@article{7596bcdd255a4fc0948993e3e928184e,
title = "A sequential algorithm for solving nonlinear optimization problems with chance constraints∗ ",
abstract = "An algorithm is presented for solving nonlinear optimization problems with chance constraints, i.e., those in which a constraint involving an uncertain parameter must be satisfied with at least a minimum probability. In particular, the algorithm is designed to solve cardinality-constrained nonlinear optimization problems that arise in sample average approximations of chance-constrained problems, as well as in other applications in which it is only desired to enforce a minimum number of constraints. The algorithm employs a novel exact penalty function which is minimized sequentially by solving quadratic optimization subproblems with linear cardinality constraints. Properties of minimizers of the penalty function in relation to minimizers of the corresponding nonlinear optimization problem are presented, and convergence of the proposed algorithm to stationarity with respect to the penalty function is proved. The effectiveness of the algorithm is demonstrated through numerical experiments with a nonlinear cash flow problem.",
keywords = "Cardinality constraints, Chance constraints, Exact penalization, Nonlinear optimization, Sample average approximation, Sequential quadratic optimization, Trust region methods",
author = "Curtis, {Frank E.} and Andreas W{\"a}chter and Zavala, {Victor M.}",
note = "Funding Information: The first author{\textquoteright}s research was partially supported by U.S. Department of Energy grant DE-SC0010615 and U.S. National Science Foundation grant DMS-1319356. The second author{\textquoteright}s research was partially supported by U.S. National Science Foundation grant DMS-1522747. The third author{\textquoteright}s research was partially supported by U.S. Department of Energy grant DE-SC0014114. Funding Information: ∗Received by the editors August 18, 2016; accepted for publication (in revised form) January 8, 2018; published electronically March 29, 2018. http://www.siam.org/journals/siopt/28-1/M109003.html Funding: The first author{\textquoteright}s research was partially supported by U.S. Department of Energy grant DE-SC0010615 and U.S. National Science Foundation grant DMS-1319356. The second author{\textquoteright}s research was partially supported by U.S. National Science Foundation grant DMS-1522747. The third author{\textquoteright}s research was partially supported by U.S. Department of Energy grant DESC0014114. †Department of Industrial and Systems Engineering, Lehigh University, Bethlehem, PA 18015 (frank.e.curtis@gmail.com). ‡Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, IL 60208 (waechter@iems.northwestern.edu). §Department of Chemical and Biological Engineering, University of Wisconsin-Madison, Madison, WI 53706 (victor.zavala@wisc.edu). Publisher Copyright: c 2018 Society for Industrial and Applied Mathematics",
year = "2018",
doi = "10.1137/16M109003X",
language = "English (US)",
volume = "28",
pages = "930--958",
journal = "SIAM Journal on Optimization",
issn = "1052-6234",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "1",
}