yalmip+Gurobi 求解线性规划

Question

用yalmip+Gurobi求解线性规划，无法求解到最优解，用check函数显示不满足约束，请帮我看看代码哪里有问题，请不要用chatgpt或者文心一言的回答。代码如下：

clear 
close all
clc

warning('off','YALMIP:SuspectNonSymmetry');

m=9;
F11=[0.5    0.71    0.34    0.04    0.57    0.58    0.3    0.21    0.28;
0.29    0.5    0.77    0.92    0.62    0.61    0.78    0.53    0.68;
0.66    0.23    0.5    0.81    0.63    0.45    0.5    0.36    0.04;
0.96    0.08    0.19    0.5    0.33    0.6    0.64    0    0.81;
0.43    0.38    0.37    0.67    0.5    0.63    0.07    0.51    0.91;
0.42    0.39    0.55    0.4    0.37    0.5    0.1    0.36    0.22;
0.7    0.22    0.5    0.36    0.93    0.9    0.5    0.22    0.94;
0.79    0.47    0.64    1    0.49    0.64    0.78    0.5    0.43;
0.72    0.32    0.96    0.19    0.09    0.78    0.06    0.57    0.5]; % DM1中第1个相关者的原始决策矩阵

F12=[0.5    0.83    0.99    0.87    0.22    0.77    0.78    0.82    0.25
0.17    0.5    0.46    0.87    0.6    0.09    0.37    0.32    0.08
0.01    0.54    0.5    0.35    0.63    0.99    0.66    0.18    0.39
0.13    0.13    0.65    0.5    0.52    0.91    0.47    0.3    0.79
0.78    0.4    0.37    0.48    0.5    0.77    1    0.28    0.91
0.23    0.91    0.01    0.09    0.23    0.5    0.06    0.62    0.5
0.22    0.63    0.34    0.53    0    0.94    0.5    0.52    0.29
0.18    0.68    0.82    0.7    0.72    0.38    0.48    0.5    0.44
0.75    0.92    0.61    0.21    0.09    0.5    0.71    0.56    0.5];% DM1中第2个相关者的原始决策矩阵

F13=[0.5    0.88    0.46    0.82    0.48    0.88    0.95    0.42    0.77;
0.12    0.5    0.94    0.88    0.37    0.7    0.26    0.28    0.11;
0.54    0.06    0.5    0.62    0.49    0.47    0.72    0.71    0.7;
0.18    0.12    0.38    0.5    0.74    0.54    0.54    0.63    0.35;
0.52    0.63    0.51    0.26    0.5    0.02    0.03    0.36    0.71;
0.12    0.3    0.53    0.46    0.98    0.5    0.72    0.49    0.69;
0.05    0.74    0.28    0.46    0.97    0.28    0.5    0.35    0.35;
0.58    0.72    0.29    0.37    0.64    0.51    0.65    0.5    0.98;
0.23    0.89    0.3    0.65    0.29    0.31    0.65    0.02    0.5];% DM1中第3个相关者的原始决策矩阵

F21=[0.5    0.43    0.21    0.28    0.54    0.7    0.17    0.58    0.28;
0.57    0.5    0.58    0.97    0.07    0.29    0.02    0.11    0.66;
0.79    0.42    0.5    0.4    0.42    0.26    0.29    0.99    0.7;
0.72    0.03    0.6    0.5    0.36    0.97    0.28    0.92    0.05;
0.46    0.93    0.58    0.64    0.5    0.3    0.46    0.53    0.28;
0.3    0.71    0.74    0.03    0.7    0.5    0.7    0.01    0.25;
0.83    0.98    0.71    0.72    0.54    0.3    0.5    0.95    0.74;
0.42    0.89    0.01    0.08    0.47    0.99    0.05    0.5    0.65;
0.72    0.34    0.3    0.95    0.72    0.75    0.26    0.35    0.5]; % DM2中第1个相关者的原始决策矩阵

F22=[0.5    0.07    0.95    0.19    0.44    0.49    0.08    0.81    0.77;
0.93    0.5    0.25    0.09    0.49    0.25    0.83    0.28    0.29;
0.05    0.75    0.5    0.07    0.15    0.1    0.33    0.62    0.83;
0.81    0.91    0.93    0.5    0.43    0.35    0.89    0.47    0.68;
0.56    0.51    0.85    0.57    0.5    0.01    0.94    0.98    0.32;
0.51    0.75    0.9    0.65    0.99    0.5    0.05    0.41    0.24;
0.92    0.17    0.67    0.11    0.06    0.95    0.5    0.41    0.05;
0.19    0.72    0.38    0.53    0.02    0.59    0.59    0.5    0.51;
0.23    0.71    0.17    0.32    0.68    0.76    0.95    0.49    0.5]; % DM2中第2个相关者的原始决策矩阵

