matlab牛頓法解無約束優(yōu)化問題

最優(yōu)化理論

實驗二

牛頓法解無約束優(yōu)化

問題院系自動化學(xué)院班級自動化3班

姓名朱軒睿學(xué)號20161336070一、實驗名稱牛頓法解無約束優(yōu)化問題所用工具Matlab2018a三、實驗流程熟悉牛頓法解無約束優(yōu)化問題的步驟。計算步驟(1)設(shè)置初始點x(6終止條件￡>0,令I(lǐng).⑵求梯度ya,*,計算I"，為|,若卜公則停止計算,輸出M/否則轉(zhuǎn)下一步.(3)構(gòu)造牛頓方向，計算代))」(4)計算卜一個迭代點3>1)=工律)一力/(3為”八萬⑹)，令k=k+h轉(zhuǎn)步驟(2),根據(jù)步驟列出matlab函數(shù)的大體結(jié)構(gòu)。計算出示例函數(shù)所需的一次導(dǎo)函數(shù)以及二次導(dǎo)函數(shù)公式，并轉(zhuǎn)化為matlab代碼。將初始點帶入到一次梯度函數(shù)中，并用norm函數(shù)計算其模，并與所要求的允許誤差進行比較。若小于允許誤差則跳出循環(huán)，帶入初始點得出最優(yōu)解，若不小于允許誤差則進行下一步，計算二次梯度，并根據(jù)上示公式得出下一個迭代點。將新迭代點帶入一次梯度函數(shù)，重復(fù)步驟4。四、Matlab代碼(包含注釋)第一個示例的代碼：Untitled..rn|Untitled.m+TOC\o"1-5"\h\z- a-L;- b=4：— c=0;- d=2;— rirstpointl=O;C— firstpoint2=l;- (㈤；— inin=niudunhanshu⑸b.c,d,firstpointl,firstpointS,E);用牛頓的數(shù)E為允許誤差。牛頓函數(shù)：Untitled.mniudunhanshu.m*yicihanshul.niercihanEhul.mfLkjcIir)j;LninJ-niudunhanshu1,atlijc,d.firstpointl,firstpointS,E)中軾IUIOHAN5HU此處顯荷關(guān)此函數(shù)的摘要% 此處顯示詳細說叨— J=[firstpointl;firstpoint2];如迭代點矩陣— yicidaD=yicihansliul(a.b,chd,firstpointl,firstpointS);- el=norintyicidao);蹌求出一次初度的模- wlii1e(el.-E) 圈比較— ercijz=ercihaiishu1'b.Cid.firstpointl.zirstpoiut2);— F次送代更新迭代點IC— X2-X-ercijz(-1)tyicidso; 用導(dǎo)下個邊代點- firstpointl=X2(l31);- first:3Oint2-X2(2rI); 呼更新迭代點— yicidao=yicihanshul(b,b,c3d,firstpointl,firstpoint2^;— el=norm(yicidao)“五芟i"莫?；疸┒鹊拿?endIS— nin:(firstpointl-a) b+(firstpoint2-c' d二— eii'-i一次梯度函數(shù):Untitled.m Untitled.mniudunhanshumyiciharishuLm++1Efunction[yicidao]=yicihanshnl(a,bTcTd,iirstpomtl：zirstpoint2)12 0研ICIHANSHl;此處城示啟“關(guān)此函數(shù)的摘要-%此處顯示詳細說明—工1ilrstpoitit1：— J.'irstpoint2;—qijdaoXl-3*{sla)'(b-l):—qiuda(jX2=d*(x2r)"(dT)對尺1和x2分別求導(dǎo)得出的函數(shù)— yicidao=[qiudacX1;qiudaoXSl;、組,禽或向；?<—encin此時帶入主函數(shù)中計算出向量模并進入循環(huán)。二次梯度函數(shù)：Untitled.mUntitled.mXnkidunhanshum*[yki山nstiuLm乂[erdhanshul,nfunctionerci.=ercihanshul(.a,b.d,firstpointl,f)^ftERCIHAXSHIl此處顯示有關(guān)此函數(shù)的摘耍-% 此處顯小詳細說明— xl=firstpoint1:— x2=firstpoiiitS;— ercil=b*(b-1)*(xl-a) (b-2)：- erci2=d京5-1)東(龍二廠(十2);轎根據(jù)?次梯度函數(shù)分別對k1?熠進行求導(dǎo)口— ercijE=[ercil,0:0,erci2];/U或二次梯度矩陣10— end第二個示例的代碼：ILIrititled2,m*+I- E=10-(-6);— firstpoint1=0.3;— fiir5tpciint2=-D.4;— tnin=Cosniudunfa(Etfirstpointl,fiTstpoint?);%中幀函數(shù)E為允許誤差。牛頓函數(shù):Untitled2,mgCosniudunfa.m;：：+-function[min=CosniddunfaE,firstpointl,firstpoint2)B%UmiTLED3此處顯示白美此函數(shù)的摘要% 此處顯示徉細說明— X-I--rstpoinTl;-irstpoint^]；- Cosyicidaol=CoEyicidao(firstpoint1：zirstpointS):— e=nortu(CosyicidaoO；— while(e^=E)— ercijz=Cosercidao'firstpointl,firstpoint2);- X=ElLrstpointl;lirstpoint2];— X2=X_ercijz"(-l)*Cosyicidaol;2- firstpointl=XSCLl):3- fir3tpaint3=X2(2,:1415- Co3yicidaol=CosyicidajO'firstpointl,firstpoint2)：IS— e=norm(CosyLcidaol):17— find— nii^=cos(sq.rt(zirstpointl 2-firstpoint22jf;— end一次梯度函數(shù)：Untitled2m Cosniudunfa.mCosyiciddo.m+1 0function[Ccsyicidso.=Cosyicidao(firstpointlhfirstpoLntS)S%C05Y[CIDA0此處啟東有關(guān)此函數(shù)的摘要■% 出處顯示詳細晚叨— j;=first]^ointl:— y=firstpoint2;— a=-Ix*sin(sqrt(x2+y 2^)]/.Lsqrt(x2+y ^2)];— b=-J.^sinLCsqrt(s 2+y~2))]/Lsqrt(s"2+y 2)];— Cosyicidao[a:b..：10— end二次梯度函數(shù)：Urrtitled2.mCosniudunla.mCtKyicidaa.m|Casercidaomt|+|L.function[Coswcidac?]z0?5ercidao{firstpointl,firslpaint^)H\COSEGCIRW此處顯而TT關(guān)此小數(shù)的摘師-%此處顯求他酬說叫- i=firstpointl：- y-f:rstpoint2;S- c-(s_2}tsinfsgrt(x-2+y-2))/(x-3+y2；(32)-1-2)os：x_2+y-2))：--y-2)-sin(aqrt{x_2+y'2)/;sqrt：,i2+y-2);7- d=x鄭%:it【sqrtlx『了？〉LH"2打"T[3I1,=挈cm(5qrt仁2+y"2K：'心"2+了？);8- ez(y"2)*5in(sqrt仁附F)/仁西飛"(3/2)-(y*2)*cqm{M(rt(K2*y2))/(^,2+y2)_sin(aqrt2))/sQrt(s“兩節(jié);9- f=x*Y*5in(sqrt(x-2+y2))/(x24y2}(3/2}-K*y*cos(sqrt(x24y2>}/(x2+y2):10-CostrcidacF[