Is it possible to obtain a closed form solution to a convex optimization problem? Specifically, the optimization function I am looking at is to maximize x over a convex polygon in x and y dimensions. Is there a way I can obtain a closed form value of the (x,y) solution pair?
The polygon is specified by the intersection of convex half-spaces, as linear inequalities. Additionally, the constraints are in pairs of parallel lines, i.e. there are 2k inequalities, with k different slopes. Also, all the slopes have negative sign. So, the topmost point is also the leftmost.