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

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 $S_k(n_k,\alpha_k,r) = \frac{\alpha_k ^{n_k+3}}{(n_k+2)!}r^{n_k}\exp(-\alpha_kr)$ ...