{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,30]],"date-time":"2024-07-30T21:55:03Z","timestamp":1722376503097},"reference-count":20,"publisher":"Institute for Operations Research and the Management Sciences (INFORMS)","issue":"6","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["INFORMS Journal on Computing"],"published-print":{"date-parts":[[2022,11]]},"abstract":" We present a gradient-based algorithm for solving a class of simulation optimization problems in which the objective function is the quantile of a simulation output random variable. In contrast with existing quantile (quantile derivative) estimation techniques, which aim to eliminate the estimator bias by gradually increasing the simulation sample size, our algorithm incorporates a novel recursive procedure that only requires a single simulation sample at each step to simultaneously obtain quantile and quantile derivative estimators that are asymptotically unbiased. We show that these estimators, when coupled with the standard gradient descent method, lead to a multitime-scale stochastic approximation type of algorithm that converges to an optimal quantile value with probability one. In our numerical experiments, the proposed algorithm is applied to optimal investment portfolio problems, resulting in new solutions that complement those obtained under the classical Markowitz mean-variance framework. <\/jats:p> History: Accepted by Alice E. Smith, Editor-in-Chief; Bruno Tuffin, Area Editor for Simulation. <\/jats:p> Funding: The work of Y. Peng was supported in part by the National Natural Science Foundation of China (NSFC) [Grants 72022001, 92146003, and 71901003], and by the Key Research and Development Programof Beijing Municipal Science and Technology Commission. <\/jats:p> Supplemental Material: The e-companion is available at https:\/\/doi.org\/10.1287\/ijoc.2022.1214 . <\/jats:p>","DOI":"10.1287\/ijoc.2022.1214","type":"journal-article","created":{"date-parts":[[2022,7,22]],"date-time":"2022-07-22T09:42:51Z","timestamp":1658482971000},"page":"2889-2907","source":"Crossref","is-referenced-by-count":7,"title":["A Stochastic Approximation Method for Simulation-Based Quantile Optimization"],"prefix":"10.1287","volume":"34","author":[{"ORCID":"http:\/\/orcid.org\/0000-0002-9999-672X","authenticated-orcid":false,"given":"Jiaqiao","family":"Hu","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics and Statistics, State University of New York at Stony Brook, Stony Brook, New York 11794;"}]},{"ORCID":"http:\/\/orcid.org\/0000-0003-2584-8131","authenticated-orcid":false,"given":"Yijie","family":"Peng","sequence":"additional","affiliation":[{"name":"Department of Management Science and Information Systems, Guanghua School of Management Peking University, Beijing 100871, China"}]},{"given":"Gongbo","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Management Science and Information Systems, Guanghua School of Management Peking University, Beijing 100871, China"}]},{"given":"Qi","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics and Statistics, State University of New York at Stony Brook, Stony Brook, New York 11794;"}]}],"member":"109","reference":[{"key":"B1","doi-asserted-by":"publisher","DOI":"10.1145\/1044322.1044326"},{"key":"B2","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-6911(97)90015-3"},{"key":"B3","doi-asserted-by":"publisher","DOI":"10.1007\/978-93-86279-38-5"},{"key":"B5","volume-title":"Linear Operators, Part 1","author":"Dunford N","year":"1966"},{"key":"B6","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.1090.1090"},{"key":"B7","doi-asserted-by":"publisher","DOI":"10.1287\/moor.2015.0728"},{"key":"B8","doi-asserted-by":"publisher","DOI":"10.1287\/opre.1080.0531"},{"key":"B9","doi-asserted-by":"publisher","DOI":"10.1287\/opre.2015.1356"},{"key":"B10","doi-asserted-by":"publisher","DOI":"10.1007\/BF02204810"},{"key":"B11","doi-asserted-by":"publisher","DOI":"10.1007\/s10479-011-0987-z"},{"key":"B12","doi-asserted-by":"publisher","DOI":"10.1134\/S0005117913060064"},{"key":"B14","volume-title":"Stochastic Approximation and Recursive Algorithms and Applications","author":"Kushner HJ","year":"1997"},{"key":"B15","doi-asserted-by":"publisher","DOI":"10.1007\/s10626-017-0247-8"},{"key":"B16","doi-asserted-by":"publisher","DOI":"10.1002\/nav.20358"},{"issue":"1","key":"B17","first-page":"77","volume":"7","author":"Markowitz HM","year":"1952","journal-title":"J. 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