優(yōu)化設(shè)計方法

《優(yōu)化設(shè)計方法》姓名：陳辰學號：10104013院系：工學院專業(yè)：機械設(shè)計制造及其自動化班級：10機制一班第四章例題functiony=OPT_fun0(x)y=3*x(1)*x(1)-2*x(1)*x(2)+x(2)*x(2);formatlong;x0=[1,1];[x,f_opt,c,d]=fminsearch(@OPT_fun0,x0);x,f_opt結(jié)果：x=1.0e-004* 2-0.10965867079967 0.19889287750638f_opt=1.192541061251568e-009第四章課后習題4-1functiony=OPT_fun0(x)y=1.5*x(1)*x(1)+0.5*x(2)*x(2)-x(1)*x(2)-2*x(1);formatlong;x0=[2,2];[x,f_opt,c,d]=fminsearch(@OPT_fun0,x0);x,f_opt,c,d結(jié)果：x=0.99999695404938 1.00001655313968f_opt=-0.99999999979866c=1d=iterations:393funcCount:77algorithm:'Nelder-Meadsimplexdirectsearch用Hession矩陣進行證明：已知f(X)=3/2x(i)*x(i)+1/2x(2)*x(2)-X(i)*x(2)-2x(i)對該函數(shù)進行求導(dǎo)：一階導(dǎo)為：f(X1)=3X(1)-X(2)-2；二階導(dǎo)為：卜(X1)=3; 4(x2)=1； f''(X1X2)=f''(x2X1)=-1;由Hession矩陣判定條件之，令一階導(dǎo)數(shù)值為0，固有E3W=0; f(fx⑴=0；得:x(1)=1; x(2)=1該函數(shù)的Hession矩陣為：--H=由該Hession矩陣知，一階主4子式為3>0,二階主子式為:3*1-(-1)*(-1)=2>0.所以該Hession矩陣為正定。即可知X=[11]為該函數(shù)的極小值點。即可知Matlab軟件所算的值是正確的。functiony=OPT_fun0(x)y=x(1)*x(1)+x(1)*x(2)+2*x(2)*x(2)+4*x(1)+6*x(2)+10;formatlong;x0=[0,0];[x,f_opt,c,d]=fminsearch(@OPT_fun0,x0);x,f_opt,c結(jié)果：x=-1.42857209403050-1.14288457948509f_opt=3.71428571580995c=1結(jié)論：由結(jié)果可知該函數(shù)的最優(yōu)點為：X=[-1.43-1.14]故此函數(shù)的極值為：fopt=3.715functiony=a123(x)y=x(1)*x(1)*x(1)+x(1)*x(2)-3*x(2)*x(2)*x(2)+3*x(1)*x(1)+3*x(2)*x(2)-9*x(1);formatlong;x0=[0,0][x,f_opt,c,d]=fminsearch(@a123,x0);x,f_opt,c結(jié)果：x0=0 0x=1.01162643167122-0.13945566799890f_opt=-5.07378442202651c=16結(jié)論：由上述結(jié)果知該函數(shù)的最優(yōu)解點為：X=[1.01-0.14]故此函數(shù)的極值為:f_opt=-5.07functiony=a123(x)y=x(1)*x(1)*x(1)*x(1)+2*x(1)*x(1)*x(2)+x(2)*x(2)+x(1)*x(1)-2*x(2)+5;formatlong;x0=[0,0][x,f_opt,c,d]=fminsearch(@a123,x0);x,f_opt,c結(jié)果：X0=0 0X=0.00001815690060 0.99998886868293f_opt=4.000000001112927C=1結(jié)論：由上述結(jié)果知該函數(shù)的最優(yōu)解點為：X=[0 1]故此函數(shù)的極值為:f_opt=4.004-2functiony=OPT_fun0(x)y=4*x(1)*x(2)+4/x(1)+4/x(2);formatlong;x0=[0.5,0.5];[x,f_opt,c,d]=fminsearch(@OPT_fun0,x0);x,f_opt,c結(jié)果:結(jié)果:1.00001878336170 1.00000069475736f_opt=12.00000000146536結(jié)論：由上述結(jié)果知該函數(shù)的最優(yōu)解點為：X=[1 1]故此函數(shù)的極值為:f_opt=12.004-3functiony=OPT_fun1(x)y=x(1)*x(1)-x(1)*x(2)+3*x(2)*x(2);formatlong;x0=[1,1][x,f_opt,c,d]=fminsearch(@OPT_fun1,x0);x,f_opt,c9結(jié)果：x0=11x=1.0e-004*0.02440977771285 0.30798296188731f_opt=2.776385560476180e-009c=1結(jié)論：有輸出的結(jié)果可知，最終在x(0)=[0.020.31]處約束，且最優(yōu)解值為：f(x)=2.78 104-4functiony=OPT_fun1(x)y=4+4.5*x(1)-4*x(2)+x(1)*x(1)+2*x(2)*x(2)-2*x(1)*x(2)+x(1)*x(1)*x(1)*x(1)-2*x(1)*x(1)*x(2);formatlong;x0=[-2,2][x,f_opt,c,d]=fminsearch(@OPT_fun1,x0);x,f_opt,c結(jié)果：X0=-2 