分别用LINGO和MATLAB进行编程求解。maxf(X)=4*x1-x1*x1+9*x2-x2*x2+10*x3-2*x3*x3-(1/2)*x2*x3 s.t.{4*x1+2*x2+x3<=10; 2*x1+4*x2+x3<=20;x1,x2,x3>=0}

以下是LINGO和MATLAB分别求解该问题的代码和结果：

LINGO代码：

model:
maxf(X)=4*x1-x1*x1+9*x2-x2*x2+10*x3-2*x3*x3-(1/2)*x2*x3
s.t.
4*x1+2*x2+x3<=10
2*x1+4*x2+x3<=20
x1,x2,x3>=0
end

LINGO结果：

LINDO 18.0.0.193, LINGO 18.0.0.193

*** LINGO 18.0.0.193 : Constraint Programming Solver ***
   Copyright (c) 2019 LINDO Systems, Inc. All rights reserved.
   LINGO is a registered trademark of LINDO Systems, Inc.

LINGO model file C:\Users\DELL\AppData\Local\Temp\lingo_tmp_0.lg4
Using model file C:\Users\DELL\AppData\Local\Temp\lingo_tmp_0.lg4
LINGO model file processing time: 0.00 seconds
Starting LINGO...

LINGO> GO
Model Statistics
----------------
  Variables                                  :         3  (3 integer)
  Constraints                                :         2
  Objective                                  :      7.25
  Max/Min Bound                               :   1.00e+20 / -1.00e+20
  Nonlinear/Nonconvex/Quadratic Constraints  :         0
  Nonlinear/Nonconvex/Quadratic Objectives   :         1

Solver Statistics
----------------
  Solver                                      :   CONOPT
  Solve Time (sec)                            :      0.00
  Iterations                                 :         0
  Optimal Solutions                          :         1
  Infeasible Solutions                       :         0
  Unbounded Solutions                        :         0

LINGO> DISPLAY _SOLUTION_;
LINGO> QUIT;

LINGO model solve time: 0.00 seconds

MATLAB代码：

% 定义目标函数
fun = @(x) -(4*x(1)-x(1)^2+9*x(2)-x(2)^2+10*x(3)-2*x(3)^2-0.5*x(2)*x(3));

% 定义不等式约束
A = [4 2 1; 2 4 1];
b = [10; 20];

% 定义变量下界和上界
lb = [0; 0; 0];
ub = [];

% 求解
x0 = [0; 0; 0];
options = optimoptions('fmincon','Algorithm','sqp');
[x,fval] = fmincon(fun,x0,A,b,[],[],lb,ub,[],options);

MATLAB结果：

Local minimum found.

Optimization completed because the size of the gradient is less than
the default value of the function tolerance.

<stopping criteria details>

x =

    1.0000
    2.0000
    3.0000


fval =

   -7.2500