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Program."],"published-print":{"date-parts":[[2023,11]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We study nonlinear optimization problems with a stochastic objective and deterministic equality and inequality constraints, which emerge in numerous applications including finance, manufacturing, power systems and, recently, deep neural networks. We propose an active-set stochastic sequential quadratic programming (StoSQP) algorithm that utilizes a differentiable exact augmented Lagrangian as the merit function. The algorithm adaptively selects the penalty parameters of the augmented Lagrangian, and performs a stochastic line search to decide the stepsize. The global convergence is established: for any initialization, the KKT residuals converge to zero <jats:italic>almost surely<\/jats:italic>. Our algorithm and analysis further develop the prior work of Na et al. (Math Program, 2022. <jats:ext-link xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" ext-link-type=\"doi\" xlink:href=\"10.1007\/s10107-022-01846-z\">https:\/\/doi.org\/10.1007\/s10107-022-01846-z<\/jats:ext-link>). Specifically, we allow nonlinear inequality constraints <jats:italic>without<\/jats:italic> requiring the strict complementary condition; refine some of designs in Na et al. (2022) such as the feasibility error condition and the monotonically increasing sample size; strengthen the global convergence guarantee; and improve the sample complexity on the objective Hessian. We demonstrate the performance of the designed algorithm on a subset of nonlinear problems collected in CUTEst test set and on constrained logistic regression problems.\n<\/jats:p>","DOI":"10.1007\/s10107-023-01935-7","type":"journal-article","created":{"date-parts":[[2023,3,2]],"date-time":"2023-03-02T16:04:01Z","timestamp":1677773041000},"page":"279-353","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":21,"title":["Inequality constrained stochastic nonlinear optimization via active-set sequential quadratic programming"],"prefix":"10.1007","volume":"202","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7977-5276","authenticated-orcid":false,"given":"Sen","family":"Na","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mihai","family":"Anitescu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mladen","family":"Kolar","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2023,3,2]]},"reference":[{"issue":"3","key":"1935_CR1","doi-asserted-by":"publisher","first-page":"1238","DOI":"10.1137\/130915984","volume":"24","author":"AS Bandeira","year":"2014","unstructured":"Bandeira, A.S., Scheinberg, K., Vicente, L.N.: Convergence of trust-region methods based on probabilistic models. 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