2016年大连理工大学优化方法上机大作业

'.年大连理工大学优化方法上机大作业上机大作业1：g(x(2)-x(1)^2);'.functionf=fun(x)f(1-x(1))^2+100*(x(2)-x(1)^2)^2;functiong=grad(x)gzerosgx-1)+400*x(1)*(x(1)^2-x(2));'.functionx_star=steepest(x0,eps)gradxwhileres>eps&&k<=1000akffunx0);ffun(x0+ak*dk);opedotgkdkwhilef1>f0+0.1*ak*slopekxk=x0+ak*dk;ffun(xk);x=xk;radxkfprintf('--The%d-thiter,theresidualis%f\n',k,res);xstar=xk;xepsgzeros'..functionf=fun(x)f(1-x(1))^2+100*(x(2)-x(1)^2)^2;functiong=grad2(x)g0*(3*x(1)^2-x(2));g*x(1);g*x(1);g;functiong=grad(x)gzerosgx-1)+400*x(1)*(x(1)^2-x(2));g(x(2)-x(1)^2);functionx_star=newton(x0,eps)gradxbkgradx1);whileres>eps&&k<=1000gkxkx+dk;x=xk;radxkbkgradxk);'.'.fprintf('--The%d-thiter,theresidualis%f\n',k,res);xstar=xk;xepsThethitertheresidualis447.213595Thethitertheresidualis0.000000x1=functionf=fun(x)f(1-x(1))^2+100*(x(2)-x(1)^2)^2;functiong=grad(x)gzerosgx-1)+400*x(1)*(x(1)^2-x(2));g(x(2)-x(1)^2);functionx_star=bfgs(x0,eps)gradxwhileres>eps&&k<=1000Hkgkakffunx0);ffun(x0+ak*dk);opedotgkdkwhilef1>f0+0.1*ak*slopekxk=x0+ak*dk;ffun(xk);faxkx0;x=xk;'.'.radxkygkgHkeyefayfay))*((eye(2)-(y0)*(fa0)')/((fa0)'*(y(fa0*(fa0)')/((fa0)'*(y0));fprintf-The%d-thiter,theresidualis%f\n'xstar=xk;functionf=fun(x)f(1-x(1))^2+100*(x(2)-x(1)^2)^2;functiong=grad(x)gzerosgx-1)+400*x(1)*(x(1)^2-x(2));g(x(2)-x(1)^2);functionx_star=CG(x0,eps)gradxwhileres>eps&&k<=1000akffunx0);ffun(x0+ak*dk);opedotgkdkwhilef1>f0+0.1*ak*slopekxk=x0+ak*dk;ffun(xk);'.'.x=xk;radxkpdkfprintf('--The%d-thiter,theresidualis%f\n',k,res);xstar=xk;上机大作业2：'..'..functionf=obj(x)f=4*x(1)-x(2)^2-12;function[h,g]=constrains(x)erosgx1)+x(1)^2-10*x(2)+x(2)^2+34;xxfunctionf=alobj(x)%拉格朗日增广函数%N_equ等式约束个数?%N_inequ不等式约束个数globalr_alpena;%全局变量x%等式约束部分?fori=1:N_equhequhequhiralipenahi2;fori=1:N_inequhinequhinequpenamaxralipenag(i))).^2-r_al(i).^2);'.'.fobjx)+h_equ+h_inequ;functionf=compare(x)globalr_alpenaN_equN_inequ;xfori=1:1fori=1:3equabsmaxgiralipenafmaxabs(h_equ),h1);inequfunction[x,fmin,k]=almain(x_al)%x_al:初始迭代点ralN-equ:%X：最优函数点FVAL:最优函数值=============等式约束个数N_inequ:不等式约束个数?%函数输出程序开始================================globalr_alpena;atera%参数(全局变量)%===========================算法迭代开始=============================whileout_itera<max_iteraxal=x_al;eFlagcomparexalnuncalobjxalxalX%得到新迭代点%判断停止条件?omparexaleal'.disp('wegettheoptpoint');c?mparexalctacompareFlagpenamincscalepena%%乘法系数最大1000disp('pena=2*pena');sxalfori=1:1alipenahifori=1:3ralimaxralipenagi)));iteraoutitera%+++++++++++++++++++++++++++迭代结束+++++++++++++++++++++++++++++++++disp('theiterationnumber');'.'