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I'm encountering the following minimization problem in my research: $$\hat b = \underset{b}{\arg\min} \sum_i^n \left( \log \frac{a_i}{b} \right)^2$$ I could iteratively optimize, but I think that th …

I have measurements of an object. Let's say I have its length $L$, mass $M$, and age $t$: $$\mathbf y = (10~\text{m},\ 0.01~\text{g},\ 5~\text{s}).$$ I also have the uncertainties on my measurements …

A colleague is optimizing a function (e.g. trying to find the minimum of a function $f(x_1, x_2, \ldots)$). We know the analytical form and it is differentiable. I suggested calculating the derivative …

I am doing constrained vector optimization using a non-convex non-linear likelihood function. …

Let's say I have a neural network $f$ that takes input $\vec x \in \mathbb {R}^n$ and produces output $f(\vec x) \in \mathbb{R}$. How can I find $\hat x = \underset{\vec x}{\arg\max} \; f(\vec x)$?

Another worry is the fact that the $\sigma$s depend on $\vec \alpha$, and so this optimization procedure may choose to inflate $\sigma_x$ and $\sigma_y$ instead of getting good estimates $x_0'$ and $y_ …

I have encountered a problem that the literature suggests linear regression is able to solve, but I am at a loss. I have a function $F$ that I want to estimate. This function obeys $N$ equations of …

I have observed a vector of quantities $\vec y$. I wish to use these to constrain a vector of initial conditions $\vec x$ that are related to $\vec y$ through a non-linear (numerically evaluated) func …

I have a theory $f$ (actually a set of coupled non-linear differential equations) that, from a vector of $n$ initial conditions $\vec x$, is able to predict $m$ values $f(\vec x) = \vec y$. I can me …

This paper gives an answer. The answer is in order to minimize $\chi^2$, one can maximize a log likelihood function $-\chi^2/2$.