# maximizing an objective function(area) with respect to location of a node

Consider two circles with radius R (They may intersect each other). We present circles by $C_A$ and $C_B$. We have additional node called $C$. We obtain Voronoi polygons with respect to center of each circle and point $C$ which are called $V_A$, $V_B$ and $V_C$. We are interested to relocate point $C$ such that it maximizes the following term:

$\min \bigg\lbrace a (C_A \cap V_A), (C_A \cap V_A)-(C_A \cap V_A^{'}) \bigg\rbrace + \min \bigg\lbrace b (C_B \cap V_B), (C_B \cap V_B)-(C_B \cap V_B^{'}) \bigg\rbrace$

Where $a$ and $b$ are constants between 0 and 1 and $V_A^{'}$ and $V_B^{'}$ are the new Voronoi polygons with respect to new location of $C$.

You can find definition of Voronoi in http://mathworld.wolfram.com/VoronoiDiagram.html