimated via zeroth-, first-, and second-order probabilistic oracles.