A stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs

Simple item page
dc.contributor.authorKannan, Rohiten
dc.contributor.authorLuedtke, James R.en
dc.date.accessioned2025-02-18T13:12:09Zen
dc.date.available2025-02-18T13:12:09Zen
dc.date.issued2021-01-23en
dc.description.abstractWe propose a stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs. Our approach is based on a bi-objective viewpoint of chance-constrained programs that seeks solutions on the efficient frontier of optimal objective value versus risk of constraints violation. To this end, we construct a reformulated problem whose objective is to minimize the probability of constraints violation subject to deterministic convex constraints (which includes a bound on the objective function value). We adapt existing smoothing-based approaches for chance-constrained problems to derive a convergent sequence of smooth approximations of our reformulated problem, and apply a projected stochastic subgradient algorithm to solve it. In contrast with exterior sampling-based approaches (such as sample average approximation) that approximate the original chance-constrained program with one having finite support, our proposal converges to stationary solutions of a smooth approximation of the original problem, thereby avoiding poor local solutions that may be an artefact of a fixed sample. Our proposal also includes a tailored implementation of the smoothing-based approach that chooses key algorithmic parameters based on problem data. Computational results on four test problems from the literature indicate that our proposed approach can efficiently determine good approximations of the efficient frontier.en
dc.description.versionAccepted versionen
dc.format.extentPages 705-751en
dc.format.extent47 page(s)en
dc.format.mimetypeapplication/pdfen
dc.identifier.doihttps://doi.org/10.1007/s12532-020-00199-yen
dc.identifier.eissn1867-2957en
dc.identifier.issn1867-2949en
dc.identifier.issue4en
dc.identifier.orcidKannan, Rohit [0000-0002-7963-7682]en
dc.identifier.urihttps://hdl.handle.net/10919/124622en
dc.identifier.volume13en
dc.language.isoenen
dc.publisherSpringeren
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectStochastic approximationen
dc.subjectChance constraintsen
dc.subjectEfficient frontieren
dc.subjectStochastic subgradienten
dc.titleA stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programsen
dc.title.serialMathematical Programming Computationen
dc.typeArticle - Refereeden
dc.type.dcmitypeTexten
dc.type.otherArticleen
dc.type.otherJournalen
pubs.organisational-groupVirginia Techen
pubs.organisational-groupVirginia Tech/Engineeringen
pubs.organisational-groupVirginia Tech/Engineering/Industrial and Systems Engineeringen
pubs.organisational-groupVirginia Tech/All T&R Facultyen
pubs.organisational-groupVirginia Tech/Engineering/COE T&R Facultyen

Files

Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
A stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs.pdf
Size:
2.07 MB
Format:
Adobe Portable Document Format
Description:
Accepted version
Download
License bundle
Now showing 1 - 1 of 1
Name:
license.txt
Size:
1.5 KB
Format:
Plain Text
Description:
Download

Collections

All Faculty Deposits
Scholarly Works, Industrial and Systems Engineering