# Tagged Questions

Optimization is the process of choosing the "best" value among possible values. They are often formulated as questions on the minimization/maximization of functions, with or without constraints.

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### Why must the determinant of the hessian of a scalar function be positive for there to be a local min/max? Intuition needed

Is there any intuition behind having the determinant of the Hessian matrix being negative corresponding to a saddle point, and positive corresponding to a max/min depending on the sign of $f_{xx}$ for ...
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### Optimal Apple Eating Strategy

You hate apples. As a result, you have angered the apple king and are being punished. You will have to eat $n$ apples before the apple king is willing to let you leave. The apples are marked from $1$ ...
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### A trigonometric problem when calculating distance to the boundary of a convex hull

Suppose we have a sphere and a point outside of the sphere. We denote the point outside as $v$ and the origin of the sphere as $x$. The convex hull of the sphere and $v$ should be like an ice cream ...
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### Best fit curve through several line segements

I have a question about creating a best fit curve that incorporates several lines on a graph. To give some background, I am working on the geometrical design of a solar reflector. The reflector is ...
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### Optimal way to partition sum of linear equitations

Suppose we know the values of $x_i$, $i=1,2,3,...,n$. How do we choose an integer $k$ such that $\sum_{i=1}^{k-1} (k-1-i)x_i + \sum_{i=k}^{n} (n-i)x_i$ is minimized; $0 \leq k \leq n$? My initial ...
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