MATLAB解二次規(guī)劃

1、黑龍江八一農墾大學數(shù)學建模選修課第八章MATLAB解二次非線性規(guī)劃一、數(shù)學模型min 1xTHx f Tx x 2A x bAeq x beqlb x ub其中H為二次型矩陣，A、Aeq分別為不等式約束與等式約束系數(shù)矩陣，f,b,beq,lb,ub,x為向量。二、求解二次規(guī)劃問題函數(shù) quadprog調用格式：X= quadprog(H,f,A,b)X= quadprog(H,f,A,b,Aeq,beq)X= quadprog(H,f,A,b,Aeq,beq,lb,ub)X= quadprog(H,f,A,b,Aeq,beq,lb,ub,x0)X= quadprog(H,f,A,b,Aeq,b

2、eq,lb,ub,x0,options)x,fval= quadprog( )x,fval,exitflag= quadprog( )x,fval,exitflag,output= quadprog()x,fval,exitflag,output,lambda= quadprog()說明：輸入?yún)?shù)中，x0為初始點；若無等式約束或無不等式約束，就將相應的矩陣和向量設置為空；options為指定優(yōu)化參數(shù)。輸出參數(shù)中，x是返回最優(yōu)解；fval是返回解所對應的目標函數(shù)值；exitflag是描述搜索是否收斂；output是返回包含優(yōu)化信息的結構。Lambda是返回解x入包含拉格朗日乘子的參數(shù)。三、舉例例

3、1：求解：二次規(guī)劃問題min f(x 1, x 2)= -2x 1-6x 2+x：-2x iX2+2x22s.t x i+X2< 2-x i+2x2< 2xi>0, x 2>0T2Xi6x2將其寫成標準形式：122 Ximin f (Xi,X2)Xi,X2,224X2S.t X 1+X2W 2-x i+2x2< 2xi>0, x 2>0程序： 編寫M文件mainG.m如下:H=1 -1;-1 2;f=-2;-6;3A=1 1;-1 2;b=2；2;Aeq=;beq=;lb=0;0;ub=;X,fval,exitflag=quadprog(H,f,A,b

4、,Aeq,beq,lb,ub) 結果：>> Warning: Large-scale method does not currently formulation, switching to medium-scale method.> In D:MATLAB6p5toolboxoptimquadprog.m at line 213In d:MATLAB6p5workUntitled5.m at line 7 Optimization terminated successfully.X = 0.66671.3333fval = -8.2222exitflag =1例2:求解：二次

5、規(guī)劃問題min x i2+2x22-2x iX2-4x i-12x 2s.t x i+x2< 2-x i+2x2< 22xi+x2< 30< xi, 0 < x2將其寫成標準形式：Ti44xi4minf(x1，x2)= xi, x2248x2i2s.t x i+x2< 2-x i+2x2< 22xi+x?w 30< xi, 0 < x2程序： 編寫M文件mainG.m如下：H=2 -2;-2 4;f=-4；-i2;A=i i；-i 2；2 i；b=2；2;3;lb=zeros(2,i);x,fval,exitflag=quadprog(H,f,A,b,lb)>> Warning: Large-scale method does not currently formulation, switching to medium-scale method.> In D:MATLAB6p5toolboxoptimquadprog.m at line 2i3In d:MATLAB6p5workUntitled5.m at line 6 Optimization terminated suc