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:
“We ought, says Kant, to become acquainted with the instrument, before we undertake the work for which it is to be employed; for if the instrument be insufficient, all our trouble will be spent in vain. The plausibility of this suggestion has won for it general assent and admiration.... But the examination can be only carried out by an act of knowledge. To examine this so-called instrument is the same as to know it.”
—Georg Wilhelm Friedrich Hegel (1770–1831)
“The General Strike has taught the working class more in four days than years of talking could have done.”
—A.J. (Arthur James)
“As a general rule, do not kick the shins of the opposite gentleman under the table, if personally unaquainted with him; your pleasantry is liable to be misunderstood—a circumstance at all times unpleasant.”
—Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)