实验五：用MATLAB求解线性规划
2-10
c=[-3,-1,-4];
a = [6,3,5;3,4,5]; b=[45,30];
[x,fval]=linprog(c,a,b);
Exiting: One or more of the residuals, duality gap, or total relative error
has grown 100000 times greater than its minimum value so far:
the dual appears to be infeasible (and the primal unbounded). (The primal residual
1.0e+29 * -1.5497 -4.6492 4.6492
4-2
>> c=[-240,-1200,-700]; A=[1,1,1;0.5,0.5,0.5] B=[30000;20000]
[x,fval]=linprog(c,A,B) A =
1.0000 1.0000 1.0000 0.5000 0.5000 0.5000 B =
30000 20000
Exiting: One or more of the residuals, duality gap, or total relative error
has stalled:
the dual appears to be infeasible (and the primal unbounded). (The primal residual 1.0e+24 * -4.6326 4.6326 0.0000 fval =-4.4473e+27 实验六：非线性规划 5-4 >> f='2*x(1)^2+2*x(2)^2-4*x(1)+2*x(1)*x(2)-4*x(1)-6*x(2)'; x0=[1,1]; [x,f_min]=fminsearch(f,x0) x = 1.6667 0.6666 f_min =-8.6667 5-10 运用直接法编写程序： h=[2,1,0;1,4,0;0,0,0]; f=[-6;-2;-12]; a=[-1,2,0]; b=[3]; aeq=[1,1,1]; beq=[2]; [x,value]=quadprog(h,f,a,b,aeq,beq,zeros(3,1)) 结果即得： Warning: Trust-region-reflective algorithm does not solve this type of problem, using active-set algorithm. For more help, see Choosing the Algorithm in the documentation. > In quadprog at 371 Warning: Your current settings will run a different algorithm (interior-point-convex) in a future release. > In quadprog at 375 Optimization terminated. x = 0 0 2 value = -24 5-12. 5-12 >> H=[2 0 0 0 ;0 1 0 0 ;0 0 0 0;0 0 0 0]; >> f=[0 0 0 0]; >>Aeq=[1 -1 1 0;-2 1 0 1]; >>beq=[2 1]; >>x0=[1;3;4;0]; >>lb=zeros(4,1); >> [x,fval,exitflag,output,lambda]=quadprog(H,f,[],[],Aeq,beq,lb,[],x0) The interior-point-convex algorithm does not accept an initial point. Ignoring X0. Minimum found that satisfies the constraints. Optimization completed because the objective function is non-decreasing in feasible directions, to within the default value of the function tolerance, and constraints are satisfied to within the default value of the constraint tolerance. 0.0001 0.0002 2.0000 1.0001 fval = 2.4780e-08 exitflag = 1 output = message: 'Minimum found that satisfies the constraints. Optimization completed because the objective function is non-decrea...' algorithm: 'interior-point-convex' firstorderopt: 2.5030e-08 constrviolation: 2.2204e-16 iterations: 9 cgiterations: [] lambda = ineqlin: [0x1 double] eqlin: [2x1 double] lower: [4x1 double] upper: [4x1 double] 实验七：动态规划6-2
