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次梯度法在求解非光滑最优化问题时的计算效果研究(英文).docx

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次梯度法在求解非光滑最优化问题时的计算效果研究(英文) Title:ACaseStudyontheComputationalEfficiencyofSubgradientMethodsforNon-SmoothOptimizationProblems Abstract: Non-smoothoptimizationproblemsariseinmanyreal-worldapplications,andtheirefficientsolutioniscrucialforvariousoptimizationtasks.Subgradientmethodshaveproventobeeffectiveintacklingsuchproblemsduetotheirabilitytohandlenon-smoothnessandscalabilitytohigh-dimensionalproblems.Thispaperpresentsacomprehensiveinvestigationofthecomputationalefficiencyofsubgradientmethodsinsolvingnon-smoothoptimizationproblems. Introduction: Non-smoothoptimizationproblemsinvolveobjectivefunctionsthatarenotdifferentiableinsomeorallpartsofthefeasibledomain.Typicalexamplesincludeproblemswithnon-differentiableconstraints,problemswithnon-differentiablecostfunctions,andproblemsinvolvingnon-smoothregularizationterms.Subgradientmethods,alsoknownassubgradientdescentorsubgradientoptimization,aregradient-basedoptimizationtechniquesthatcanbeappliedtosolvenon-smoothproblems.Theyofferapracticalandversatileapproachtohandlenon-smoothnessinoptimization. Methods: Inthisstudy,wefocusonthreepopularsubgradientmethods:theclassicsubgradientmethod,thesubgradientmethodwithlinesearch,andthebundlemethod.Weconsiderasetofbenchmarknon-smoothoptimizationproblemsandcomparetheperformanceofthesemethodsintermsofcomputationalefficiency.Thebenchmarksetincludesproblemsfromvariousapplicationdomains,suchasmachinelearning,signalprocessing,andimagereconstruction. Results: Theresultsdemonstratethatsubgradientmethodsexhibitfavorablecomputationalefficiencyinsolvingnon-smoothoptimizationproblems.Theclassicsubgradientmethodprovidesagoodbaselineperformance,whilethesubgradientmethodwithlinesearchimprovesconvergencebyadaptivelyadjustingthestepsize.Thebundlemethod,ontheotherhand,incorporatestheinformationobtainedfrompastiterationstoaccelerateconvergenceandachievebettercomputationalefficiency.Overall,thesemethodsshowpromisingresultsintermsofconvergencerateandtime-to-solution. Discussion: Thecomputationalefficienc