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Optim."],"published-print":{"date-parts":[[2026,6,30]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>We consider the minimization of a Lipschitz continuous and expectation-valued function, denoted by [Formula: see text] and defined as [Formula: see text], over a closed and convex set [Formula: see text]. Our focus lies on - both deriving asymptotics as well as obtaining rate and complexity guarantees for computing an approximate stationary point (in a Clarke sense) via zeroth-order schemes. We adopt a smoothing-based approach reliant on minimizing [Formula: see text],\u00a0where [Formula: see text], [Formula: see text] is a random variable defined on a unit sphere, and [Formula: see text]. In fact, it has been observed that a stationary point of the [Formula: see text]-smoothed problem is an [Formula: see text]-stationary point for the original problem in the Clarke sense. In such a setting, we develop two sets of schemes with promising empirical behavior. (I) We develop a smoothing-enabled variance-reduced zeroth-order gradient framework for minimizing [Formula: see text] over [Formula: see text]. In this setting, we make two sets of contributions for the sequence generated by the proposed zeroth-order gradient scheme. (a) The residual function of the smoothed problem tends to zero almost surely along the generated sequence, allowing for making guarantees for [Formula: see text]-Clarke stationary solutions of the original problem. (b) To compute an [Formula: see text] that ensures that the expected norm of the residual of the [Formula: see text]-smoothed problem is within [Formula: see text] requires no greater than [Formula: see text] projection steps and [Formula: see text] function evaluations. (II) Our second scheme is a zeroth-order stochastic quasi-Newton scheme reliant on a combination of randomized and Moreau smoothing; the corresponding iteration and sample complexities for this scheme are [Formula: see text] and [Formula: see text], respectively. These statements appear to be novel in the case of both constrained problems as well as in stochastic quasi-Newton settings, as there appear to be few available results that can contend with general nonsmooth, nonconvex, and stochastic regimes via zeroth-order approaches.<\/jats:p>","DOI":"10.1137\/23m1626724","type":"journal-article","created":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T08:00:24Z","timestamp":1775116824000},"page":"564-596","source":"Crossref","is-referenced-by-count":0,"title":["Zeroth-Order Gradient and Quasi-Newton Methods for Nonsmooth Nonconvex Stochastic Optimization"],"prefix":"10.1137","volume":"36","author":[{"given":"Luke","family":"Marrinan","sequence":"first","affiliation":[{"name":"Industrial and Manufacturing Engineering, Pennsylvania State University, University Park, PA 16802-4400 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5869-9561","authenticated-orcid":true,"given":"Uday V.","family":"Shanbhag","sequence":"additional","affiliation":[{"name":"Industrial and Operations Engineering, University of Michigan at Ann Arbor, Ann Arbor, MI 48109 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2628-741X","authenticated-orcid":true,"given":"Farzad","family":"Yousefian","sequence":"additional","affiliation":[{"name":"Industrial and Systems Engineering, Rutgers University, Piscataway, NJ 08854 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2026,4,2]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1007\/s10208-021-09499-8"},{"key":"ref2","doi-asserted-by":"crossref","unstructured":"A. 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