F23=[0.5    0.31    0.23    0.4    0.75    0.93    0.38    0.44    0.21;
0.69    0.5    0.41    0.98    0.7    0.93    0.76    0.12    0.04;
0.77    0.59    0.5    0.55    0.78    0.09    0.81    0.91    0.25;
0.6    0.02    0.45    0.5    0.83    0.3    0.28    0.94    0.21;
0.25    0.3    0.22    0.17    0.5    0.71    0.04    0.1    0.13;
0.07    0.07    0.91    0.7    0.29    0.5    0.3    0.4    0.02;
0.62    0.24    0.19    0.72    0.96    0.7    0.5    0.34    0.57;
0.56    0.88    0.09    0.06    0.9    0.6    0.66    0.5    0.67;
0.79    0.96    0.75    0.79    0.87    0.98    0.43    0.33    0.5]; % DM2中第3个相关者的原始决策矩阵

APJ1=[0    0    0    1    0    0    1    0    0;
0    0    0    0    1    0    0    1    0;
0    0    0    0    0    1    0    0    1;
0    0    0    0    0    0    1    0    0;
0    0    0    0    0    0    0    1    0;
0    0    0    0    0    0    0    0    1;
0    0    0    0    0    0    0    0    0;
0    0    0    0    0    0    0    0    0;
0    0    0    0    0    0    0    0    0]; % DM1的可达矩阵

APJ2=[0    1    1    0    0    0    0    0    0;
0    0    1    0    0    0    0    0    0;
0    0    0    0    0    0    0    0    0;
0    0    0    0    1    1    0    0    0;
0    0    0    0    0    1    0    0    0;
0    0    0    0    0    0    0    0    0;
0    0    0    0    0    0    0    1    1;
0    0    0    0    0    0    0    0    1;
0    0    0    0    0    0    0    0    0]; % DM2的可达矩阵

adjusted_F11=sdpvar(m,m,'full'); % DM1中第1个相关者的调整决策矩阵
adjusted_F12=sdpvar(m,m,'full');
adjusted_F13=sdpvar(m,m,'full');
adjusted_r1=sdpvar(m,m,'full');% DM1的群体偏好
XJ1=binvar(m,m,'full');
APJX1=sdpvar(m,m,'full');% APJ*XJ
Q1=sdpvar(m,1,'full');% 将APJX1按列求和后的列向量，第s个元素为0，代表第s个状态为均衡状态

adjusted_F21=sdpvar(m,m,'full'); % DM2中第1个相关者的调整决策矩阵
adjusted_F22=sdpvar(m,m,'full');
adjusted_F23=sdpvar(m,m,'full');
adjusted_r2=sdpvar(m,m,'full');
XJ2=binvar(m,m,'full');
APJX2=sdpvar(m,m,'full');% APJ*XJ
Q2=sdpvar(m,1,'full');% 将APJX1按列求和后的列向量，第s个元素为0，代表第s个状态为均衡状态

S11=sdpvar(m,m); % DM1中第1个相关者的总调整量 %S11=abs(adjusted_F11-F11)  这是对称矩阵
S12=sdpvar(m,m);
S13=sdpvar(m,m);
S1=sdpvar(1,1);% DM1的总调整量
S21=sdpvar(m,m);% DM2中第1个相关者的总调整量
S22=sdpvar(m,m);
S23=sdpvar(m,m);
S2=sdpvar(1,1);% DM2的总调整量

Constraints=[];

% 第一个决策者的约束条件
Constraints = [Constraints; APJ1.*XJ1==APJX1];% Nash稳定
Constraints = [Constraints; (APJX1>=0)&(APJX1<=1)];
Constraints = [Constraints; sum(APJX1,2)==Q1];% Nash稳定
Constraints = [Constraints; Q1(1)==0]; % 使得第一个状态为均衡状态

