Challenge: The Log Barrier Method

Problem statement

Consider a real-life example of traffic flow optimization. In a city, optimize the timing of traffic signals to minimize the total time cars spend on the roads. This can be formulated as a convex optimization problem with inequality constraints.

Here,

• $n$ is the total number of traffic signals.

• $x_i$ is the duration (in minutes) for which the $i^{th}$ traffic signal is green.

• $g_i$ ...