Distributionally robust optimization: a novel approach with decision-dependent ambiguity sets and an application to mode estimation

Este trabajo fue elaborado como uno de los requisitos para obtener el título de doctor en matemáticas. Adicionalmente, la investigación desarrollada no presenta ningún tipo de conflicto de intereses.

Autores:
Fonseca Valero, Diego Fernando
Tipo de recurso:
Doctoral thesis
Fecha de publicación:
2023
Institución:
Universidad de los Andes
Repositorio:
Séneca: repositorio Uniandes
Idioma:
eng
OAI Identifier:
oai:repositorio.uniandes.edu.co:1992/69263
Acceso en línea:
http://hdl.handle.net/1992/69263
Palabra clave:
Distributionally robust optimization
Wasserstein metric
Conditional value at risk
Stochastic optimization
Matemáticas
Rights
openAccess
License
Attribution-NonCommercial-NoDerivatives 4.0 Internacional
id UNIANDES2_c96fe119add8437e5690db1f637eb33f
oai_identifier_str oai:repositorio.uniandes.edu.co:1992/69263
network_acronym_str UNIANDES2
network_name_str Séneca: repositorio Uniandes
repository_id_str
dc.title.none.fl_str_mv Distributionally robust optimization: a novel approach with decision-dependent ambiguity sets and an application to mode estimation
title Distributionally robust optimization: a novel approach with decision-dependent ambiguity sets and an application to mode estimation
spellingShingle Distributionally robust optimization: a novel approach with decision-dependent ambiguity sets and an application to mode estimation
Distributionally robust optimization
Wasserstein metric
Conditional value at risk
Stochastic optimization
Matemáticas
title_short Distributionally robust optimization: a novel approach with decision-dependent ambiguity sets and an application to mode estimation
title_full Distributionally robust optimization: a novel approach with decision-dependent ambiguity sets and an application to mode estimation
title_fullStr Distributionally robust optimization: a novel approach with decision-dependent ambiguity sets and an application to mode estimation
title_full_unstemmed Distributionally robust optimization: a novel approach with decision-dependent ambiguity sets and an application to mode estimation
title_sort Distributionally robust optimization: a novel approach with decision-dependent ambiguity sets and an application to mode estimation
dc.creator.fl_str_mv Fonseca Valero, Diego Fernando
dc.contributor.advisor.none.fl_str_mv Junca Peláez, Mauricio José
dc.contributor.author.none.fl_str_mv Fonseca Valero, Diego Fernando
dc.contributor.jury.none.fl_str_mv Avella Medina, Marco
Díaz Díaz, Mateo
Quiroz Salazar, Adolfo José
dc.subject.keyword.none.fl_str_mv Distributionally robust optimization
Wasserstein metric
Conditional value at risk
Stochastic optimization
topic Distributionally robust optimization
Wasserstein metric
Conditional value at risk
Stochastic optimization
Matemáticas
dc.subject.themes.es_CO.fl_str_mv Matemáticas
description Este trabajo fue elaborado como uno de los requisitos para obtener el título de doctor en matemáticas. Adicionalmente, la investigación desarrollada no presenta ningún tipo de conflicto de intereses.
publishDate 2023
dc.date.accessioned.none.fl_str_mv 2023-08-04T22:18:50Z
dc.date.available.none.fl_str_mv 2023-08-04T22:18:50Z
dc.date.issued.none.fl_str_mv 2023-04-14
dc.type.es_CO.fl_str_mv Trabajo de grado - Doctorado
dc.type.driver.none.fl_str_mv info:eu-repo/semantics/doctoralThesis
dc.type.version.none.fl_str_mv info:eu-repo/semantics/acceptedVersion
dc.type.coar.none.fl_str_mv http://purl.org/coar/resource_type/c_db06
dc.type.content.es_CO.fl_str_mv Text
dc.type.redcol.none.fl_str_mv https://purl.org/redcol/resource_type/TD
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dc.identifier.uri.none.fl_str_mv http://hdl.handle.net/1992/69263
dc.identifier.doi.none.fl_str_mv 10.57784/1992/69263
dc.identifier.instname.es_CO.fl_str_mv instname:Universidad de los Andes
dc.identifier.reponame.es_CO.fl_str_mv reponame:Repositorio Institucional Séneca
dc.identifier.repourl.es_CO.fl_str_mv repourl:https://repositorio.uniandes.edu.co/
url http://hdl.handle.net/1992/69263
identifier_str_mv 10.57784/1992/69263
instname:Universidad de los Andes
reponame:Repositorio Institucional Séneca
repourl:https://repositorio.uniandes.edu.co/
dc.language.iso.es_CO.fl_str_mv eng
language eng
