任意锥上的混合多目标不可微对称对偶规划问题

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2025-02-11 DOI:10.1002/mma.10762

Balram, Shubham Jaiswal, Ramu Dubey

{"title":"任意锥上的混合多目标不可微对称对偶规划问题","authors":"Balram, Shubham Jaiswal, Ramu Dubey","doi":"10.1002/mma.10762","DOIUrl":null,"url":null,"abstract":"<div>\n \n In the present article, we formulate mixed-type multiobjective nondifferentiable symmetric duality over cone and derive the duality results under \n<math>\n <semantics>\n <mrow>\n <mi>K</mi>\n </mrow>\n <annotation>$$ K $$</annotation>\n </semantics></math>-\n<math>\n <semantics>\n <mrow>\n <mo>(</mo>\n <mi>C</mi>\n <mo>,</mo>\n <mi>ρ</mi>\n <mo>,</mo>\n <mi>d</mi>\n <mo>)</mo>\n </mrow>\n <annotation>$$ \\left(C,\\rho, d\\right) $$</annotation>\n </semantics></math>-convex and \n<math>\n <semantics>\n <mrow>\n <mi>K</mi>\n </mrow>\n <annotation>$$ K $$</annotation>\n </semantics></math>-\n<math>\n <semantics>\n <mrow>\n <mo>(</mo>\n <mi>C</mi>\n <mo>,</mo>\n <mi>ρ</mi>\n <mo>,</mo>\n <mi>d</mi>\n <mo>)</mo>\n </mrow>\n <annotation>$$ \\left(C,\\rho, d\\right) $$</annotation>\n </semantics></math>-pseudoconvex. Also, we give non-trivial examples of \n<math>\n <semantics>\n <mrow>\n <mi>K</mi>\n </mrow>\n <annotation>$$ K $$</annotation>\n </semantics></math>-\n<math>\n <semantics>\n <mrow>\n <mo>(</mo>\n <mi>C</mi>\n <mo>,</mo>\n <mi>ρ</mi>\n <mo>,</mo>\n <mi>d</mi>\n <mo>)</mo>\n </mrow>\n <annotation>$$ \\left(C,\\rho, d\\right) $$</annotation>\n </semantics></math>-convex and \n<math>\n <semantics>\n <mrow>\n <mi>K</mi>\n </mrow>\n <annotation>$$ K $$</annotation>\n </semantics></math>-\n<math>\n <semantics>\n <mrow>\n <mo>(</mo>\n <mi>C</mi>\n <mo>,</mo>\n <mi>ρ</mi>\n <mo>,</mo>\n <mi>d</mi>\n <mo>)</mo>\n </mrow>\n <annotation>$$ \\left(C,\\rho, d\\right) $$</annotation>\n </semantics></math>-pseudoconvex and show that every \n<math>\n <semantics>\n <mrow>\n <mi>K</mi>\n </mrow>\n <annotation>$$ K $$</annotation>\n </semantics></math>-\n<math>\n <semantics>\n <mrow>\n <mo>(</mo>\n <mi>C</mi>\n <mo>,</mo>\n <mi>ρ</mi>\n <mo>,</mo>\n <mi>d</mi>\n <mo>)</mo>\n </mrow>\n <annotation>$$ \\left(C,\\rho, d\\right) $$</annotation>\n </semantics></math>-convex need not be \n<math>\n <semantics>\n <mrow>\n <mi>K</mi>\n </mrow>\n <annotation>$$ K $$</annotation>\n </semantics></math>-\n<math>\n <semantics>\n <mrow>\n <mo>(</mo>\n <mi>C</mi>\n <mo>,</mo>\n <mi>ρ</mi>\n <mo>,</mo>\n <mi>d</mi>\n <mo>)</mo>\n </mrow>\n <annotation>$$ \\left(C,\\rho, d\\right) $$</annotation>\n </semantics></math>-pseudoconvex. We give non-trivial examples of some basic definitions used in this research area. Also, some graphs are used to understand the information better. The outcomes we obtained expand upon several earlier discoveries in the field.\n </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 8","pages":"8890-8902"},"PeriodicalIF":2.1000,"publicationDate":"2025-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Mixed-Type Multiobjective Nondifferentiable Symmetric Duality Programming Problem Over Arbitrary Cones\",\"authors\":\"Balram, Shubham Jaiswal, Ramu Dubey\",\"doi\":\"10.1002/mma.10762\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>\\n \\n In the present article, we formulate mixed-type multiobjective nondifferentiable symmetric duality over cone and derive the duality results under \\n<math>\\n <semantics>\\n <mrow>\\n <mi>K</mi>\\n </mrow>\\n <annotation>$$ K $$</annotation>\\n </semantics></math>-\\n<math>\\n <semantics>\\n <mrow>\\n <mo>(</mo>\\n <mi>C</mi>\\n <mo>,</mo>\\n <mi>ρ</mi>\\n <mo>,</mo>\\n <mi>d</mi>\\n <mo>)</mo>\\n </mrow>\\n <annotation>$$ \\\\left(C,\\\\rho, d\\\\right) $$</annotation>\\n </semantics></math>-convex and \\n<math>\\n <semantics>\\n <mrow>\\n <mi>K</mi>\\n </mrow>\\n <annotation>$$ K $$</annotation>\\n </semantics></math>-\\n<math>\\n <semantics>\\n <mrow>\\n <mo>(</mo>\\n <mi>C</mi>\\n <mo>,</mo>\\n <mi>ρ</mi>\\n <mo>,</mo>\\n <mi>d</mi>\\n <mo>)</mo>\\n </mrow>\\n <annotation>$$ \\\\left(C,\\\\rho, d\\\\right) $$</annotation>\\n </semantics></math>-pseudoconvex. Also, we give non-trivial examples of \\n<math>\\n <semantics>\\n <mrow>\\n <mi>K</mi>\\n </mrow>\\n <annotation>$$ K $$</annotation>\\n </semantics></math>-\\n<math>\\n <semantics>\\n <mrow>\\n <mo>(</mo>\\n <mi>C</mi>\\n <mo>,</mo>\\n <mi>ρ</mi>\\n <mo>,</mo>\\n <mi>d</mi>\\n <mo>)</mo>\\n </mrow>\\n <annotation>$$ \\\\left(C,\\\\rho, d\\\\right) $$</annotation>\\n </semantics></math>-convex and \\n<math>\\n <semantics>\\n <mrow>\\n <mi>K</mi>\\n </mrow>\\n <annotation>$$ K $$</annotation>\\n </semantics></math>-\\n<math>\\n <semantics>\\n <mrow>\\n <mo>(</mo>\\n <mi>C</mi>\\n <mo>,</mo>\\n <mi>ρ</mi>\\n <mo>,</mo>\\n <mi>d</mi>\\n <mo>)</mo>\\n </mrow>\\n <annotation>$$ \\\\left(C,\\\\rho, d\\\\right) $$</annotation>\\n </semantics></math>-pseudoconvex and show that every \\n<math>\\n <semantics>\\n <mrow>\\n <mi>K</mi>\\n </mrow>\\n <annotation>$$ K $$</annotation>\\n </semantics></math>-\\n<math>\\n <semantics>\\n <mrow>\\n <mo>(</mo>\\n <mi>C</mi>\\n <mo>,</mo>\\n <mi>ρ</mi>\\n <mo>,</mo>\\n <mi>d</mi>\\n <mo>)</mo>\\n </mrow>\\n <annotation>$$ \\\\left(C,\\\\rho, d\\\\right) $$</annotation>\\n </semantics></math>-convex need not be \\n<math>\\n <semantics>\\n <mrow>\\n <mi>K</mi>\\n </mrow>\\n <annotation>$$ K $$</annotation>\\n </semantics></math>-\\n<math>\\n <semantics>\\n <mrow>\\n <mo>(</mo>\\n <mi>C</mi>\\n <mo>,</mo>\\n <mi>ρ</mi>\\n <mo>,</mo>\\n <mi>d</mi>\\n <mo>)</mo>\\n </mrow>\\n <annotation>$$ \\\\left(C,\\\\rho, d\\\\right) $$</annotation>\\n </semantics></math>-pseudoconvex. We give non-trivial examples of some basic definitions used in this research area. Also, some graphs are used to understand the information better. The outcomes we obtained expand upon several earlier discoveries in the field.\\n </div>\",\"PeriodicalId\":49865,\"journal\":{\"name\":\"Mathematical Methods in the Applied Sciences\",\"volume\":\"48 8\",\"pages\":\"8890-8902\"},\"PeriodicalIF\":2.1000,\"publicationDate\":\"2025-02-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Methods in the Applied Sciences\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1002/mma.10762\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Methods in the Applied Sciences","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/mma.10762","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

