{"title":"多目标基数约束优化问题的惩罚分解方法","authors":"M. Lapucci","doi":"10.1080/10556788.2022.2060972","DOIUrl":null,"url":null,"abstract":"In this manuscript, we consider multi-objective optimization problems with a cardinality constraint on the vector of decision variables and additional linear constraints. For this class of problems, we analyse necessary and sufficient conditions of Pareto optimality. We afterwards propose a Penalty Decomposition type algorithm, exploiting multi-objective descent methods, to tackle the aforementioned family of problems. We conduct a rigorous convergence analysis for the proposed method, where we prove that the produced sequence of points has limit points, each one being feasible and satisfying first-order optimality conditions. Numerical computational experiments, carried out on instances of relevant real-world problems such as sparse mean/variance portfolio selection and sparse regularized logistic regression, in their multi-objective formulation, show that the proposed procedure is effective at finding solutions forming good Pareto sets approximations.","PeriodicalId":124811,"journal":{"name":"Optimization Methods and Software","volume":"181 17","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"A penalty decomposition approach for multi-objective cardinality-constrained optimization problems\",\"authors\":\"M. Lapucci\",\"doi\":\"10.1080/10556788.2022.2060972\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this manuscript, we consider multi-objective optimization problems with a cardinality constraint on the vector of decision variables and additional linear constraints. For this class of problems, we analyse necessary and sufficient conditions of Pareto optimality. We afterwards propose a Penalty Decomposition type algorithm, exploiting multi-objective descent methods, to tackle the aforementioned family of problems. We conduct a rigorous convergence analysis for the proposed method, where we prove that the produced sequence of points has limit points, each one being feasible and satisfying first-order optimality conditions. Numerical computational experiments, carried out on instances of relevant real-world problems such as sparse mean/variance portfolio selection and sparse regularized logistic regression, in their multi-objective formulation, show that the proposed procedure is effective at finding solutions forming good Pareto sets approximations.\",\"PeriodicalId\":124811,\"journal\":{\"name\":\"Optimization Methods and Software\",\"volume\":\"181 17\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-04-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Optimization Methods and Software\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1080/10556788.2022.2060972\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Optimization Methods and Software","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/10556788.2022.2060972","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A penalty decomposition approach for multi-objective cardinality-constrained optimization problems
In this manuscript, we consider multi-objective optimization problems with a cardinality constraint on the vector of decision variables and additional linear constraints. For this class of problems, we analyse necessary and sufficient conditions of Pareto optimality. We afterwards propose a Penalty Decomposition type algorithm, exploiting multi-objective descent methods, to tackle the aforementioned family of problems. We conduct a rigorous convergence analysis for the proposed method, where we prove that the produced sequence of points has limit points, each one being feasible and satisfying first-order optimality conditions. Numerical computational experiments, carried out on instances of relevant real-world problems such as sparse mean/variance portfolio selection and sparse regularized logistic regression, in their multi-objective formulation, show that the proposed procedure is effective at finding solutions forming good Pareto sets approximations.