8-4 ?芥暩?勬サ灏忓?

MATLAB 矗ㄑ计ㄓ秈︽计厩ㄧ计程ㄎてセ竊盢ざ残

セ竊┮癚阶程ㄎてよ猭琌ゑ耕膀セよ猭璝弄Τ砍届ㄏノ耕狡馒よ猭ㄏノ程ㄎてㄣ絚Optimization Toolbox

иざ残虫跑ㄧ计程て狦眤璶碝― humps  [0.3, 1] い程ノ fminbnd ㄓт程祇ネ翴ㄒ

Example 1: 08-计厩ㄧ计矪瞶籔だ猂/fminbnd01.m[x, minValue] = fminbnd(@humps, 0.3, 1) % ㄏノ fminbnd т程祇ネ翴 fplot(@humps, [0.3, 1]); grid on line(x, minValue, 'marker', 'o', 'color', 'r'); % Plot the minimum point x = 0.6370 minValue = 11.2528

パㄒMATLAB ―眔程祇ネ x = 0.637程 11.2528璝璶笵碝―程い丁筁祘ㄏノ optimset ㄓ砞﹚陪ボ匡兜盢 optimset 肚挡篶跑计癳 fminbndㄒ

Example 2: 08-计厩ㄧ计矪瞶籔だ猂/fminbnd02.mopt = optimset('disp', 'iter'); % 陪ボ–˙艼挡狦 [x, minValue] = fminbnd(@humps, 0.3, 1, opt) Func-count x f(x) Procedure 1 0.567376 12.9098 initial 2 0.732624 13.7746 golden 3 0.465248 25.1714 golden 4 0.644416 11.2693 parabolic 5 0.6413 11.2583 parabolic 6 0.637618 11.2529 parabolic 7 0.636985 11.2528 parabolic 8 0.637019 11.2528 parabolic 9 0.637052 11.2528 parabolic Optimization terminated: the current x satisfies the termination criteria using OPTIONS.TolX of 1.000000e-04 x = 0.6370 minValue = 11.2528

 x 跑ての癸莱ㄧ计 f(x)程逆―伐よ猭硄盽琌独だ澄穓碝Golden Section Search┪琌┻絬ず础猭Parabolic Interpolationパゅ癟笵┮衡 x 粇畉 10  -4 Ωよ

璝璶肞粇畉恨ㄏ fminbnd 矗Ν肚璸衡挡狦ョパ optimset ㄓ笷Θㄒ盢 x 粇畉絛瞅矗蔼 0.1

Example 3: 08-计厩ㄧ计矪瞶籔だ猂/fminbnd03.mopt = optimset( 'disp', 'iter', 'TolX', 0.1); % 陪ボ–˙艼挡狦砞﹚粇畉甧г [x, minValue] = fminbnd(@humps, 0.3, 1, opt) Func-count x f(x) Procedure 1 0.567376 12.9098 initial 2 0.732624 13.7746 golden 3 0.465248 25.1714 golden 4 0.644416 11.2693 parabolic 5 0.611083 11.4646 parabolic 6 0.677749 11.7353 parabolic Optimization terminated: the current x satisfies the termination criteria using OPTIONS.TolX of 1.000000e-01 x = 0.6444 minValue = 11.2693

絛ㄒА琌癸虫跑ㄧ计―の璝璶―跑计ㄧ计伐パ fminsearch ―眔眤ゲ斗﹚癬﹍翴琵 fminsearch 沮―癬﹍翴Ы场程Local Minima安砞眤ヘ夹ㄧ计琌 $$f(x_1, x_2, x_3)=(x_1-1)^2+5(x_2-2)^2+(x_3-3)^2$$

眤ゲ斗玻ネ MATLAB ㄧ计 objective.mㄤず甧陪ボ

function y = objective(x) y = (x(1)-1).^2 + 5*(x(2)-2).^2 + (x(3)-3).^2;

璝癬﹍翴 $(x_1, x_2, x_3)=(0, 0, 0)$玥и块―程祇ネ竚

Example 4: 08-计厩ㄧ计矪瞶籔だ猂/fminsearch01.mx0 = [0, 0, 0]; x = fminsearch(@objective, x0) x = 1.0000 2.0000 3.0000

fminsearch ㄏノよ猭琌℡Α Simplex 穓碝Downhill Simplex Search冈灿把σ戈ǎ 掸セ璣ゅ帝Neuro  Fuzzy and Soft Computing, Prentice Hall, 1997

MATLAB 程ㄎてよ猭Τ砛ぃ匡兜硂ㄇ匡兜琌竒パ块ま计Input Argumentㄓ秈 fminbnd ┪ fminsearchㄤㄏノ粂猭

x = fminbnd(@function, x1, x2, options)

x = fminsearch(@function, x0, options )

ㄤい options 琌挡篶跑计せ逆贺程ㄎて匡兜┪把计饼砞﹚硂ㄇ程ㄎて匡兜ノ optimset ㄤㄏノ粂猭

options = optimset(prop1, value1, prop2, value2, )

