Pub Date : 2023-07-08DOI: 10.1007/s00186-023-00822-3
Meghan Shanks, Ge Yu, S. Jacobson
{"title":"Approximation algorithms for stochastic online matching with reusable resources","authors":"Meghan Shanks, Ge Yu, S. Jacobson","doi":"10.1007/s00186-023-00822-3","DOIUrl":"https://doi.org/10.1007/s00186-023-00822-3","url":null,"abstract":"","PeriodicalId":49862,"journal":{"name":"Mathematical Methods of Operations Research","volume":"5 1","pages":"43 - 56"},"PeriodicalIF":1.2,"publicationDate":"2023-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72772378","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-05DOI: 10.1007/s00186-023-00825-0
Gustavo Portillo-Ramírez, R. Cavazos-Cadena, H. Cruz-Suárez
{"title":"Contractive approximations in average Markov decision chains driven by a risk-seeking controller","authors":"Gustavo Portillo-Ramírez, R. Cavazos-Cadena, H. Cruz-Suárez","doi":"10.1007/s00186-023-00825-0","DOIUrl":"https://doi.org/10.1007/s00186-023-00825-0","url":null,"abstract":"","PeriodicalId":49862,"journal":{"name":"Mathematical Methods of Operations Research","volume":"40 1","pages":"75 - 91"},"PeriodicalIF":1.2,"publicationDate":"2023-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81526477","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-01DOI: 10.1007/s00186-023-00824-1
J. M. Alonso-Meijide, Julián Costa-Bouzas, I. García-Jurado, J. C. Gonçalves-Dosantos
{"title":"On egalitarian values for cooperative games with level structures","authors":"J. M. Alonso-Meijide, Julián Costa-Bouzas, I. García-Jurado, J. C. Gonçalves-Dosantos","doi":"10.1007/s00186-023-00824-1","DOIUrl":"https://doi.org/10.1007/s00186-023-00824-1","url":null,"abstract":"","PeriodicalId":49862,"journal":{"name":"Mathematical Methods of Operations Research","volume":"20 1","pages":"57 - 73"},"PeriodicalIF":1.2,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90166828","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-26DOI: 10.1007/s00186-023-00823-2
Stephan Helfrich, Arne Herzel, Stefan Ruzika, Clemens Thielen
Abstract We study the approximation of general multiobjective optimization problems with the help of scalarizations. Existing results state that multiobjective minimization problems can be approximated well by norm-based scalarizations. However, for multiobjective maximization problems, only impossibility results are known so far. Countering this, we show that all multiobjective optimization problems can, in principle, be approximated equally well by scalarizations. In this context, we introduce a transformation theory for scalarizations that establishes the following: Suppose there exists a scalarization that yields an approximation of a certain quality for arbitrary instances of multiobjective optimization problems with a given decomposition specifying which objective functions are to be minimized/maximized. Then, for each other decomposition, our transformation yields another scalarization that yields the same approximation quality for arbitrary instances of problems with this other decomposition. In this sense, the existing results about the approximation via scalarizations for minimization problems carry over to any other objective decomposition—in particular, to maximization problems—when suitably adapting the employed scalarization. We further provide necessary and sufficient conditions on a scalarization such that its optimal solutions achieve a constant approximation quality. We give an upper bound on the best achievable approximation quality that applies to general scalarizations and is tight for the majority of norm-based scalarizations applied in the context of multiobjective optimization. As a consequence, none of these norm-based scalarizations can induce approximation sets for optimization problems with maximization objectives, which unifies and generalizes the existing impossibility results concerning the approximation of maximization problems.
