# Questions tagged [numerical-optimization]

Numerical methods for continuous optimization.

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### Recommendation for intro to geometric integrators?

Explicit Request Looking for book or lecture note recommendations on numerical optimization that (ideally) have the following: Emphasis on geometric and physical intuition Emphasis on symplectic ...
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### Jacobian of exponential mapping in SO3/SE3

Following this post Jacobian matrix of the Rodrigues' formula (exponential map) What if I really need the Jacobian of the exponential mapping function in $\omega \neq 0$? Basically, I want to ...
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### What is known about optimizing a function whose evaluation cost is variable?

Let's imagine I have a function $f(x)$ whose evaluation cost (monetary or in time) is not constant: for instance, evaluating $f(x)$ costs $c(x)\in\mathbb{R}$ for a known function $c$. I am not ...
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### Gradient Descent Divergence

I am curious about divergence conditions of the Gradient Descent method. In the reading that I have done I have only ever seen it mentioned that this method diverges when $\alpha$ is too large. It ...
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### Accelerated gradient descent versus nonlinear conjugate gradient descent

Let's consider smooth and convex minimization problem, i.e. $min f(x)$, where $f$ is not necessarily a quadratic function. If measured by iterations, Accelerated Gradient Descend (AGD) has $O(1/T^2)$...
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### Globalized BFGS (Quasi-Newton method) condition

I didn't find any information on the internet about the globalized $\textit{BFGS}$ method. Wikipedia only talks about the normal BFGS, without this ...
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### A “divide-and-conquer” iterative procedure for minimizing a sum of convex functions

For simplicity, let's assume $f_i: \mathbb{R} \to \mathbb{R}$ is convex and define $$g(x) := \sum_{i=1}^{n}f_i(x)$$ Suppose we want to compute $$x^* := \arg\min_{x \in \mathbb{R}} g(x)$$ ...
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### Finding the domain shape, where the fundamental Helmholtz Eigenmode has certain properties at a boundary

The following is a problem about finding the shape of a domain such that the fundamental Helmholtz eigenmode has certain properties at the boundary of the domain. I search for an analytical or ...
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### How do I pack 2D objects into an arbitrary shape?

I've heard of packing problems in general, and I've seen a couple questions on this site that address specific cases (e.g. how to pack 45-45-90 triangles into an arbitrary shape), but after a search I ...
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### Using Coordinate Descent on Projected Space

My goal is to maximize an objective function using coordinate descent over a 3-dimensional vector. In the simple case the domain over which I am maximizing is defined as follows: $X \in \mathcal{X}$ ...
Consider the following convex optimization problem in vectors $x$ and $y$ $$\begin{array}{ll} \text{minimize} & f(x,y)\\ \text{subject to} & g_1 (x)\le 0\\ & g_2 (y)\le 0\end{array}$$ ...