运筹学光盘内容实验指导第四章非线性

本章,我们介绍两种解决非线性规划问题的软件第一种:中的optimizationtoolbox中的若干程序;第二种:LINGO软件.程序名unpfun1函数unpfun2unpfun1实例Minimizethe

f(x)3x22xx 1 在命令窗口输入以下信息>>x0=[1,1];%Thencallfminunctofindaminimumofunpfun1near>>输出以下信息OptimizationterminatedSearchdirectionlessthan2*options.TolXx=1.0e-008 fval=unpfun2实例：将上述的实例用梯度法做>>options=optimset('GradObj','on');%Tominimizethisfunctionwiththegradientprovided>>x0=>>[x,fval]=输出以下信息OptimizationterminatedFirst-orderoptimalitylessthanOPTIONS.TolFun,andnonegative/zerocurvaturedetectedx1.0e-015 fval=第一种fminsearchFindaminimumofanunconstrainedmultivariablewherexisavectorandf(x)isafunctionthatreturnsa语法如下x=x=fminsearch(fun,x0,options)[x,fval]=fminsearch(...)[x,fval,exitflag]=fminsearch(...)[x,fval,exitflag,output]=解释fminsearchattemptstofindaminimumofascalarfunctionofseveralvariables,startingataninitialestimate.Thisisgenerallyreferredtoasunconstrainednonlinearoptimization.x=fminsearch(fun,x0)startsatthepointx0andattemptstofindalocalminimumxofthefunctiondescribedinfun.funisafunctionhandleforeitheranM-filefunctionorananonymousfunction.x0canbeascalar,vector,ormatrix.x=fminsearch(fun,x0,options)minimizeswiththeoptimizationoptionsspecifiedinthestructureoptions.Useoptimsettosetthese[x,fval]=fminsearch(...)returnsinfvalthevalueoftheobjectivefunctionfunatthesolutionx.[x,fval,exitflag]=fminsearch(...)returnsavalueexitflagthatdescribestheexitconditionoffminsearch.[x,fval,exitflag,output]=fminsearch(...)returnsastructureoutputthatcontainsinformationabouttheoptimization.AvoidingGlobalVariablesviaAnonymousandNestedFunctionsex inshowtoparameterizetheobjectivefunctionfun,ifnecessary.第二种:Findaminimumofanunconstrainedmultivariablewherexisavectorandf(x)isafunctionthatreturnsax=x=fminunc(fun,x0,options)[x,fval]=fminunc(...)[x,fval,exitflag]=fminunc(...)[x,fval,exitflag,output]=fminunc(...)[x,fval,exitflag,output,grad]=fminunc(...)[x,fval,exitflag,output,grad,hessian]=fminunc(...)fminuncattemptstofindaminimumofascalarfunctionofseveralvariables,startingataninitialestimate.Thisisgenerallyreferredtoasunconstrainednonlinearoptimization.x=fminunc(fun,x0)startsatthepointx0andattemptstofindalocalminimumxofthefunctiondescribedinfun.x0canbeascalar,vector,orx=fminunc(fun,x0,options)minimizeswiththeoptimizationoptionsspecifiedinthestructureoptions.Useoptimsettosettheseoptions.[x,fval]=fminunc(...)returnsinfvalthevalueoftheobjectivefunctionfunatthesolutionx.[x,fval,exitflag]=fminunc(...)returnsavalueexitflagthatdescribestheexitcondition.[x,fval,exitflag,output]=fminunc(...)returnsastructureoutputthatcontainsinformationabouttheoptimization.[x,fval,exitflag,output,grad]=fminunc(...)returnsingradthevalueofthegradientoffunatthesolutionx.[x,fval,exitflag,output,grad,hessian]=fminunc(...)returnsinhessianthevalueoftheHessianoftheobjectivefunctionfunatthesolutionx.SeeAvoidingGlobalVariablesviaAnonymousandNestedFunctionsex inshowtoparameterizetheobjectivefunctionfun,ifnecessary.程序名cnpfuncnfun实例

