運籌學（四川師范大學）知到課后答案智慧樹章節測試答案2025年春四川師范大學第一章單元測試

AbasicfeasiblesolutionofanLPproblemhaveoneandonlyonerelatedfeasiblebasis.

A:對B:錯

答案:錯IftheprimalLPproblemisunbounded,thenthefeasibleregionofdualproblemmustbeempty.

A:錯B:對

答案:對IftheLPproblemissolvable,then

A:ThereisafeasibleregularsolutionofthisLPproblemB:ThevalueoftheLPproblemisfiniteC:ThereexistsanoptimalbasicfeasiblesolutiontothisLPproblemD:ThefeasibleregionofthisLPproblemisnonempty

答案:ThereisafeasibleregularsolutionofthisLPproblem###ThevalueoftheLPproblemisfinite###ThereexistsanoptimalbasicfeasiblesolutiontothisLPproblem###ThefeasibleregionofthisLPproblemisnonemptyIftheprimalLPproblemhasoptimalsolutions,then

A:ThefeasibleregionofthedualproblemisnonemptyB:ThedualproblemisboundedC:ThedualproblemhasanoptimalbasicfeasiblesolutionD:Thedualproblemisnon-degenerate

答案:Thefeasibleregionofthedualproblemisnonempty###Thedualproblemisbounded###ThedualproblemhasanoptimalbasicfeasiblesolutionWhichofthefollowingassertionsforthefeasibleregionofastandardLPproblemisincorrect?

A:ThefeasibleregionisconvexB:ThefeasibleregionmighthaveinfinitelymanyverticesC:ThefeasibleregionmightnothavevertexD:Thefeasibleregionmightbeunbounded

答案:Thefeasibleregionmighthaveinfinitelymanyvertices

第二章單元測試

IftherelaxedLPproblemhasfeasiblesolution,thentherelatedILPproblemhasnonemptyfeasibleregion

A:對B:錯

答案:錯Afteraddingthecuttingplane,thenewsimplextablecorrespondstoaregularsolutiontothenewLPproblem

A:錯B:對

答案:對Inthebranch-and-boundmethod,theboundisthevalueofcostfunctiononaintegeroptimalsolutiontosomerelaxedsub-problem

A:錯B:對

答案:對Whichofthefollowingassertionsforthebranch-and-boundmethodarecorrect?

A:IfthecorrespondingrelaxedLPproblemhasanintegeroptimalsolution,thenthissolutionistheoptimalsolutionofILPproblemB:Ifthevalueofthesub-problemissmallerthanthecurrentboundandtheoptimalsolutionisnotanintegersolution,thenthisbranchshouldbecutoff.C:Ifthevalueofcurrentsub-problemislargerthanthebound,thebranchforthissub-problemshouldbecutoff.D:Ifthecurrentsub-problemhasintegeroptimalsolutionandthevalueissmallerthanthebound,thentheintegeroptimalsolutionisthesolutiontotheoriginalproblem.

答案:IfthecorrespondingrelaxedLPproblemhasanintegeroptimalsolution,thenthissolutionistheoptimalsolutionofILPproblem###Ifthevalueofcurrentsub-problemislargerthanthebound,thebranchforthissub-problemshouldbecutoff.Whichofthefollowingassertionsforthecuttingplanemethodarecorrect?

A:Afteraddingthecuttingplane,ifthenewrelaxedproblemisunsolvablethen,theoriginalILPisunsolvableB:Afteraddingthecuttingplane,oneshouldusingthedualsimplexmethodtosolvethenewrelaxedproblemC:Iftherelaxedproblemhasfeasiblesolution,thentheILPproblemhasfeasiblesolutionD:IntheprocedureofsolvingILPbycuttingplanemethod,thefeasibleregionoftherelaxedLPproblemwillbecomesmallerineachiteration.

答案:Afteraddingthecuttingplane,ifthenewrelaxedproblemisunsolvablethen,theoriginalILPisunsolvable###Afteraddingthecuttingplane,oneshouldusingthedualsimplexmethodtosolvethenewrelaxedproblem###IntheprocedureofsolvingILPbycuttingplanemethod,thefeasibleregionoftherelaxedLPproblemwillbecomesmallerineachiteration.

第三章單元測試

Whichofthefollowingassertionsforthedescentdirectionisincorrect?

A:Whenoneusesthedescentdirectiontoconstructaiterationalgorithm,thestepsizeshouldbesufficientlylarge.B:ThevalueofthecostfunctionwilldecreasealongthedescentdirectionC:Inanoptimizationproblem,thedescentdirectionmightnotbeafeasibledirection.D:Foranunconstrainedoptimizationproblem,thereisnodescentdirectiononthelocalminimizerofthecostfunction

答案:Whenoneusesthedescentdirectiontoconstructaiterationalgorithm,thestepsizeshouldbesufficientlylarge.Whichofthefollowingassertionsfortheconvexfunctionareincorrect?

A:IftheHessianmatrixofafunctionispositivesemi-definite,thenthisfunctionisaconvexfunctionB:ThesumoffinitelymanyconvexfunctionisstillaconvexfunctionC:TheHessianmatrixofstrictlyconvexfunctionispositivedefiniteD:Ifanylevelsetofafunctionisconvexthenthisfunctionisaconvexfunction

答案:TheHessianmatrixofstrictlyconvexfunctionispositivedefinite###IfanylevelsetofafunctionisconvexthenthisfunctionisaconvexfunctionInaconvexprogrammingproblem,theequalityconstraintfunctionsshouldbelinearfunctions

A:對B:錯

答案:對Inthefollowingassertions,whichonesareincorrect?

A:Iftheinnerproductofavectorpandthegradientvectorisnegative,thenpisadescentdirectionB:Inanunconstrainedoptimizationproblem,iftheHessianmatrixonastationarypointofthecostfunctionispositivesemi-definitethen,thestationarypointisalocalminimizerC:Tosolveaconstrainedconvexprogrammingproblem,weonlyneedtofindtheKKTpointsofthisconvexprogrammingproblemD:Inanunconstrainedoptimizationproblem,thestationarypointsoftheconvexcostfunctionareglobalminimizers

答案:Inanunconstrainedoptimizationproblem,iftheHessianmatrixonastationarypointofthecostfunctionispositivesemi-definitethen,thestationarypointisalocalminimizerInthesteepestdescentalgorithm,anytwoadjacentsearchdirectionsareorthogonaltoeachother

A:錯B:對

答案:對

第四章單元測試

Whenwewritescientificpapers,whatkindofwordsareoftenused?

A:antonymsB:acronymsC:oralwordsD:compoundwords

答案:antonyms###acronyms###compoundwordsIf