本文给出了锥上的混合型多目标不可微对称对偶性，并在K $$ K $$ - (C, ρ，d) $$ \left(C,\rho, d\right) $$ -convex和K $$ K $$ - (C, ρ, d) $$ \left(C,\rho, d\right) $$ -pseudoconvex。同样，我们给出K $$ K $$ - (C, ρ，d) $$ \left(C,\rho, d\right) $$ -凸，K $$ K $$ - (C, ρ，d) $$ \left(C,\rho, d\right) $$ -伪凸并证明每个K $$ K $$ - (C, ρ，d) $$ \left(C,\rho, d\right) $$ -convex不必是K $$ K $$ - (C, ρ, d) $$ \left(C,\rho, d\right) $$ -pseudoconvex。我们给出了在这个研究领域中使用的一些基本定义的重要例子。此外，还使用一些图表来更好地理解信息。我们获得的结果是在该领域先前的几项发现的基础上进行扩展的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Mixed-Type Multiobjective Nondifferentiable Symmetric Duality Programming Problem Over Arbitrary Cones

In the present article, we formulate mixed-type multiobjective nondifferentiable symmetric duality over cone and derive the duality results under $K$ - $(C, ρ, d)$ -convex and $K$ - $(C, ρ, d)$ -pseudoconvex. Also, we give non-trivial examples of $K$ - $(C, ρ, d)$ -convex and $K$ - $(C, ρ, d)$ -pseudoconvex and show that every $K$ - $(C, ρ, d)$ -convex need not be $K$ - $(C, ρ, d)$ -pseudoconvex. We give non-trivial examples of some basic definitions used in this research area. Also, some graphs are used to understand the information better. The outcomes we obtained expand upon several earlier discoveries in the field.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.