# Questions tagged [numerical-optimization]

Numerical methods for continuous optimization.

1,101 questions
Filter by
Sorted by
Tagged with
26 views

### For continuous optimizations, what is the condition that says an optimal value lies on the boundary and not in the interior?

Suppose I want to solve the problem \begin{equation} \min_{x \in \mathcal{X}} f(x) \end{equation} where $f$ is assumed to be continuously differentiable, and $\mathcal{X}$ is closed and possibly ...
11 views

17 views

### Single objective non-linear optimization with multiple constraints

I am trying to solve a non-linear optimization problem with single objective function $$\operatorname*{min} J(u)+P(f_u)$$ with constraints $$R(u;f_u)=0$$ $$Q(a,u;f_{a})=0$$ Here $J(u)$ is the ...
63 views

33 views

### What is the relationship between linear convergence in gradient descent and linear convergence in real analysis?

In undergraduate analysis/calculus courses, we often learn about linear convergence of a sequence: a sequence $x_n\rightarrow x_\infty$ in $\mathbb{R}^n$ linearly if there exists $r\in (0,1)$ such ...
19 views

I have a pentadiagonal symmetric matrix , with elements on the diagonal, on the 1st upper-diagonal and 1st lower-diagonal and at the n-th upper and lower diagonal. ( n changes values from one matrix ...
12 views

### Efficient intersection of linear subspaces? How to solve a big nonlinear least squares with linear constraints?

Problem: I want to solve a big linearly constrained nonlinear least squares problem. The number of unknowns is between millions and billions. In terms of cost functions, the Hessian would be pretty ...
40 views

### How to avoid overflow when evaluating the exponential smoothing function?

The exponential smoothing function is $f:\Bbb R^n\to \Bbb R$ defined as $$f(x):= \log\left(\sum_{i=1}^{n}e^{x_i}\right).$$ Obviously, when $x_i$ is large for some $i$, the term inside the logarithmic ...