{"title":"Using scalarizations for the approximation of multiobjective optimization problems: towards a general theory","authors":"Stephan Helfrich, Arne Herzel, Stefan Ruzika, Clemens Thielen","doi":"10.1007/s00186-023-00823-2","DOIUrl":"https://doi.org/10.1007/s00186-023-00823-2","url":null,"abstract":"Abstract We study the approximation of general multiobjective optimization problems with the help of scalarizations. Existing results state that multiobjective minimization problems can be approximated well by norm-based scalarizations. However, for multiobjective maximization problems, only impossibility results are known so far. Countering this, we show that all multiobjective optimization problems can, in principle, be approximated equally well by scalarizations. In this context, we introduce a transformation theory for scalarizations that establishes the following: Suppose there exists a scalarization that yields an approximation of a certain quality for arbitrary instances of multiobjective optimization problems with a given decomposition specifying which objective functions are to be minimized/maximized. Then, for each other decomposition, our transformation yields another scalarization that yields the same approximation quality for arbitrary instances of problems with this other decomposition. In this sense, the existing results about the approximation via scalarizations for minimization problems carry over to any other objective decomposition—in particular, to maximization problems—when suitably adapting the employed scalarization. We further provide necessary and sufficient conditions on a scalarization such that its optimal solutions achieve a constant approximation quality. We give an upper bound on the best achievable approximation quality that applies to general scalarizations and is tight for the majority of norm-based scalarizations applied in the context of multiobjective optimization. As a consequence, none of these norm-based scalarizations can induce approximation sets for optimization problems with maximization objectives, which unifies and generalizes the existing impossibility results concerning the approximation of maximization problems.","PeriodicalId":49862,"journal":{"name":"Mathematical Methods of Operations Research","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135558340","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-01DOI: 10.1007/s00186-023-00819-y
José-Manuel Giménez-Gómez, Peter Sudhölter, Cori Vilella
{"title":"Average monotonic cooperative games with nontransferable utility","authors":"José-Manuel Giménez-Gómez, Peter Sudhölter, Cori Vilella","doi":"10.1007/s00186-023-00819-y","DOIUrl":"https://doi.org/10.1007/s00186-023-00819-y","url":null,"abstract":"","PeriodicalId":49862,"journal":{"name":"Mathematical Methods of Operations Research","volume":"11 1","pages":"383 - 390"},"PeriodicalIF":1.2,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88706176","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-05-30DOI: 10.1007/s00186-023-00818-z
F. García-Castaño, Miguel Ángel Melguizo-Padial, G. Parzanese
{"title":"Sublinear scalarizations for proper and approximate proper efficient points in nonconvex vector optimization","authors":"F. García-Castaño, Miguel Ángel Melguizo-Padial, G. Parzanese","doi":"10.1007/s00186-023-00818-z","DOIUrl":"https://doi.org/10.1007/s00186-023-00818-z","url":null,"abstract":"","PeriodicalId":49862,"journal":{"name":"Mathematical Methods of Operations Research","volume":"21 1","pages":"367 - 382"},"PeriodicalIF":1.2,"publicationDate":"2023-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81521953","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-05-26DOI: 10.1007/s00186-023-00820-5
Seyfe Belete Worku, B. Tsegaw, Semu Mitiku Kassa
{"title":"Existence and computations of best affine strategies for multilevel reverse Stackelberg games","authors":"Seyfe Belete Worku, B. Tsegaw, Semu Mitiku Kassa","doi":"10.1007/s00186-023-00820-5","DOIUrl":"https://doi.org/10.1007/s00186-023-00820-5","url":null,"abstract":"","PeriodicalId":49862,"journal":{"name":"Mathematical Methods of Operations Research","volume":"43 1","pages":"339 - 366"},"PeriodicalIF":1.2,"publicationDate":"2023-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87718669","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-05-18DOI: 10.1007/s00186-023-00814-3
Zijun Li, F. Meng
{"title":"The α-Egalitarian Myerson value of games with communication structure","authors":"Zijun Li, F. Meng","doi":"10.1007/s00186-023-00814-3","DOIUrl":"https://doi.org/10.1007/s00186-023-00814-3","url":null,"abstract":"","PeriodicalId":49862,"journal":{"name":"Mathematical Methods of Operations Research","volume":"44 11","pages":"311 - 338"},"PeriodicalIF":1.2,"publicationDate":"2023-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72480866","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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