# Questions tagged [optimization]

This tag is intended for questions on methods for the (constrained or unconstrained) minimization or maximization of functions.

759 questions
5k views

### Are there any heuristics for optimizing the successive over-relaxation (SOR) method?

As I understand it, successive over relaxation works by choosing a parameter $0\leq\omega\leq2$ and using a linear combination of a (quasi) Gauss-Seidel iteration and the value at the previous ...
11k views

### Minimizing the Sum of Absolute Deviation (${L}_{1}$ Distance)

I have a data set $x_{1}, x_{2}, \ldots, x_{k}$ and want to find the parameter $m$ such that it minimizes the sum $$\sum_{i=1}^{k}\big|m-x_i\big|.$$ that is $$\min_{m}\sum_{i=1}^{k}\big|m-x_i\big|.$$...
286 views

### How to fill a 2D set over a cartesian lattice with as few rectangles as possible?

Suppose I have a black and white image (composed of binary pixel values in a 2D cartesian array) that contains an irregular, nonconvex shape. Let's further suppose that the shape is one connected ...
4k views

### Efficient solution of mixed integer linear programs

Many important problems can be expressed as a mixed integer linear program. Unfortunately computing the optimal solution to this class of problems is NP-Complete. Luckily there are approximation ...
290 views

### Multi-objective optimization problem - Euclidean space

I am looking for some clues for an optimization problem. My problem consists on arriving to a image by optimizing multiple layers with the pixel position probability. This is an overview of the ...
3k views

### Software package for constrained optimization?

I am looking to solve a constrained optimization problem where I know the bounds on some of the variables (specifically a boxed constraint). $$\arg \min_u f(u,x)$$ subject to $$c(u,x) = 0$$  ...
19k views

### BFGS vs. Conjugate Gradient Method

What considerations should I be making when choosing between BFGS and conjugate gradient for optimization? The function I am trying to fit with these variables are exponential functions; however, the ...
I am trying to fit some raw data using a function of the form $f(r) = \sum_{i=1}^{K} d_kS_k(n_k,\alpha_k,r)$ where $S_k(n_k,\alpha_k,r) = \frac{\alpha_k ^{n_k+3}}{(n_k+2)!}r^{n_k}\exp(-\alpha_kr)$ ...