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一类线性比式和问题的全局优化算法(英文).docx

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一类线性比式和问题的全局优化算法(英文) Introduction: Linearprogrammingisawidelyusedtechniqueinoptimization.Ithasabroadrangeofapplicationsinvariousfields,includingfinance,economics,operationsresearch,andengineering.Linearprogrammingisusedtosolveavarietyofoptimizationproblems,includingthetransportationproblem,thedietproblem,andthesimplexproblem. However,insomeinstances,linearprogrammingmayresultininfeasiblesolutions,especiallywhentheprobleminvolvesnon-linearvariables.Non-linearvariablesareoftenpresentintherealworld,andtheyincreasethecomplexityoftheoptimizationproblem.Therefore,thereisaneedforaglobaloptimizationalgorithmthatcanhandlenon-linearvariablesandlinearconstraints. Inthispaper,wewillexploretheuseofaclassofglobaloptimizationalgorithmsknownasLinearFractionalProgramming(LFP)forsolvingnon-linearoptimizationproblemsinvolvinglinearconstraints.WewilldiscussthefeaturesofLFPalgorithmsandtheirapplicationsinreal-worldproblems. FeaturesofLFPAlgorithms: LinearFractionalProgrammingisaclassofglobaloptimizationtechniquesthatcanhandlenon-linearvariablesandlinearconstraints.LFPalgorithmsusealinearfunction(numerator)dividedbyafractionalprograminthedenominator.Thefractionalprogramcontainssomenon-linearvariables,whichmakestheproblemnon-linear.LFPalgorithmscanhandleproblemswithmultiplelinearconstraintsandnon-linearvariables. LFPalgorithmshavesomeuniquefeaturesthatdistinguishthemfromotheroptimizationtechniques.Firstly,LFPalgorithmscanhandlehardoptimizationproblemsthatotheroptimizationtechniquesfinddifficulttosolve.Secondly,LFPalgorithmshaveahighconvergencerate,whichmeanstheycanfindtheglobalminimuminashorttime.Thirdly,LFPalgorithmscanhandleintegerandmixed-integerprogrammingproblems. ApplicationsofLFPAlgorithms: LFPalgorithmshavenumerousapplicationsintherealworld.Someoftheapplicationsinclude: 1.PortfolioOptimization:LFPalgorithmscanbeusedtooptimizeinvestmentportfolios.Theobjectiveistomaximizereturnswhileminimizingtherisk.Thenon-linearvariablesincludetheexpectedreturnsandcovariancematrixoftheportfolio. 2