Global optimization Totally Explained

Everything about Global Optimization totally explained

Global optimization is a branch of applied mathematics and numerical analysis that deals with the optimization of a function or a set of functions to some criteria.

General

The most common form is the minimization of one real-valued function

f

in the parameter-space

vec

.
In real-life problems, functions of many variables have a large number of local minima and maxima. Finding an arbitrary local optimum is relatively straightforward by using local optimisation methods. Finding the global maximum or minimum of a function is a lot more challenging and has been practically impossible for many problems so far.
The maximization of a real-valued function

g(x)

can be regarded as the minimization of the transformed function

f(x):=(-1)cdot g(x)

Applications of global optimization

Typical examples of global optimization applications include:

Protein structure prediction (minimize the energy/free energy function)
Traveling salesman problem and circuit design (minimize the path length)
Chemical engineering (for example, analyzing the Gibbs free energy)
Safety verification, safety engineering (for example, of mechanical structures, buildings)
Worst case analysis
Mathematical problems (for example, the Kepler conjecture)
The starting point of several molecular dynamics simulations consists of an initial optimization of the energy of the system to be simulated.
Spin glasses
Calibration of propagation models

Approaches

Deterministic

The most successful are:

Branch and bound methods

Methods based on real algebraic geometry

Stochastic, thermodynamics

Several Monte-Carlo-based algorithms exist:

Simulated annealing

Direct Monte-Carlo sampling

Stochastic tunneling

Parallel tempering

Monte-Carlo with minimization

Continuation Methods

Heuristics and metaheuristics

Other approaches include heuristic strategies to search the search space in a (more or less) intelligent way, including

Evolutionary algorithms (for example, genetic algorithms)

Swarm-based optimization algorithms (for example, particle swarm optimization and ant colony optimization)

Memetic algorithms, combining global and local search strategies

Differential evolutionFurther Information

Get more info on 'Global Optimization'.

External Link Exchanges

Do you know how hard it is to get a link from a large encyclopaedia? Well we're different and will prove it. To get a link from us just add the following HTML to your site on a relevant page:

<a href="http://global_optimization.totallyexplained.com">Global optimization Totally Explained</a>

Then simply click through this link from your web page. Our crawlers will verify your link, extract the title of your web page and instantly add a link back to it. If you like you can remove the words Totally Explained and embed the link in article text.
As long as your link remains in place, we'll keep our link to you right here. Please play fair - our crawlers are watching. Your site must be closely related to this one's topic. Any kind of spamming, dubious practises or removing the link will result in your link from us being dropped and, potentially, your whole site being banned.