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:
“‘A thing is called by a certain name because it instantiates a certain universal’ is obviously circular when particularized, but it looks imposing when left in this general form. And it looks imposing in this general form largely because of the inveterate philosophical habit of treating the shadows cast by words and sentences as if they were separately identifiable. Universals, like facts and propositions, are such shadows.”
—David Pears (b. 1921)
“There seems almost a general wish of descrying the capacity and undervaluing the labour of the novelist, and of slighting the performances which have only genius, wit, and taste to recommend them.”
—Jane Austen (1775–1817)
“Pleasure is necessarily reciprocal; no one feels it who does not at the same time give it. To be pleased, one must please. What pleases you in others, will in general please them in you.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)