Pub Date : 2023-10-10DOI: 10.1007/s11590-023-02056-y
Malick Ndiaye, Ahmed Osman, Said Salhi, Batool Madani
{"title":"The truck–drone routing optimization problem: mathematical model and a VNS approach","authors":"Malick Ndiaye, Ahmed Osman, Said Salhi, Batool Madani","doi":"10.1007/s11590-023-02056-y","DOIUrl":"https://doi.org/10.1007/s11590-023-02056-y","url":null,"abstract":"","PeriodicalId":49720,"journal":{"name":"Optimization Letters","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136353588","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 : 2023-10-09DOI: 10.1007/s11590-023-02045-1
Bogdan Grechuk, Michael Zabarankin, Alexander Mafusalov, Stan Uryasev
Abstract For a random variable, superdistribution has emerged as a valuable probability concept. Similar to cumulative distribution function (CDF), it uniquely defines the random variable and can be evaluated with a simple one-dimensional minimization formula. This work leverages the structure of that formula to introduce buffered CDF (bCDF) and reduced CDF (rCDF) for random vectors. bCDF and rCDF are shown to be the minimal Schur-convex upper bound and the maximal Schur-concave lower bound of the multivariate CDF, respectively. Special structure of bCDF and rCDF is used to construct an algorithm for solving optimization problems with bCDF and rCDF in objective or constraints. The efficiency of the algorithm is demonstrated in a case study on optimization of a collateralized debt obligation with bCDF functions in constraints.
{"title":"Buffered and Reduced Multidimensional Distribution Functions and Their Application in Optimization","authors":"Bogdan Grechuk, Michael Zabarankin, Alexander Mafusalov, Stan Uryasev","doi":"10.1007/s11590-023-02045-1","DOIUrl":"https://doi.org/10.1007/s11590-023-02045-1","url":null,"abstract":"Abstract For a random variable, superdistribution has emerged as a valuable probability concept. Similar to cumulative distribution function (CDF), it uniquely defines the random variable and can be evaluated with a simple one-dimensional minimization formula. This work leverages the structure of that formula to introduce buffered CDF (bCDF) and reduced CDF (rCDF) for random vectors. bCDF and rCDF are shown to be the minimal Schur-convex upper bound and the maximal Schur-concave lower bound of the multivariate CDF, respectively. Special structure of bCDF and rCDF is used to construct an algorithm for solving optimization problems with bCDF and rCDF in objective or constraints. The efficiency of the algorithm is demonstrated in a case study on optimization of a collateralized debt obligation with bCDF functions in constraints.","PeriodicalId":49720,"journal":{"name":"Optimization Letters","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135044277","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 : 2023-10-05DOI: 10.1007/s11590-023-02064-y
Matthew K. Tam
Abstract Frugal resolvent splittings are a class of fixed point algorithms for finding a zero in the sum of the sum of finitely many set-valued monotone operators, where the fixed point operator uses only vector addition, scalar multiplication and the resolvent of each monotone operator once per iteration. In the literature, the convergence analyses of these schemes are performed in an inefficient, algorithm-by-algorithm basis. In this work, we address this by developing a general framework for frugal resolvent splitting which simultaneously covers and extends several important schemes in the literature. The framework also yields a new resolvent splitting algorithm which is suitable for decentralised implementation on regular networks.
{"title":"Frugal and decentralised resolvent splittings defined by nonexpansive operators","authors":"Matthew K. Tam","doi":"10.1007/s11590-023-02064-y","DOIUrl":"https://doi.org/10.1007/s11590-023-02064-y","url":null,"abstract":"Abstract Frugal resolvent splittings are a class of fixed point algorithms for finding a zero in the sum of the sum of finitely many set-valued monotone operators, where the fixed point operator uses only vector addition, scalar multiplication and the resolvent of each monotone operator once per iteration. In the literature, the convergence analyses of these schemes are performed in an inefficient, algorithm-by-algorithm basis. In this work, we address this by developing a general framework for frugal resolvent splitting which simultaneously covers and extends several important schemes in the literature. The framework also yields a new resolvent splitting algorithm which is suitable for decentralised implementation on regular networks.","PeriodicalId":49720,"journal":{"name":"Optimization Letters","volume":"440 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134977169","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 : 2023-10-04DOI: 10.1007/s11590-023-02065-x
A. Farajzadeh
{"title":"On maximal and minimal elements for sets with respect to cones","authors":"A. Farajzadeh","doi":"10.1007/s11590-023-02065-x","DOIUrl":"https://doi.org/10.1007/s11590-023-02065-x","url":null,"abstract":"","PeriodicalId":49720,"journal":{"name":"Optimization Letters","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135645040","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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