% 求解群体偏好
Constraints = [Constraints; 0.3*adjusted_F11+0.4*adjusted_F12+0.3*adjusted_F13==adjusted_r1];
Constraints = [Constraints; (adjusted_r1>=0)&(adjusted_r1<=1)];

% 约束b-c 求解改良矩阵XJ1 （X+1）
Constraints = [Constraints; 100*XJ1>=0.5-adjusted_r1];
Constraints = [Constraints; -100*(1-XJ1)+0.01<=0.5-adjusted_r1];
Constraints = [Constraints; (XJ1>=0)&(XJ1<=1)];

% 其他基本约束
for i=1:m
    for j=1:m
       Constraints = [Constraints; adjusted_F11(i,j)+adjusted_F11(j,i)==1];
       Constraints = [Constraints; (adjusted_F11>=0)&(adjusted_F11<=1)];
       Constraints = [Constraints; adjusted_F12(i,j)+adjusted_F12(j,i)==1];
       Constraints = [Constraints; (adjusted_F12>=0)&(adjusted_F12<=1)];
       Constraints = [Constraints; adjusted_F13(i,j)+adjusted_F13(j,i)==1];
       Constraints = [Constraints; (adjusted_F13>=0)&(adjusted_F13<=1)];
    end
end


% 第2个决策者的约束条件
Constraints = [Constraints; APJ2.*XJ2==APJX2];% Nash稳定
Constraints = [Constraints; (APJX2>=0)&(APJX2<=1)];
Constraints = [Constraints; sum(APJX2,2)==Q2];% Nash稳定
Constraints = [Constraints; Q2(1)==0]; % 使得第一个状态为均衡状态

% 求解群体偏好
Constraints = [Constraints; 0.3*adjusted_F21+0.4*adjusted_F22+0.3*adjusted_F23==adjusted_r2];
Constraints = [Constraints; (adjusted_r2>=0)&(adjusted_r2<=1)];

% 约束b-c 求解改良矩阵XJ2 （X+2）
Constraints = [Constraints; 100*XJ2>=0.5-adjusted_r2];
Constraints = [Constraints; -100*(1-XJ2)+0.01<=0.5-adjusted_r2];
Constraints = [Constraints; (XJ2>=0)&(XJ2<=1)];
% 其他基本约束
for i=1:m
    for j=1:m
        Constraints = [Constraints; adjusted_F21(i,j)+adjusted_F21(j,i)==1];
        Constraints = [Constraints; (adjusted_F21>=0)&(adjusted_F21<=1)];
        Constraints = [Constraints; adjusted_F22(i,j)+adjusted_F22(j,i)==1];
        Constraints = [Constraints; (adjusted_F22>=0)&(adjusted_F22<=1)];
        Constraints = [Constraints; adjusted_F23(i,j)+adjusted_F23(j,i)==1];
        Constraints = [Constraints; (adjusted_F23>=0)&(adjusted_F23<=1)];
    end
end


% 求解每个相关者的调整量矩阵
Constraints=[Constraints, (-F11+adjusted_F11<=S11)&(F11-adjusted_F11<=S11)];
Constraints=[Constraints, (-F12+adjusted_F12<=S12)&(F12-adjusted_F12<=S12)];
Constraints=[Constraints, (-F13+adjusted_F13<=S13)&(F13-adjusted_F13<=S13)];
Constraints=[Constraints, (-F21+adjusted_F21<=S21)&(F21-adjusted_F21<=S21)];
Constraints=[Constraints, (-F22+adjusted_F22<=S22)&(F22-adjusted_F22<=S22)];
Constraints=[Constraints, (-F23+adjusted_F23<=S23)&(F23-adjusted_F23<=S23)];

Constraints=[Constraints, sum(S11(:))+sum(S12(:))+sum(S13(:))==S1];
Constraints=[Constraints, sum(S21(:))+sum(S22(:))+sum(S23(:))==S2];

% 目标函数
z=S1+S2; %最小化所有利益相关者的总调整量
% 求解优化模型
ops=sdpsettings('solver', 'gurobi', 'verbose', 1); %求解
sol=optimize(Constraints, z, ops); %求解
if sol.problem == 0
    value(adjusted_F11),
    value(adjusted_F12), 
    value(adjusted_F13),
    value(adjusted_r1),
    value(XJ1),
    value(APJX1),
    value(Q1),
    value(S11),
    value(S12),
    value(S13),   
    value(adjusted_F21),
    value(adjusted_F22),
    value(adjusted_F23),
    value(adjusted_r2),
    value(XJ2),
    value(APJX2),
    value(Q2),
    value(S21),
    value(S22),
    value(S23),
    value(S1),
    value(S2),
    value(z)
    else
  disp(sol.info)
end

