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Optimization for Machine Learning with NumPy and SciPy

Solution: The Log Barrier Method

Explore how the log barrier method is used to solve constrained optimization problems by approximating objectives and applying Newton's method. Understand how to implement this method with Python, including gradient and Hessian calculations, to find optimal solutions in practical scenarios.

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Explanation

The traffic flow optimization problem is given as follows:

The approximated objective at the parameter tt for the problem above can be written as follows:

Because there are three constraints, the difference in the optimal values of the original and the approximated problem is bounded as follows:

Choosing t=512t=512 ...