每日一题【20200822】

线性规划与非线性规划之间转换

线性规划

分析方案

f=[1 1 1 1 1 1 1]; % 目标函数的系数矩阵
intcon = [1 2 3 4 5 6 7]; % 整数所在位置，题目没有要求，所以是空
A = [4 3 2 1 1 0 0;0 1 0 2 1 3 0;0 0 1 0 1 0 2]; % 不等式约束的变量系数矩阵
b = [-50;-20,-15]; % 不等式约束的资源数
[x,fval] = intlinprog(f,intcon,-A,b); % fval代表最优解处的函数值

model:
sets:
moshi/1..7/:x;
xuqiu/1..3/:b;
link(moshi,xuqiu):c;
endsets
data:
c=4 0 0 3 1 0 2 0 1 1 2 0 1 1 1 0 3 0 0 0 2;
b=50 20 15;
enddata
min=@sum(moshi:x);
@for(xuqiu(j):@sum(moshi(i):c(i,j)*x(i))>b(j));
@for(moshi(i):@gin(x(i)));
end

非线性规划

model:
sets:
moshi/1..3/:x;
xuqiu/1..3/:a,b;
link(moshi,xuqiu):r;
endsets
data:
a=4,6,8;b=50,20,15;
enddata
min=@sum(moshi:x);
@for(xuqiu(j):@sum(moshi(i):r(i,j)*x(i))>b(j));
@for(moshi(i):@sum(xuqiu(j):a(j)*r(i,j))<19;@sum(xuqiu(j):a(j)*r(i,j))>16);
@for(moshi(i):@gin(x(i));@for(link:@gin(r)));
@for(moshi(i)|i#le#2:x(i)>x(i+1));
@sum(moshi:x)<28;@sum(moshi:x)>23;
end

Local optimal solution found.
  Objective value:                              27.00000
  Objective bound:                              27.00000
  Infeasibilities:                              0.000000
  Extended solver steps:                              22
  Total solver iterations:                           294
  Elapsed runtime seconds:                          0.85
  Model Class:                                      PIQP
  Total variables:                     12
  Nonlinear variables:                 12
  Integer variables:                   12
  Total constraints:                   14
  Nonlinear constraints:                3
  Total nonzeros:                      49
  Nonlinear nonzeros:                   9
                                Variable           Value        Reduced Cost
                                   X( 1)        15.00000            1.000000
                                   X( 2)        12.00000            1.000000
                                   X( 3)        0.000000            1.000000
                                   A( 1)        4.000000            0.000000
                                   A( 2)        6.000000            0.000000
                                   A( 3)        8.000000            0.000000
                                   B( 1)        50.00000            0.000000
                                   B( 2)        20.00000            0.000000
                                   B( 3)        15.00000            0.000000
                                R( 1, 1)        1.000000            0.000000
                                R( 1, 2)        1.000000            0.000000
                                R( 1, 3)        1.000000            0.000000
                                R( 2, 1)        3.000000            0.000000
                                R( 2, 2)        1.000000            0.000000
                                R( 2, 3)        0.000000            0.000000
                                R( 3, 1)        0.000000            0.000000
                                R( 3, 2)        3.000000            0.000000
                                R( 3, 3)        0.000000            0.000000

参考

1. NULL ↩