看利用KKT求解函数最小值,函数为(c+h+v)-ρ[w-v-Θ(m-g)][1-F(Q)]-t1+t2=0;约束条件为:t1*(-Q)=0,t2(Q-T)=0,利用matlab进行KKT求解,列出代码过程
时间: 2024-03-30 17:38:37 浏览: 65
好的,根据您的要求,我会回答您的问题,并且不会透露您的任何要求。对于您的问题,我们可以使用matlab中的fmincon函数进行KKT求解。具体步骤如下:
1.定义目标函数和约束条件
我们可以先定义该函数及其约束条件:
```
function [f, grad] = objfun(x)
w = x(1);
v = x(2);
Q = x(3);
m = x(4);
g = x(5);
F = x(6);
t1 = x(7);
t2 = x(8);
c = 1; h = 1; rho = 1; Theta = 1; T = 1;
f = c + h + v - rho * (w - v - Theta * (m - g)) * (1 - F) - t1 + t2;
% Constraints
c1 = t1 * (-Q);
c2 = t2 * (Q - T);
c3 = Q - m + g;
c4 = w - v - Theta * (m - g);
grad = [c4 * rho * (1 - F), -rho * (1 - F), -rho * (w - v - Theta * (m - g)) * dF(Q), ...
-rho * Theta * (w - v - Theta * (m - g)) * dF(Q), rho * Theta * (w - v - Theta * (m - g)) * dF(Q), ...
-1, 1, -Q, T-m+g];
end
function [c, ceq, grad_c, grad_ceq] = confun(x)
Q = x(3);
m = x(4);
g = x(5);
T = 1;
% Inequality constraints
c = [x(7) * (1-Q);
x(8) * (Q-T)];
grad_c = [0, 0, -x(7), 0, 0, 0, 1-Q, 0;
0, 0, x(8), 0, 0, 0, 0, Q-T];
% Equality constraints
ceq = Q - m + g;
grad_ceq = [0, 0, 1, -1, 1, 0, 0, 0];
end
```
2.使用fmincon函数求解
我们可以使用fmincon函数进行求解:
```
x0 = [0, 0, 0, 0, 0, 0, 0, 0]; % 初始值
A = []; b = []; % 无线性约束
Aeq = []; beq = []; % 无等式约束
lb = []; ub = []; % 无界约束
options = optimoptions('fmincon', 'GradObj', 'on', 'GradConstr', 'on');
[x,fval] = fmincon(@objfun, x0, A, b, Aeq, beq, lb, ub, @confun, options);
```
3.计算导数
我们需要计算目标函数和约束条件的导数,可以使用matlab的Symbolic Math Toolbox进行计算:
```
syms w v Q m g F t1 t2 c h rho Theta T real
f = c + h + v - rho * (w - v - Theta * (m - g)) * (1 - F) - t1 + t2;
grad_f = [diff(f, w); diff(f, v); diff(f, Q); diff(f, m); diff(f, g); diff(f, F); diff(f, t1); diff(f, t2)]
c1 = t1 * (-Q);
c2 = t2 * (Q - T);
c3 = Q - m + g;
c4 = w - v - Theta * (m - g);
c = [c1; c2];
ceq = [c3];
grad_c = [diff(c, w), diff(c, v), diff(c, Q), diff(c, m), diff(c, g), diff(c, F), diff(c, t1), diff(c, t2)]
grad_ceq = [diff(ceq, w), diff(ceq, v), diff(ceq, Q), diff(ceq, m), diff(ceq, g), diff(ceq, F), diff(ceq, t1), diff(ceq, t2)]
```
这样,我们就可以使用matlab进行KKT求解了。
阅读全文