※ 引述《hina09 (Hina*)》之銘言：
: 已知x+2y+4z+u=8
: 求4x+5y+6z+3u的最大值
: 1. 0≦x.y.z.u
: 2. 0≦x.y.z.u≦3
: 不知道題目是否有誤
: 煩請版上高手指點，謝謝～
用個程式硬幹的手法 cvx (convex optimization) 有興趣知道數學背景請參閱
Stanford教授 Stephen Boyd網頁
http://stanford.edu/~boyd/
敲個程式碼大約1分鐘! 答案26 @.@
cvx_begin
variable x(4)
maximize(4*x(1)+5*x(2)+6*x(3)+3*x(4))
subject to
x(1)+2*x(2)+4*x(3)+x(4)==8
x>=0
x<=3
cvx_end
Calling SDPT3 4.0: 8 variables, 3 equality constraints
For improved efficiency, SDPT3 is solving the dual problem.
------------------------------------------------------------
num. of constraints = 3
dim. of linear var = 8
*******************************************************************
SDPT3: Infeasible path-following algorithms
*******************************************************************
version predcorr gam expon scale_data
NT 1 0.000 1 0
it pstep dstep pinfeas dinfeas gap prim-obj dual-obj cputime
-------------------------------------------------------------------
0|0.000|0.000|7.8e-01|3.7e+00|8.0e+02| 1.200000e+02 0.000000e+00| 0:0:00|
chol 1 1
1|1.000|1.000|4.5e-07|4.3e-02|8.8e+01| 8.345473e+01 1.580001e+00| 0:0:00|
chol 1 1
2|0.900|1.000|1.2e-07|4.3e-03|8.5e+00| 1.144400e+01 3.019397e+00| 0:0:00|
chol 1 1
3|0.927|0.880|2.7e-08|8.9e-04|1.8e+00| 7.495398e+00 5.755842e+00| 0:0:00|
chol 1 1
4|0.992|0.927|1.3e-07|1.0e-04|1.1e-01| 6.561668e+00 6.455986e+00| 0:0:00|
chol 1 1
5|0.987|0.987|2.3e-09|5.6e-06|1.4e-03| 6.500784e+00 6.499494e+00| 0:0:00|
chol 1 1
6|0.989|0.989|2.5e-10|6.2e-08|1.5e-05| 6.500009e+00 6.499994e+00| 0:0:00|
chol 1 1
7|0.989|0.989|4.2e-12|7.3e-10|1.7e-07| 6.500000e+00 6.500000e+00| 0:0:00|
stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
number of iterations = 7
primal objective value = 6.50000009e+00
dual objective value = 6.49999994e+00
gap := trace(XZ) = 1.66e-07
relative gap = 1.19e-08
actual relative gap = 1.12e-08
rel. primal infeas = 4.25e-12
rel. dual infeas = 7.29e-10
norm(X), norm(y), norm(Z) = 4.3e+00, 3.2e+00, 5.7e+00
norm(A), norm(b), norm(C) = 3.6e+00, 4.5e+00, 6.6e+00
Total CPU time (secs) = 0.14
CPU time per iteration = 0.02
termination code = 0
DIMACS: 5.5e-12 0.0e+00 1.2e-09 0.0e+00 1.1e-08 1.2e-08
-------------------------------------------------------------------
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +26
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※ 編輯: snaredrum (172.5.42.156), 03/12/2016 13:25:50