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 constitutional statesman is in general a man of common opinions and uncommon abilities.”
—Walter Bagehot (1826–1877)
“A private should preserve a respectful attitude toward his superiors, and should seldom or never proceed so far as to offer suggestions to his general in the field. If the battle is not being conducted to suit him, it is better for him to resign. By the etiquette of war, it is permitted to none below the rank of newspaper correspondent to dictate to the general in the field.”
—Mark Twain [Samuel Langhorne Clemens] (1835–1910)
“I suggested to them also the great desirability of a general knowledge on the Island of the English language. They are under an English speaking government and are a part of the territory of an English speaking nation.... While I appreciated the desirability of maintaining their grasp on the Spanish language, the beauty of that language and the richness of its literature, that as a practical matter for them it was quite necessary to have a good comprehension of English.”
—Calvin Coolidge (1872–1933)