2x=-1.05275631816673 1.0277208586455611f_opt=-0.51340925137577c=1結(jié)論：由上述結(jié)果知該函數(shù)的最優(yōu)解點為：X=[1.05 1.03]故此函數(shù)的極值為：f_opt=-0.514-5functiony=OPT_fun1(x)y=x(1)*x(1)+2*x(2)*x(2);formatlong;x0=[1,1][x,f_opt,c,d]=fminsearch(@OPT_fun1,x0);x,f_opt12結(jié)果：x0=11x=1.0e-004*0.03454644575964 0.17587500087544f_opt=6.305748878049377e-010c=1結(jié)論：由上述結(jié)果知該函數(shù)的最13優(yōu)解點為：X=[0 0.18]故此函數(shù)的極值為：f_opt=6.314-6functiony=OPT_fun1(x)y=x(1)*x(1)-x(1)*x(2)+x(2)*x(2)+2*x(1)-4*x(2);formatlong;x0=[2,2][x,f_opt,c,d]=fminsearch(@OPT_fun1,x0);x,f_opt,c結(jié)果：X0=2 2x=0.00003131889914 2.0000196982037114f_opt=-3.99999999924803c=結(jié)論：由上述結(jié)果知該函數(shù)的最優(yōu)解為：X=[02]故此函數(shù)的極值為：f_opt=-4.00第五章例題Aeq=[];Beq=[];f=[-60,-120];A=[9,4;3,10;4,5];B=[360;300;200];LB=zeros(2,1);UB=[];15[X,fopt,key]=linprog(f,A,B,Aeq,Beq,LB,UB);X,fopt,key>>A11Optimizationterminatedsuccessfully.X=20.000024.0000fopt=-4.0800e+003key=1第五章課后習題5-1 16①Aeq=[1,1,1,0;1,2,2.5,3];Beq=[4;5];f=[-1.1,-2.2,3.3,-4.4];A=[];B=[];LB=zeros(4,1);UB=[];[X,fopt,key]=linprog(f,A,B,Aeq,Beq,LB,UB);X,fopt,key>>cc2Optimizationterminatedsuccessfully.X=3.999999999914530.000000000085390.000000000000140.33333333330478fopt=-5.86666666663444key=1結(jié)論：由上述結(jié)果知該函數(shù)的最優(yōu)點為：X=4.00.00.00.3故此函數(shù)的極小值為：fopt=-5.87②Aeq=[];Beq=[];f=[-7,-12];A=[9,4;4,5;3,10];B=[360;200;300];LB=zeros(2,1);UB=[];[X,fopt,key]=linprog(f,A,B,Aeq,Beq,LB,UB);X,fopt,key>>cc3Optimizationterminatedsuccessfully.X=1819.9999999999951323.99999999999991fopt=-4.279999999999648e+002key=1結(jié)論：由上述結(jié)果知該函數(shù)的最優(yōu)解點為:X=20.024.0故此函數(shù)的最小值為：fopt=-4.28e+0025-2Aeq=[];Beq=[];f=[-7000,-12000]; 19A=[9,4;4,5;3,10];B=[360;200;300];LB=zeros(2,1);UB=[];[X,fopt,key]=linprog(f,A,B,Aeq,Beq,LB,UB);X,fopt,keyOptimizationterminatedsuccessfully.X=19.9999999999967323.99999999999963fopt=-4.279999999999726e+005key=1結(jié)論：由上述結(jié)果知該函數(shù)的最優(yōu)解點為:X=20.024.0故此函數(shù)的最小值為：fopt=-4.28e+005…20f=[-0.30,-0.15];A=[-1,-1;1,1];B=[-600;1000];LB=zeros(2,1);UB=[800;1200];[X,fopt,key]=linprog(f,A,B,Aeq,Beq,LB,UB);X,fopt,keyX=7.999999999999761.99999999999523fopt=-2.699999999999213e+002key=1結(jié)論：由上述結(jié)果知該函數(shù)的最優(yōu)解點為:X=8.02.0故此函數(shù)的最小值為：fopt=-2.70e+0025-6 21Aeq=[];Beq=[];f=[1,-2]；A=[1,1;-2,-1];B=[5;-3];LB=zeros(2,1);UB=[];[X,fopt,key]=linprog(f,A,B,Aeq,Beq,LB,UB);X,fopt,key>>cc4Optimizationterminatedsuccessfully.X=0.000000000167344.99999999277444fopt=-9.9999999853815322key=1結(jié)論：由上述結(jié)果知該函數(shù)的最優(yōu)解點為:X=0.05.0故此函數(shù)的最小值為：fopt=-10.005-7Aeq=[1,2,1];Beq=[6];f=[-5,-4,-8];A=[5,3,0;2,-1,0];B=[15;4];LB=zeros(3,1);UB=[];[X,fopt,key]=linprog(f,A,B,Aeq,Beq,LB,UB);X,fopt,keyOptimizationterminatedsuccessfully.X=0.00000000000002 230.000000000000005.99999999999997fopt=-47.99999999999991key=

