以下优化问题的解决方案是什么

Question

max g(x,y)= x*k+(1-x)*log(1+((x*y)*l)/(1-x))
s.t: 0<=x<=1,0<=y<=1,
where k,l>0. 

保持一个约束不变，函数g(x(/g(y(是一个凹函数。并通过不同k和l的Matlab仿真进行了验证。g(x，y(的仿真结果也给出了凹函数。当存在两个约束时，g(x，y(的最大值是多少？

Answer 1

也许你可以像下面的一样尝试fmincon

fn = @(v) -(v(1)*k+(1-v(1))*log(1+((v(1)*v(2))*l)/(1-v(1))));
Xopt = fmincon(fn,[0.5,0.5],[],[],[],[],[0;0]+eps,[1;1]-eps);

示例

k = 5;
l = 2;
fn = @(v) -(v(1)*k+(1-v(1))*log(1+((v(1)*v(2))*l)/(1-v(1))));
Xopt = fmincon(fn,[0.5,0.5],[],[],[],[],[0;0]+eps,[1;1]-eps);

使得

>> Xopt
Xopt =
0.99800
0.54714