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Optimization for Machine Learning with NumPy and SciPy

Challenge: The Log Barrier Method

Explore the log barrier method to solve a constrained convex optimization problem involving traffic signal timing. Understand how to implement this technique to optimize traffic flow by minimizing total car wait time under inequality constraints.

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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,

  • nn is the total number of traffic signals.

  • xix_i ...