Optimization of a simple expansion problem
minimise: $$ \sum_{t=1}^{5}\left[\sum_{i=1}^{2}x_{i,t}CC_i\left(\frac{1+EIC}{1+r}\right)^t+UE_t*C_{UE}\right] $$ subject to: $$ 0 \leq x_{i,t} \leq 5 \\ ED_B(I+\alpha)^t=\sum_{i=1}^{2}\sum_{j=1}^{t}x_{ij}G_{ij}+UE_t\\ ED_B,\alpha\in\Bbb{R}\\ UE=[\;4.5,4.8,4.2,4.0,5.0\;]\;kWH\\ C_{UE}=0.05$ \\ (Escalation\;in\;CC)\;EIC=4\;\% \\ (Annual\;Discount)\;r=5\;\% $$
I want to minimize a cost function accumulating over 5 years with some constraints on energy balance and bounds on the integer variables. It could be a mixed-integer problem.
How to formulate in MatLab or any other tools that I can use to write and solve.
CVX tutorial for such a problem is highly appreciated.