fx1x2 0x12x22x3在命令窗口输入以下信息>>A=[-1,-2,->>>>x0=[10;10;10];%Startingguessatthe>>[x,fval]=输出以下信息OptimizationterminatedMagnitudeofdirectionalderivativeinsearchdirectionlessthan2*options.TolFunand umconstraintviolationislessthanoptions.TolConActiveConstraints:x=fval程序的相关知识Findaminimumofaconstrainednonlinearmultivariablesubjectwherex,b,beq,lb,andubarevectors,AandAeqarematrices,c(x)andceq(x)arefunctionsthatreturnvectors,andf(x)isafunctionthatreturnsascalar.f(x),c(x),andceq(x)canbenonlinearfunctions.x=x=x=x=x=fmincon(fun,x0,A,b,Aeq,beq,lb,ub,nonlcon,options)[x,fval]=fmincon(...)[x,fval,exitflag]=fmincon(...)[x,fval,exitflag,output]=fmincon(...)[x,fval,exitflag,output,lambda]=fmincon(...)[x,fval,exitflag,output,lambda,grad]=fmincon(...)[x,fval,exitflag,output,lambda,grad,hessian]=fminconattemptstofindaconstrainedminimumofascalarfunctionofseveralvariablesstartingataninitialestimate.Thisisgenerallyreferredtoasconstrainednonlinearoptimizationornonlinearprogramming.x=fmincon(fun,x0,A,b)startsatx0andattemptstofindaminimumxtothefunctiondescribedinfunsubjecttothelinearinequalitiesA*x<=b.x0canbeascalar,vector,ormatrix.x=fmincon(fun,x0,A,b,Aeq,beq)minimizesfunsubjecttothelinearequalitiesAeq*x=beqaswellasA*x<=b.SetA=[]andb=[]ifnoinequalitiesexist.x=fmincon(fun,x0,A,b,Aeq,beq,lb,ub)definesasetoflowerandupperboundsonthedesignvariablesinx,sothatthesolutionisalwaysintherangelb<=x<=ub.SetAeq=[]andbeq=[]ifnoequalitiesexist.x=fmincon(fun,x0,A,b,Aeq,beq,lb,ub,nonlcon)subjectstheminimizationtothenonlinearinequalitiesc(x)orequalitiesceq(x)definedinnonlcon.fminconoptimizessuchthatc(x)<=0andceq(x)=0.Setlb=[]and/orub=[]ifnoboundsexist.x=fmincon(fun,x0,A,b,Aeq,beq,lb,ub,nonlcon,options)minimizeswiththeoptimizationoptionsspecifiedinthestructureoptions.Useoptimsettosettheseoptions.Setnonlcon=[]iftherearenononlinearinequalityorequalityconstraints.[x,fval]=fmincon(...)returnsthevalueoftheobjectivefunctionfunatthesolutionx.[x,fval,exitflag]=fmincon(...)returnsavalueexitflagthatdescribestheexitconditionoffmincon.[x,fval,exitflag,output]=fmincon(...)returnsastructureoutputwithinformationabouttheoptimization.[x,fval,exitflag,output,lambda]=fmincon(...)returnsastructurelambdawhosefieldscontaintheLagrangemultipliersatthesolutionx.[x,fval,exitflag,output,lambda,grad]=fmincon(...)returnsthevalueofthegradientoffunatthesolutionx.[x,fval,exitflag,output,lambda,grad,hessian]=fmincon(...)returnsthevalueoftheHessianatthesolutionx.SeeHessian.AvoidingGlobalVariablesviaAnonymousandNestedFunctionsexinshowtoparameterizetheobjectivefunctionfun,ifnecessary.程序名qprogramqprogram实例:

f(x)x2x2 42x1x x1,x2在命令窗口输入以下信息theprogramiswiththequadraticPleaseinputtheconstraintsnumberoftheprogrammingm4Pleaseinputthevariantnumberoftheprogrammingn4PleaseinputcostmatrixoftheobjectivefunctionH Pleaseinputcostarrayoftheobjectivefunctionc60PleaseinputthecoefficientmatrixoftheconstraintsA(m,n)=[-2,-1;-1,0;0,-A Pleaseinputtheresourcearrayoftheprogramb(m)_T=[-b00命令窗口输出信息Optimizationterminatedsuccessfully.Thesolutionofthequadraticis:x=程序的相关知识SolvethequadraticprogrammingwhereH,A,andAeqarematrices,andf,b,beq,lb,ub,andxare语法如下x=x=x=x=x=quadprog(H,f,A,b,Aeq,beq,lb,ub,x0,options)[x,fval]=quadprog(...)[x,fval,exitflag]=quadprog(...)[x,fval,exitflag,output]=quadprog(...)[x,fval,exitflag,output,lambda]=quadprog(...)解释x=quadprog(H,f,A,b)returnsavectorxthatminimizes1/2*x'*H*x+f'*xsubjecttoA*x<=b.x=quadprog(H,f,A,b,Aeq,beq)solvestheprecedingproblemwhileadditionallysatisfyingtheequalityconstraintsAeq*x=beq.x=quadprog(H,f,A,b,Aeq,beq,lb,ub)definesasetoflowerandupperboundsonthedesignvariables,x,sothatthesolutionisintherangelb<=x<=x=quadprog(H,f,A,b,Aeq,beq,lb,ub,x0)setsthestartingpointtox0.x=quadprog(H,f,A,b,Aeq,beq,lb,ub,x0,options)minimizeswiththeoptimizationoptionsspecifiedinthestructureoptions.Useoptimsettosettheseoptions.[x,fva