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:
“Mathematics is merely the means to a general and ultimate knowledge of man.”
—Friedrich Nietzsche (1844–1900)
“There are two great rules in life, the one general and the other particular. The first is that every one can in the end get what he wants if he only tries. This is the general rule. The particular rule is that every individual is more or less of an exception to the general rule.”
—Samuel Butler (1835–1902)
“We all have known
Good critics, who have stamped out poet’s hopes;
Good statesmen, who pulled ruin on the state;
Good patriots, who, for a theory, risked a cause;
Good kings, who disembowelled for a tax;
Good Popes, who brought all good to jeopardy;
Good Christians, who sat still in easy-chairs;
And damned the general world for standing up.—
Now, may the good God pardon all good men!”
—Elizabeth Barrett Browning (1806–1861)