{"title":"分段不定二次规划问题的一种算法","authors":"R. Arora, Kavita Gupta","doi":"10.17535/crorr.2020.0004","DOIUrl":null,"url":null,"abstract":"An indefinite quadratic programming problem is a mathematical programming problem which is a product of two linear factors. In this paper, the piece-wise indefinite quadratic programming problem (PIQPP) is considered. Here, the objective function is a product of two continuous piecewise linear functions defined on a non-empty and compact feasible region. In the present paper, the optimality criterion is derived and explained in order to solve PIQPP. While solving PIQPP, we will come across certain variables which will not satisfy the optimality condition. For these variables, cases have been elaborated so as to move from one basic feasible solution to another till we reach the optimality. An algorithmic approach is proposed and discussed for the pr PIQPP problem. A numerical example is presented to decipher the tendered method.","PeriodicalId":44065,"journal":{"name":"Croatian Operational Research Review","volume":"11 1","pages":"39-51"},"PeriodicalIF":0.5000,"publicationDate":"2020-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.17535/crorr.2020.0004","citationCount":"0","resultStr":"{\"title\":\"An algorithm for piece-wise indefinite quadratic programming problem\",\"authors\":\"R. Arora, Kavita Gupta\",\"doi\":\"10.17535/crorr.2020.0004\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"An indefinite quadratic programming problem is a mathematical programming problem which is a product of two linear factors. In this paper, the piece-wise indefinite quadratic programming problem (PIQPP) is considered. Here, the objective function is a product of two continuous piecewise linear functions defined on a non-empty and compact feasible region. In the present paper, the optimality criterion is derived and explained in order to solve PIQPP. While solving PIQPP, we will come across certain variables which will not satisfy the optimality condition. For these variables, cases have been elaborated so as to move from one basic feasible solution to another till we reach the optimality. An algorithmic approach is proposed and discussed for the pr PIQPP problem. A numerical example is presented to decipher the tendered method.\",\"PeriodicalId\":44065,\"journal\":{\"name\":\"Croatian Operational Research Review\",\"volume\":\"11 1\",\"pages\":\"39-51\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2020-07-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.17535/crorr.2020.0004\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Croatian Operational Research Review\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.17535/crorr.2020.0004\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"ECONOMICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Croatian Operational Research Review","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.17535/crorr.2020.0004","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"ECONOMICS","Score":null,"Total":0}
An algorithm for piece-wise indefinite quadratic programming problem
An indefinite quadratic programming problem is a mathematical programming problem which is a product of two linear factors. In this paper, the piece-wise indefinite quadratic programming problem (PIQPP) is considered. Here, the objective function is a product of two continuous piecewise linear functions defined on a non-empty and compact feasible region. In the present paper, the optimality criterion is derived and explained in order to solve PIQPP. While solving PIQPP, we will come across certain variables which will not satisfy the optimality condition. For these variables, cases have been elaborated so as to move from one basic feasible solution to another till we reach the optimality. An algorithmic approach is proposed and discussed for the pr PIQPP problem. A numerical example is presented to decipher the tendered method.
期刊介绍：
Croatian Operational Research Review (CRORR) is the journal which publishes original scientific papers from the area of operational research. The purpose is to publish papers from various aspects of operational research (OR) with the aim of presenting scientific ideas that will contribute both to theoretical development and practical application of OR. The scope of the journal covers the following subject areas: linear and non-linear programming, integer programing, combinatorial and discrete optimization, multi-objective programming, stohastic models and optimization, scheduling, macroeconomics, economic theory, game theory, statistics and econometrics, marketing and data analysis, information and decision support systems, banking, finance, insurance, environment, energy, health, neural networks and fuzzy systems, control theory, simulation, practical OR and applications. The audience includes both researchers and practitioners from the area of operations research, applied mathematics, statistics, econometrics, intelligent methods, simulation, and other areas included in the above list of topics. The journal has an international board of editors, consisting of more than 30 editors – university professors from Croatia, Slovenia, USA, Italy, Germany, Austria and other coutries.
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