General
A common (standard) model form is the minimization of one real-valued function in the parameter-space, or its specified subset : here denotes the set defined by the constraints.
(The maximization of a real-valued function is equivalent to the minimization of the function .)
In many nonlinear optimization problems, the objective function has a large number of local minima and maxima. Finding an arbitrary local optimum is relatively straightforward by using classical local optimisation methods. Finding the global minimum (or maximum) of a function is far more difficult: symbolic (analytical) methods are frequently not applicable, and the use of numerical solution strategies often leads to very hard challenges.
Read more about this topic: Global Optimization
Famous quotes containing the word general:
“The General Order is always to manoeuver in a body and on the attack; to maintain strict but not pettifogging discipline; to keep the troops constantly at the ready; to employ the utmost vigilance on sentry go; to use the bayonet on every possible occasion; and to follow up the enemy remorselessly until he is utterly destroyed.”
—Lazare Carnot (1753–1823)
“It is a general popular error to suppose the loudest complainers for the public to be the most anxious for its welfare.”
—Edmund Burke (1729–1797)
“In communist society, where nobody has one exclusive sphere of activity but each can become accomplished in any branch he wishes, society regulates the general production and thus makes it possible for me to do one thing today and another tomorrow, to hunt in the morning, fish in the afternoon, rear cattle in the evening, criticize after dinner, just as I have a mind, without ever becoming hunter, fisherman, shepherd or critic.”
—Karl Marx (1818–1883)