Can anyone help me with the following optimization problem please?
I have to find the $\max f(c,y_1^1,\cdots,y_{N-1}^1,\cdots,y_1^M,\cdots,y_{N-1}^M)=c$
subject to the constraints $\mathbb{E}[\exp{(-\alpha_i(X_i(w_j)+Y_i(w_j)))}]\leq \gamma$ and $Y_i(w_j)>b_i$
where $\gamma,\alpha_i,c,b_i$ are constants, and $X_i,Y_i$ are random variables. I know I have to use KKT, can anyone help me only with the lagrangian and the conditions please?
Any kind of help will be much appreciated!