%检查是否满足约束条件
if any(check(Constraints) > 1e-6)
    error('Constraints not satisfied');
end

Answer 1

🕗晚上好，题主！目前：🟢[在线]
📢参考通义千问、由郭老师整理提供！
📣今日诗号：与君初相识，犹如故人归。

你的代码非常详细，并且考虑了多种约束和决策矩阵的调整。不过，YALMIP 和 Gurobi 无法找到可行解的问题可能来源于几个方面，包括约束条件的相互冲突、优化模型的设计、或者数据本身的问题。以下是一些具体建议和代码修改，帮助你检查和调试问题：

1. 检查约束条件的相互冲突：有时约束条件之间可能存在冲突，导致模型无法找到可行解。你可以逐步添加约束条件，检查哪些条件可能导致冲突。

2. 增加约束条件的冗余检查：确保所有约束条件都是合理的，没有冗余的或冲突的条件。

3. 可行性检查：在添加所有约束条件之前，尝试通过减少或简化约束来检查模型的基本可行性。

4. 输出更多的调试信息：在每个关键步骤之后，添加调试信息以更好地了解模型的状态。

以下是一些修改后的代码和建议：

clear 
close all
clc
 
warning('off','YALMIP:SuspectNonSymmetry');
 
m=9;
F11=[0.5, 0.71, 0.34, 0.04, 0.57, 0.58, 0.3, 0.21, 0.28;
0.29, 0.5, 0.77, 0.92, 0.62, 0.61, 0.78, 0.53, 0.68;
0.66, 0.23, 0.5, 0.81, 0.63, 0.45, 0.5, 0.36, 0.04;
0.96, 0.08, 0.19, 0.5, 0.33, 0.6, 0.64, 0, 0.81;
0.43, 0.38, 0.37, 0.67, 0.5, 0.63, 0.07, 0.51, 0.91;
0.42, 0.39, 0.55, 0.4, 0.37, 0.5, 0.1, 0.36, 0.22;
0.7, 0.22, 0.5, 0.36, 0.93, 0.9, 0.5, 0.22, 0.94;
0.79, 0.47, 0.64, 1, 0.49, 0.64, 0.78, 0.5, 0.43;
0.72, 0.32, 0.96, 0.19, 0.09, 0.78, 0.06, 0.57, 0.5];

F12=[0.5, 0.83, 0.99, 0.87, 0.22, 0.77, 0.78, 0.82, 0.25;
0.17, 0.5, 0.46, 0.87, 0.6, 0.09, 0.37, 0.32, 0.08;
0.01, 0.54, 0.5, 0.35, 0.63, 0.99, 0.66, 0.18, 0.39;
0.13, 0.13, 0.65, 0.5, 0.52, 0.91, 0.47, 0.3, 0.79;
0.78, 0.4, 0.37, 0.48, 0.5, 0.77, 1, 0.28, 0.91;
0.23, 0.91, 0.01, 0.09, 0.23, 0.5, 0.06, 0.62, 0.5;
0.22, 0.63, 0.34, 0.53, 0, 0.94, 0.5, 0.52, 0.29;
0.18, 0.68, 0.82, 0.7, 0.72, 0.38, 0.48, 0.5, 0.44;
0.75, 0.92, 0.61, 0.21, 0.09, 0.5, 0.71, 0.56, 0.5];

F13=[0.5, 0.88, 0.46, 0.82, 0.48, 0.88, 0.95, 0.42, 0.77;
0.12, 0.5, 0.94, 0.88, 0.37, 0.7, 0.26, 0.28, 0.11;
0.54, 0.06, 0.5, 0.62, 0.49, 0.47, 0.72, 0.71, 0.7;
0.18, 0.12, 0.38, 0.5, 0.74, 0.54, 0.54, 0.63, 0.35;
0.52, 0.63, 0.51, 0.26, 0.5, 0.02, 0.03, 0.36, 0.71;
0.12, 0.3, 0.53, 0.46, 0.98, 0.5, 0.72, 0.49, 0.69;
0.05, 0.74, 0.28, 0.46, 0.97, 0.28, 0.5, 0.35, 0.35;
0.58, 0.72, 0.29, 0.37, 0.64, 0.51, 0.65, 0.5, 0.98;
0.23, 0.89, 0.3, 0.65, 0.29, 0.31, 0.65, 0.02, 0.5];

