Hey Folks
I've encountered an optimization problem which has a linear programming structure but it's coefficients are nonlinear function of another variable. here is the problem: $$\max _{{p_i},\theta} \sum_{i=1}^N (\omega_i p_i e^{-1.2\times (\frac{\theta-\theta_i}{\theta_{3dB}})^2}-\eta\times p_i) $$
$$s.t. \sum_{i=1}^N p_i = P$$ $$\forall i \qquad p_i\ge0 \qquad and \qquad 0\le\theta\le 90^\circ$$ $$\forall i \qquad \omega_i\ge0 \qquad are \; known \; real \; positive \; numbers$$ $$\forall i \qquad 0\le\theta_i\le 90^\circ \qquad are \; known \; real \; positive \; numbers \; (degrees)$$ $$0\le\eta\le 1 \qquad and \qquad \theta_{3dB}=6^\circ \qquad and \qquad P\ge0 \qquad are \; known\; constants$$ $$e \qquad is \; neper \; exponential \; function$$
I'm interested in finding global maximum of the above function.
I think closed form solution is not possible however an algorithm that guarantees to approach global maximum is highly probable to exist.
Thanks a lot in Advance and Best Regards