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:
“Amid the pressure of great events, a general principle gives no help.”
—Georg Wilhelm Friedrich Hegel (1770–1831)
“When General Motors has to go to the bathroom ten times a day, the whole country’s ready to let go. You heard of that market crash in ‘29? I predicted that.... I was nursing a director of General Motors. Kidney ailment, they said; nerves, I said. Then I asked myself, “What’s General Motors got to be nervous about?” “Overproduction,” I says. “Collapse.””
—John Michael Hayes (b. 1919)
“The most general deficiency in our sort of culture and education is gradually dawning on me: no one learns, no one strives towards, no one teaches—enduring loneliness.”
—Friedrich Nietzsche (1844–1900)