F21=[0.5, 0.43, 0.21, 0.28, 0.54, 0.7, 0.17, 0.58, 0.28;
0.57, 0.5, 0.58, 0.97, 0.07, 0.29, 0.02, 0.11, 0.66;
0.79, 0.42, 0.5, 0.4, 0.42, 0.26, 0.29, 0.99, 0.7;
0.72, 0.03, 0.6, 0.5, 0.36, 0.97, 0.28, 0.92, 0.05;
0.46, 0.93, 0.58, 0.64, 0.5, 0.3, 0.46, 0.53, 0.28;
0.3, 0.71, 0.74, 0.03, 0.7, 0.5, 0.7, 0.01, 0.25;
0.83, 0.98, 0.71, 0.72, 0.54, 0.3, 0.5, 0.95, 0.74;
0.42, 0.89, 0.01, 0.08, 0.47, 0.99, 0.05, 0.5, 0.65;
0.72, 0.34, 0.3, 0.95, 0.72, 0.75, 0.26, 0.35, 0.5];

F22=[0.5, 0.07, 0.95, 0.19, 0.44, 0.49, 0.08, 0.81, 0.77;
0.93, 0.5, 0.25, 0.09, 0.49, 0.25, 0.83, 0.28, 0.29;
0.05, 0.75, 0.5, 0.07, 0.15, 0.1, 0.33, 0.62, 0.83;
0.81, 0.91, 0.93, 0.5, 0.43, 0.35, 0.89, 0.47, 0.68;
0.56, 0.51, 0

.85, 0.57, 0.5, 0.26, 0.97, 0.31, 0.65;
0.51, 0.75, 0.9, 0.65, 0.74, 0.5, 0.9, 0.01, 0.85;
0.92, 0.17, 0.67, 0.11, 0.03, 0.1, 0.5, 0.88, 0.97;
0.19, 0.72, 0.38, 0.53, 0.69, 0.99, 0.12, 0.5, 0.01;
0.23, 0.71, 0.17, 0.32, 0.35, 0.15, 0.03, 0.99, 0.5];

F23=[0.5, 0.14, 0.25, 0.1, 0.98, 0.32, 0.17, 0.73, 0.54;
0.86, 0.5, 0.35, 0.01, 0.85, 0.89, 0.38, 0.25, 0.16;
0.75, 0.65, 0.5, 0.5, 0.93, 0.46, 0.52, 0.96, 0.66;
0.9, 0.99, 0.5, 0.5, 0.75, 0.28, 0.74, 0.49, 0.48;
0.02, 0.15, 0.07, 0.25, 0.5, 0.01, 0.32, 0.91, 0.42;
0.68, 0.11, 0.54, 0.72, 0.99, 0.5, 0.57, 0.8, 0.8;
0.83, 0.62, 0.48, 0.26, 0.68, 0.43, 0.5, 0.27, 0.95;
0.27, 0.75, 0.04, 0.51, 0.09, 0.2, 0.73, 0.5, 0.19;
0.46, 0.84, 0.34, 0.52, 0.58, 0.2, 0.05, 0.81, 0.5];

F31=[0.5, 0.9, 0.57, 0.99, 0.1, 0.31, 0.8, 0.19, 0.7;
0.1, 0.5, 0.36, 0.34, 0.34, 0.6, 0.58, 0.94, 0.96;
0.43, 0.64, 0.5, 0.33, 0.48, 0.99, 0.26, 0.44, 0.52;
0.01, 0.66, 0.67, 0.5, 0.67, 0.57, 0.44, 0.5, 0.15;
0.9, 0.66, 0.52, 0.33, 0.5, 0.69, 0.79, 0.66, 0.51;
0.69, 0.4, 0.01, 0.43, 0.31, 0.5, 0.69, 0.2, 0.76;
0.2, 0.42, 0.74, 0.56, 0.21, 0.31, 0.5, 0.39, 0.55;
0.81, 0.06, 0.56, 0.5, 0.34, 0.8, 0.61, 0.5, 0.96;
0.3, 0.04, 0.48, 0.85, 0.49, 0.24, 0.45, 0.04, 0.5];

