\begin{eqnarray} {\textbf{maximise}} \hspace{2mm} Ar^{-(a+b)} + Br^{-(a+b+c)}-C \nonumber \end{eqnarray} such that, \begin{eqnarray} c= l(h-m_{0}) \nonumber\\ m_{1} \leq h \leq m_{2} \nonumber\\ a+ b \geq m_{3} \nonumber \\ a\leq l(h-m_{4}) \nonumber \\ b \leq l(h-m_{5}) \nonumber \\ \tan\theta=\frac{m_{6}+m_{7}a/b}{m_{8}+m_{9}a/b} \nonumber \\ h= \frac{(n_{1}-n_{2}\cos(\theta-k_{0}))+a/b(n_{3}-n_{4}\cos(\theta-k_{2}))}{Z(1+a/b)} \nonumber \\ 0 \leq \theta \leq 2\pi \nonumber \end{eqnarray}
The decision variables are $a,b,c,h,\theta$. All other variables are constants.
Objective functions is strictly convex on a,b,c.
The problem domain is not convex.
How do I solve this problem?
You have to use dummy variables to get rid of functional inequalities and then you may use Kuhn-Tucker conditions. If you are still interested in the solution I can provide further info...