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:
“Towards him they bend
With awful reverence prone; and as a God
Extoll him equal to the highest in Heav’n:
Nor fail’d they to express how much they prais’d,
That for the general safety he despis’d
His own: for neither do the Spirits damn’d
Loose all thir vertue; lest bad men should boast
Thir specious deeds on earth, which glory excites,
Or close ambition varnisht o’er with zeal.”
—John Milton (1608–1674)
“Everyone confesses in the abstract that exertion which brings out all the powers of body and mind is the best thing for us all; but practically most people do all they can to get rid of it, and as a general rule nobody does much more than circumstances drive them to do.”
—Harriet Beecher Stowe (1811–1896)
“We will win this war because we are willing to sacrifice 10,000,000 lives. How many lives is the White Man willing to sacrifice?”
—Jerome Cady, U.S. screenwriter, and Lewis Milestone. General Mitsubi (Richard Loo)