1結(jié)論：由上述結(jié)果知該函數(shù)的最優(yōu)解點為:X=0.00.06.0故此函數(shù)的最小值為：fopt=-48.00第六章已知約束優(yōu)化問題：24minf(x)=4氣-x;-12s.t.g(X)=x；+x；-25<0,g2(X)=-氣<0,g3(X)=-%<0,試以Xo=E,1L,Xo=",1｝，Xo二晶]為復(fù)合型的初始點，用復(fù)合型法進行二次迭代計算。主程序：functionf=exefun(x)f=4*x(1)-x(2)*x(2)-12;function[c,ceq]=execonfun(x)c=[x(1)*x(1)+x(2)*x(2)-25;-x(1)；-x(2)];ceq=[];x0=[2,1];lb=[0,0]；ub=[];options=optimset('LargeScale','off,'display','iter','tolx',1e-6);[x,fval,exitflag,output]=fmincon('exefun',x0,[],[],[],[],lb,ub,'execonfun',options)25輸出結(jié)果:maxDirectionalFirst-orderIterF-count f(x)constraintStep-sizederivativeoptimalityProcedureTOC\o"1-5"\h\z7 -21 0 1-20 611 -44.1111 7.111 1 -30.25.53Hessianmodifiedtwice

TOC\o"1-5"\h\z15 -37.3937 0.3937 1 6.320.409Hessianmodifiedtwice19 -37.0015 0.001526 10.391 0.123 -37 2.327e-008 10.00153 0.1Hessianmodified27 -37 4.416e-022 12.3e-008 4HessianmodifiedtwiceOptimizationterminatedsuccessfully:Searchdirectionlessthan2*options.TolXandmaximumconstraintviolationislessthanoptions.TolConActiveConstraints:326ActiveConstraints:326x=-0 5fval=-37exitflag=1output=iterations:6funcCount:27stepsize:1algorithm:'medium-scale:SQP,Quasi-Newton,line-searchfirstorderopt:4.0000cgiterations:[]

用外點法求解下列問題的最優(yōu)解，并用MATLAB計算下列約束優(yōu)化問題。minf(x)=氣+七s.t.g1(X)=3-七<0,g2(X)=氣20，主程序為：functionf=exefun(x)f=x(1)+x(2);function[c,ceq]=execonfun(x)27c=[3-x(2);27-x(1);x(2)];ceq=[];x0=[2,1];lb=[0,0];ub=[];options=optimset('LargeScale','off,'display','iter','tolx',1e-6);[x,fval,exitflag,output]=fmincon('exefun',x0,[],[],[],[],lb,ub,'execonfun',options)輸出結(jié)果：maxDirectionalFirst-orderIterF-count f(x)constraintStep-sizederivativeoptimalityProcedureTOC\o"1-5"\h\z7 3.5 1.5 10.5 1infeasible11 3.5 1.5 1-8.59e-009 1Hessianmodifiedtwice;infeasibleOptimizationterminated:Nofeasiblesolutionfound.Searchdirectionlessthan2*options.TolXbutconstraintsarenotsatisfied. 28x=2 1.5fval=3.5000exitflag=-1output=iterations:2funcCount:11stepsize:1algorithm:'medium-scale:SQP,Quasi-Newton,line-searchfirstorderopt:1.00006-46-4用內(nèi)點法求解下列問題的最優(yōu)解，并用Matlab計算下列約束優(yōu)化問題。minf(x)=氣+氣stg1(X)二一X2+X>0,,g2(X)=x1>0,主程序為：functionf=exefun(x)f=x(1)+