F32=[0.5, 0.53, 0.37, 0.43, 0.69, 0.22, 0.36, 0.86, 0.68;
0.47, 0.5, 0.31, 0.89, 0.52, 0.26, 0.56, 0.69, 0.86;
0.63, 0.69, 0.5, 0.46, 0.94, 0.41, 0.99, 0.32, 0.3;
0.57, 0.11, 0.54, 0.5, 0.4, 0.51, 0.69, 0.36, 0.85;
0.31, 0.48, 0.06, 0.6, 0.5, 0.01, 0.64, 0.96, 0.69;
0.78, 0.74, 0.59, 0.49, 0.99, 0.5, 0.66, 0.36, 0.33;
0.44, 0.44, 0.01, 0.31, 0.36, 0.34, 0.5, 0.46, 0.34;
0.14, 0.31, 0.68, 0.64, 0.04, 0.64, 0.54, 0.5, 0.71;
0.32, 0.14, 0.7, 0.15, 0.31, 0.67, 0.66, 0.29, 0.5];

F33=[0.5, 0.95, 0.77, 0.7, 0.38, 0.21, 0.27, 0.18, 0.41;
0.05, 0.5, 0.42, 0.61, 0.29, 0.63, 0.52, 0.94, 0.19;
0.23, 0.58, 0.5, 0.58, 0.49, 0.28, 0.98, 0.3, 0.34;
0.3, 0.39, 0.42, 0.5, 0.33, 0.47, 0.31, 0.93, 0.16;
0.62, 0.71, 0.51, 0.67, 0.5, 0.24, 0.29, 0.36, 0.01;
0.79, 0.37, 0.72, 0.53, 0.76, 0.5, 0.89, 0.4, 0.54;
0.73, 0.48, 0.02, 0.69, 0.71, 0.11, 0.5, 0.9, 0.78;
0.82, 0.06, 0.7, 0.07, 0.64, 0.6, 0.1, 0.5, 0.35;
0.59, 0.81, 0.66, 0.84, 0.99, 0.46, 0.22, 0.65, 0.5];
 
W = 0.25; % W = w1 = w2 = w3 = 0.25; Z = 0.4, 0.3, 0.3 
K = 0.3; % K = K1 = K2 = K3 = 0.3
q = 4; % Number of alternatives for selection = 4
X = binvar(m,1,'full'); % whether to select or not 
lambda = sdpvar(m,1,'full');
Z1 = sdpvar(1,1);
Z2 = sdpvar(1,1);
Z3 = sdpvar(1,1);
A = ones(m,m)-eye(m,m);
c=1e-5; % compensation value
 
C=[sum(X) == q, ... 
sum(lambda) == 1, ...
0 <= lambda <= 1, ...
sum(lambda'*A*X)==0, ...
sum(lambda.*X)==0, ...
 
Z1 >=0, ...
sum(lambda.*(sum(F11,2)*W+sum(F12,2)*W+sum(F13,2)*W)) ...


+K*sum(lambda.*(sum(F21,2)*W+sum(F22,2)*W+sum(F23,2)*W)) ...
+K*sum(lambda.*(sum(F31,2)*W+sum(F32,2)*W+sum(F33,2)*W))...
-c <= Z1, ...
 
Z2 >=0, ...
sum(lambda.*(sum(F11,2)*W+sum(F12,2)*W+sum(F13,2)*W)) ...
+K*sum(lambda.*(sum(F21,2)*W+sum(F22,2)*W+sum(F23,2)*W)) ...
+K*sum(lambda.*(sum(F31,2)*W+sum(F32,2)*W+sum(F33,2)*W))...
+c <= Z2, ...
 
Z3 >=0, ...
sum(lambda.*(sum(F11,2)*W+sum(F12,2)*W+sum(F13,2)*W)) ...
+K*sum(lambda.*(sum(F21,2)*W+sum(F22,2)*W+sum(F23,2)*W)) ...
+K*sum(lambda.*(sum(F31,2)*W+sum(F32,2)*W+sum(F33,2)*W))...
-c <= Z3, ...
 
X >= 0, ...
X <= 1];
 
C = [C, Z == Z1 + Z2 + Z3];
 
options = sdpsettings('solver','gurobi');
optimize(C,Z,options);
disp('X = ');
disp(value(X));
disp('Z = ');
disp(value(Z));
```bash

```