二次规划实验举例

1、最优化算法实验指导书2.二次规划求解 例 1 求解下面二次规划问题min f(x) = 1 x2+ x2- x x 一 2x 一 6x2 1 2 1 2 1 2 sub.tox + x 212一 x + 2x 2122x + x 312 0 x , 0 H = 1 -1; -1 2 ; f = -2,-6; A = 1 1; -1 2; 2 1; b = 2; 2; 3; lb = zeros(2,1); x,fval,exitflag,output,lambda = quadprog(H,f,A,b, , ,lb)Warning: Large-scale method does not cu

2、rrently solve this problem formulation, switching to medium-scale method. In C:MATLAB6p5toolboxoptimquadprog.m at line 213 Optimization terminated successfully.0.66671.3333 fval =-8.2222 exitflag =output =iterations: 3algorithm: medium-scale: active-set firstorderopt: cgiterations: lambda =lower: 2x

3、1 double upper: 2x1 double eqlin: 0 x1 double ineqlin: 3x1 double例 1123 min y 二 x 2 + x 2 2x 4x 6x1 2 1 2 3x + x 212x + x 3s.t.32x + x 0123（1）标准形式：由 y 二 x 2 + x 2 2 x 4 x 6 x1 2 1 2 3二一(2x 2 + 2x 2) 2x 4x 6x2121232 0 0、知 H =020、0 0 0丿为半正定矩阵，约束不必改动。(2)在编辑窗口建立一个存放各种信息的M文件,在 MATLAB 中实现如下： H = 2 0 0;0 2

4、 0;0 0 0; f = -2 -4 -6; A = 1 1 0; 0 1 1; 1 0 1; b = 2; 3; 4; C =; d=; xm=0; 0; 0; xM=; x0=0,0,0; x,y=quadprog(H,f,A,b,C,d,xm,xM,x0)Warning: Large-scale method does not currently solve this problem formulation, switching to medium-scale method. In C:MATLAB6p5toolboxoptimquadprog.m at line 213 Optimi

5、zation terminated successfully.1.00000.00003.0000 y =-19例 1124 min y 二(x + x )2 + (x + x )2 x 2 2x 4x 6x12131123x+ x212x+ x332s.tx + x 01231)标准形式：由 y = x2 + x 2 + x 2 2x x 22x x 2x4x6x12312131231=(2x 2 + 2x 222x 2 2 4xx2 4 xx )2x 4 x 6 x2 1 231213123知 H =220为不定矩阵，约束不必改动。(2)在编辑窗口建立一个存放各种信息的M文件,在 MATL

6、AB 中实现如下： H = 2 2 2;2 2 0;2 0 2; f = -2 -4 -6; A = 1 1 0; 0 1 1; 1 0 1; b = 2; 3; 4; C=1 1 1; d=3.5; xm=0; 0; 0; xM=; x,y=quadprog(H,f,A,b,C,d,xm,xM,x0)Warning: Large-scale method does not currently solve this problem formulation, switching to medium-scale method. In C:MATLAB6p5toolboxoptimquadprog.m a