I hope you are having a nice day.
I am learning MATLAB at the moment and the best way for me to learn is to use it to tackle some of my problems.
I am currently trying to solve the following problem
$\arg \underset{v_H \in [0,1]}{\min}\bar{C} + b \log \left(\frac{1}{x} \right) + k_H v_H + \alpha \left(\bar{C} + b \log \left(\frac{1}{x + c v_H (1-x) + \beta x(1-x) - \gamma x} \right) \right)$
such that: $\bar{C}, k_H, b > 0 \\ c, \gamma, \alpha \in [0,1], \\ 0 < \beta < \gamma, \\ 0 \leq x \leq 1$
I have attempted to differentiate the above equation and I get an answer but I can only do this if the $v_H \in [0,1]$ constraint isn't satisfied.
Is Matlab able to minimise this expression with the constraints symbolically? If so, can you assist me in the code? I have tried Mathematica but the Reduce formulas seem like they will take longer than the age of the universe to evaluate.
Thank you!