ㄤい prop1prop2 单琌逆嘿value1value2 单琌癸莱逆ㄒ玡┮瓃璝璶ㄏ MATLAB –程ㄎて˙艼い丁挡狦肞粇畉絛瞅玥砞﹚

Example 5: 08-计厩ㄧ计矪瞶籔だ猂/optimset01.moptions = optimset('Disp', 'iter', 'TolX', 0.1); fieldNames=fieldnames(options); fprintf('No. of fields = %d\n', length(fieldNames)); options No. of fields = 65 options = Display: 'iter' MaxFunEvals: [] MaxIter: [] TolFun: [] TolX: 0.1000 FunValCheck: [] OutputFcn: [] PlotFcns: [] ActiveConstrTol: [] Algorithm: [] AlwaysHonorConstraints: [] BranchStrategy: [] DerivativeCheck: [] Diagnostics: [] DiffMaxChange: [] DiffMinChange: [] FinDiffRelStep: [] FinDiffType: [] GoalsExactAchieve: [] GradConstr: [] GradObj: [] HessFcn: [] Hessian: [] HessMult: [] HessPattern: [] HessUpdate: [] InitialHessType: [] InitialHessMatrix: [] InitBarrierParam: [] InitTrustRegionRadius: [] Jacobian: [] JacobMult: [] JacobPattern: [] LargeScale: [] LineSearchType: [] MaxNodes: [] MaxPCGIter: [] MaxProjCGIter: [] MaxRLPIter: [] MaxSQPIter: [] MaxTime: [] MeritFunction: [] MinAbsMax: [] NodeDisplayInterval: [] NodeSearchStrategy: [] NoStopIfFlatInfeas: [] ObjectiveLimit: [] PhaseOneTotalScaling: [] Preconditioner: [] PrecondBandWidth: [] RelLineSrchBnd: [] RelLineSrchBndDuration: [] ScaleProblem: [] Simplex: [] SubproblemAlgorithm: [] TolCon: [] TolConSQP: [] TolGradCon: [] TolPCG: [] TolProjCG: [] TolProjCGAbs: [] TolRLPFun: [] TolXInteger: [] TypicalX: [] UseParallel: []

パㄒoptions Τせ逆骸ì渤程ㄎて惠―ㄤウ程ㄎてǎ程ㄎてㄣ絚Optimization Toolbox瘤礛 options 逆渤ㄆ龟ぃ琌–逆常穦砆ノ狦逆陪ボ琌痻皚 MATLAB 穦ㄏノ逆箇砞ㄓ秈︽笲衡optimset 穦沮块程ㄎてㄧ计嘿τ肚ぃ挡狦ㄒи浪跌籔 fminbnd 闽程ㄎて匡兜

Example 6: 08-计厩ㄧ计矪瞶籔だ猂/optimset02.moptions = optimset('fminbnd'); fieldNames=fieldnames(options); fprintf('No. of fields = %d\n', length(fieldNames)); for i=1:length(fieldNames) if ~isempty(options.(fieldNames{i})) fprintf('options.%s=%s\n', fieldNames{i}, num2str(options.(fieldNames{i}))); end endNo. of fields = 65 options.Display=notify options.MaxFunEvals=500 options.MaxIter=500 options.TolX=0.0001 options.FunValCheck=off

计絛ㄒいи疭盢逆﹃逆秈︽埃竊陪ボ丁

璝璶浪跌籔 fminsearch 闽程ㄎて匡兜块

Example 7: 08-计厩ㄧ计矪瞶籔だ猂/optimset03.moptions = optimset('fminsearch'); fieldNames=fieldnames(options); fprintf('No. of fields = %d\n', length(fieldNames)); for i=1:length(fieldNames) if ~isempty(options.(fieldNames{i})) fprintf('options.%s=%s\n', fieldNames{i}, num2str(options.(fieldNames{i}))); end end No. of fields = 65 options.Display=notify options.MaxFunEvals=200*numberofvariables options.MaxIter=200*numberofvariables options.TolFun=0.0001 options.TolX=0.0001 options.FunValCheck=off

籔 fminbnd ㎝ fminsearch 闽璶程ㄎて匡兜弧

  1. Display 璝 0 箇砞玥ぃ陪ボい丁笲衡挡狦はぇ璝ぃ 0玥陪ボ笲衡筁祘い丁挡狦
  2. MaxFunEvals 琌ㄧ计―笲衡Function Evaluation程蔼Ω计癸 fminbnd 箇砞琌 500癸 fminsearch 箇砞琌 200  x0 
  3. MaxIter 琌程舼Ω计癸 fminbnd 箇砞琌 500癸 fminsearch 箇砞琌 200  x0 
  4. TolFun 琌∕﹚沧ゎ穓碝ㄧ计甧г箇砞 $10^{-4}$匡兜砆 fminsearch ノfminbnd ぃㄏノ
  5. TolX 琌∕﹚沧ゎ穓碝跑计甧г箇砞 $10^{-4}$

Hint
  • 程ㄎて獶绵の硄盽ㄤ筁祘琌滦程Μ滥程ㄎ翴程ㄎて挡狦㎝癬﹍翴匡﹚Τ闽羛▆癬﹍翴е程ㄎてΜ滥硉矗蔼т办程ㄎGlobal Optimum诀穦
  • ぃセ MATLABパ optimset 肚匡兜Τ┮ぃ琌畉钵┦ぃ


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