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spelling Attribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Junca Peláez, Mauricio Josévirtual::10694-1Fonseca Valero, Diego Fernando386d4a66-ebc7-47fd-96ef-d2280cb045ce600Avella Medina, MarcoDíaz Díaz, MateoQuiroz Salazar, Adolfo José2023-08-04T22:18:50Z2023-08-04T22:18:50Z2023-04-14http://hdl.handle.net/1992/6926310.57784/1992/69263instname:Universidad de los Andesreponame:Repositorio Institucional Sénecarepourl:https://repositorio.uniandes.edu.co/Este trabajo fue elaborado como uno de los requisitos para obtener el título de doctor en matemáticas. Adicionalmente, la investigación desarrollada no presenta ningún tipo de conflicto de intereses.This Ph.D. thesis explores stochastic optimization from a Distributionally Robust perspective, focusing on two significant themes: the innovative use of decision variable-dependent ambiguity sets in Distributionally Robust optimization (DRO), and the estimation of the mode of a random vector using the DRO perspective. Regarding the first topic, new techniques utilizing p-Wasserstein metrics in stochastic programming are proposed, where ambiguity sets are uniquely decision variable-dependent. These developments, under certain assumptions, can be reduced to finite-dimensional optimization problems, sometimes convex. They are tested within the portfolio optimization context against standard methodologies. The research also extends to stochastic programming with expected value constraints, setting feasibility criteria relative to the Wasserstein radius and constraint parameters, and benchmarking model performance using both simulated and real financial market data. Additionally, in the realm of mode estimation, an innovative strategy is devised for identifying a mode estimator in a random vector sample, even in the absence of known probability distribution or density function. This strategy employs a DRO approach and Wasserstein distance, demonstrating the resulting estimator is consistent.Doctor en MatemáticasDoctoradoApplied mathematics109application/pdfengUniversidad de los AndesDoctorado en MatemáticasFacultad de CienciasDepartamento de MatemáticasDistributionally robust optimization: a novel approach with decision-dependent ambiguity sets and an application to mode estimationTrabajo de grado - Doctoradoinfo:eu-repo/semantics/doctoralThesisinfo:eu-repo/semantics/acceptedVersionhttp://purl.org/coar/resource_type/c_db06Texthttps://purl.org/redcol/resource_type/TDDistributionally robust optimizationWasserstein metricConditional value at riskStochastic optimizationMatemáticasZ. Akhtar, A. S. Bedi, and K. Rajawat. ¿Conservative Stochastic Optimization With Expectation Constraints¿. In: IEEE Transactions on Signal Processing 69 (2021), pp. 3190¿3205.Y. 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In: Journal of Econometrics 197.2 (2017), pp. 273¿283.A.R. Hota, A. Cherukuri, and J. Lygeros. ¿Data-Driven Chance Constrained Optimization under Wasserstein Ambiguity Sets¿. In: 2019 American Control Conference (ACC) (2019), pp. 1501¿1506.CY. Hsu and TJ. Wu. ¿Efficient estimation of the mode of continuous multivariate data¿. In: Computational Statistics & Data Analysis 63 (2013), pp. 148¿159.H. Jiang and S. Kpotufe. ¿Modal-set estimation with an application to clustering.¿ In: Proceedings of the 20th International Conference on Artificial Intelligence and Statistics 54 (2017), pp. 1197¿1206.R. Jiang and Y. Guan. ¿Data-driven chance constrained stochastic program¿. In: Mathematical Programming 158 (2016), pp. 291¿327.C. Kamanchi et al. ¿An Online Sample-Based Method for Mode Estimation Using ODE Analysis of Stochastic Approximation Algorithms¿. In: IEEE Control Systems Letters 3.3 (2019), pp. 697¿702.Z. 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In: European Journal of Operational Research 210.2 (2011), pp. 410¿424.200720140Publicationhttps://scholar.google.es/citations?user=CoIlxH0AAAAJvirtual::10694-10000-0002-5541-0758virtual::10694-1https://scienti.minciencias.gov.co/cvlac/visualizador/generarCurriculoCv.do?cod_rh=0000155861virtual::10694-11e5c3dc6-4d9c-406b-9f99-5c91523b7e49virtual::10694-11e5c3dc6-4d9c-406b-9f99-5c91523b7e49virtual::10694-1ORIGINALDoctoral_Thesis_Diego Fonseca.pdfDoctoral_Thesis_Diego Fonseca.pdfTesis de doctoradoapplication/pdf3187633https://repositorio.uniandes.edu.co/bitstreams/646923db-6ccb-4a19-940d-1febf52547ff/downloadbd27b92a74f97bf4a878a7cac83b7d8fMD54Formato de autorización y entrega de tesistrabajo de grado al Sistema de Bibliotecas.pdfFormato de autorización y entrega de tesistrabajo de grado al Sistema de Bibliotecas.pdfHIDEapplication/pdf290866https://repositorio.uniandes.edu.co/bitstreams/2f0414e2-b55e-41cb-99b1-a4416c92f95c/download37b0e83d6f0a74bbcb44e18ec0493dabMD53LICENSElicense.txtlicense.txttext/plain; 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