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

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