In optimization problem $$\arg\max_{\substack{l_1 \in [0, 1],\cdots,l_{M} \in [0,1]}} T$$ I have $m=1\cdots,M$ constraints such that $$\ln \left[a_m\right] + \ln \left[ \left(\frac{l_m}{l_m + \sigma_m}\right) \right] + \sum \limits_{i=1}^{m-1} {\ln \left[\left(1-l_i\right)\right]} \geq T$$ where $\sigma_m,~a_m>0$.
In MATLAB, I will use fmincon function.
How do I need to treat above constraints, e.g., as linear or non-linear constraints? It is important because if they are non-linear, I may need gradient equations as well.
Please help me, and thanks !!!