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:
“As a general rule never take your whole fee in advance, nor any more than a small retainer. When fully paid beforehand, you are more than a common mortal if you can feel the same interest in the case, as if something was still in prospect for you, as well as for your client.”
—Abraham Lincoln (1809–1865)
“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)
“We do not need to minimize the poverty of the ghetto or the suffering inflicted by whites on blacks in order to see that the increasingly dangerous and unpredictable conditions of middle- class life have given rise to similar strategies for survival. Indeed the attraction of black culture for disaffected whites suggests that black culture now speaks to a general condition.”
—Christopher Lasch (b. 1932)