.disp('thevalueofconstrains'aldisp('theoptpoint');xxal;fminobjX;kalmainxal上机大作业3：n=3;c=[-3,-1,-3]';A=[2,1,1;1,2,3;2,2,1;-1,0,0;0,-1,0;0,0,-1];b=[2,5,6,0,0,0]';nariablexn'..cttoAx<=bCallingSDPTvariablesequalityconstraints------------------------------------------------------------num.ofconstraints=3dim.oflinearvar=6******************************************************asiblepathfollowingalgorithms******************************************************versionpredcorrgamexponscale_dataNT10.00010itpstepdsteppinfeasdinfeasgapprim-objdual-objcputime-------------------------------------------------------------------0|0.000|0.000|1.1e+01|5.1e+00|6.0e+02|-7.000000e+010.000000e+00|0:0:00|1eee1|-5.606627e+00-2.967567e+01|0:0:01|chol.000|1.3e-07|4.6e-03|8.5e+00|-2.723981e+00-1.113509e+01|0:0:01|chol11111'.2.3e-08|6.2e-04|1.8e+00|-4.348354e+00-6.122853e+00|0:0:01|chol1|1.000|2.2e-08|4.6e-05|3.7e-01|-5.255152e+00-5.622375e+00|0:0:01|chol5|0.962|1.6e-09|6.2e-06|1.5e-02|-5.394782e+00-5.409213e+00|0:0:01|chol9|0.989|2.7e-10|5.2e-07|1.7e-04|-5.399940e+00-5.400100e+00|0:0:01|chol9|0.989|5.3e-11|5.8e-09|1.8e-06|-5.399999e+00-5.400001e+00|0:0:01|chol8|1.000|0.994|2.8e-13|4.3e-11|2.7e-08|-5.400000e+00-5.400000e+00|0:0:01|stopmaxrelativegap,infeasibilities)<1.49e-08-------------------------------------------------------------------numberofiterations=8rimalobjectivevalueedualobjectivevalue=-5.40000002e+00gap:=trace(XZ)=2.66e-08relativegap=2.26e-09actualrelativegap=2.21e-09rel.primalinfeas(scaledproblem)=2.77e-13rel.dual"""=4.31e-11lprimalinfeasunscaledproblemerel.dual"""=0.00e+00normXnormynormZe0,1.3e+00,1.9e+00normAnormbnormCe9.1e+00,5.4e+00TotalCPUtime(secs)=0.71Utimeperiterationterminationcode=0DIMACS:3.6e-130.0e+005.8e-110.0e+002.2e-092.3e-09111111111-------------------------------------------------------------------'.'.------------------------------------------------------------edmalvaluecvxoptvaln=2;c=[-2,-4]';G=[0.5,0;0,1];A=[1,1;-1,0;0,-1];b=[1,0,0]';nariablexncxcttoAx<=bCallingSDPTvariablesequalityconstraintsForimprovedefficiency,SDPT3issolvingthedualproblem.------------------------------------------------------------num.ofconstraints=3dim.ofsocpvar=4,num.ofsocpblk=1dim.oflinearvar=3******************************************************asiblepathfollowingalgorithms******************************************************versionpredcorrgamexponscale_data'.110itpstepdsteppinfeasdinfeasgapprim-objdual-objcputime-------------------------------------------------------------------0|0.000|0.000|8.0e-01|6.5e+00|3.1e+02|1.000000e+010.000000e+00|0:0:00|choleee|9.043148e+00-2.714056e-01|0:0:00|chol000|2.6e-07|7.6e-03|1.4e+00|1.234938e+00-5.011630e-02|0:0:00|chol2.4e-07|7.6e-04|3.0e-01|4.166959e-014|0.892|0.877|6.4e-08|1.6e-04|5.2e-02|2.773022e-015|1.000|1.000|1.0e-08|7.6e-06|1.5e-02|2.579468e-016|0.905|0.904|3.1e-09|1.4e-06|2.3e-03|2.511936e-017|1.000|1.000|6.1e-09|7.7e-08|6.6e-04|2.503336e-018|0.903|0.903|1.8e-09|1.5e-08|1.0e-04|2.500507e-019|1.000|1.000|4.9e-10|3.5e-10|2.9e-05|2.500143e-01eee6|2.500022e-01eee6|2.500006e-01eee7|2.500001e-01eee8|2.500000e-01eee9|2.500000e-01stopmaxrelativegap,infeasibilities)<1.49e-08-------------------------------------------------------------------numberofiterations=14primalobjectivevalue=2.50000004e-01dualobjectivevalue=2.49999996e-01e1|e1|e1|e1|e1|e1|e1|e1|e1|e1|e1|