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fix github latex
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peterdsharpe committed Nov 30, 2023
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Expand Up @@ -6,8 +6,13 @@ This folder compares optimization performance with AeroSandbox to various other

This chart shows optimization performance on the [N-dimensional Rosenbrock problem](https://en.wikipedia.org/wiki/Rosenbrock_function#Multidimensional_generalizations). Here, $N$ is the number of design variables, which is a convenient knob to dial up or down the difficulty of the problem. The problem is defined as:

* minimize $\sum_{i=1}^{N-1} [ 100(x_{i+1} - x_i^2)^2 + (1 - x_i)^2]$
* minimize $\sum\limits_{i=1}^{N-1} [ 100(x_{i+1} - x_i^2)^2 + (1 - x_i)^2]$

For all $N$, the global optimum is at $\vec{x} = \vec{1}$, where the objective function evaluates to $0$.

This problem is chosen here because it shares many difficult aspects with engineering design optimization problems: it is nonlinear, nonconvex, and poorly-scaled. Furthermore, **we deliberately choose awful initial guesses**, with each element of the vector of initial guesses drawn from a random uniform distribution in the interval $[-10, 10]$.

The performance of AeroSandbox (with CasADi backend) is compared against existing methods using black-box optimization techniques. AeroSandbox offers faster practical and asymptotic optimization performance than existing black-box optimization methods, demonstrating the magnitude of acceleration that is possible.

![benchmark_nd_rosenbrock](./nd_rosenbrock/benchmark_nd_rosenbrock.png)

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