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)
“The general review of the past tends to satisfy me with my political life. No man, I suppose, ever came up to his ideal. The first half [of] my political life was first to resist the increase of slavery and secondly to destroy it.... The second half of my political life has been to rebuild, and to get rid of the despotic and corrupting tendencies and the animosities of the war, and other legacies of slavery.”
—Rutherford Birchard Hayes (1822–1893)
“Everyone confesses in the abstract that exertion which brings out all the powers of body and mind is the best thing for us all; but practically most people do all they can to get rid of it, and as a general rule nobody does much more than circumstances drive them to do.”
—Harriet Beecher Stowe (1811–1896)