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Optim."],"published-print":{"date-parts":[[2026,3,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>In this paper, we study a class of deterministically constrained stochastic nonconvex optimization problems. Existing methods typically aim to find an [Formula: see text]- expectedly feasible stochastic stationary point, where the expected violations of both constraints and first-order stationarity are within a prescribed tolerance [Formula: see text]. However, in many practical applications, it is crucial that the constraints be nearly satisfied with certainty, making such an [Formula: see text]-stochastic stationary point potentially undesirable due to the risk of substantial constraint violations. To address this issue, we propose single-loop variance-reduced stochastic first-order methods, where the stochastic gradient of the stochastic component is computed using either a truncated recursive momentum scheme or a truncated Polyak momentum scheme for variance reduction, while the gradient of the deterministic component is computed exactly. Under the error bound condition with a parameter [Formula: see text] and\u00a0other suitable assumptions, we establish that these methods respectively achieve sample complexity and first-order oracle complexity of [Formula: see text] and [Formula: see text] for finding an [Formula: see text]- surely feasible stochastic stationary point ([Formula: see text] represents [Formula: see text] with logarithmic factors hidden), where the constraint violation is within [Formula: see text] with certainty, and the expected violation of first-order stationarity is within [Formula: see text]. For [Formula: see text], these complexities reduce to [Formula: see text] and [Formula: see text],\u00a0respectively, which match, up to a logarithmic factor, the best-known complexities achieved by existing methods for finding an [Formula: see text]-stochastic stationary point of unconstrained smooth stochastic nonconvex optimization problems.<\/jats:p>","DOI":"10.1137\/24m1693933","type":"journal-article","created":{"date-parts":[[2026,1,2]],"date-time":"2026-01-02T08:07:27Z","timestamp":1767341247000},"page":"1-31","source":"Crossref","is-referenced-by-count":0,"title":["Variance-Reduced First-Order Methods for Deterministically Constrained Stochastic Nonconvex Optimization with Strong Convergence Guarantees"],"prefix":"10.1137","volume":"36","author":[{"given":"Zhaosong","family":"Lu","sequence":"first","affiliation":[{"name":"Department of Industrial and Systems Engineering, University of Minnesota, Minneapolis, MN 55455 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sanyou","family":"Mei","sequence":"additional","affiliation":[{"name":"Department of Industrial Engineering and Decision Analytics, the Hong Kong University of Science and Technology, Hong Kong, China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yifeng","family":"Xiao","sequence":"additional","affiliation":[{"name":"Department of Industrial and Systems Engineering, University of Minnesota, Minneapolis, MN 55455 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2026,1,2]]},"reference":[{"key":"ref1","unstructured":"A. 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