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Optim."],"published-print":{"date-parts":[[2026,9,30]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>We discuss in this paper uniform exponential convergence of sample average approximation (SAA) with adaptive multiple importance sampling (AMIS) and asymptotics of its optimal value. Using a concentration inequality for bounded martingale differences, we obtain a new exponential convergence rate. To study the asymptotics, we first derive an important functional central limit theorem for martingale difference sequences. Subsequently, exploiting this result with the Delta theorem, we prove the asymptotics of optimal values for SAA with AMIS.<\/jats:p>","DOI":"10.1137\/24m1695129","type":"journal-article","created":{"date-parts":[[2026,7,7]],"date-time":"2026-07-07T07:00:58Z","timestamp":1783407658000},"page":"1326-1355","source":"Crossref","is-referenced-by-count":0,"title":["Uniform Exponential Convergence of SAA with AMIS and Asymptotics of Its Optimal Value"],"prefix":"10.1137","volume":"36","author":[{"given":"Wenjin","family":"Zhang","sequence":"first","affiliation":[{"name":"College of Mathematics, Jilin University, Changchun, People\u2019s Republic of China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yong","family":"Li","sequence":"additional","affiliation":[{"name":"College of Mathematics, Jilin University; and Center for Mathematics and Interdisciplinary Sciences and School of Mathematics and Statistics, Northeast Normal University, Changchun, People\u2019s Republic of China."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2026,7,7]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600012780"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-69033-9"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1109\/MSP.2017.2699226"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1137\/21M145536X"},{"key":"ref5","volume-title":"Optimization and Nonsmooth Analysis","author":"Clarke F. 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