what is global minium
global minium
Started by ●March 29, 2007
Reply by ●March 29, 20072007-03-29
RUCHI wrote:> what is global miniumThe smallest overall value of a set, function, etc., over its entire range. It is impossible to construct an algorithm that will find a global minimum for an arbitrary function. citing : http://mathworld.wolfram.com/GlobalMinimum.html
Reply by ●March 29, 20072007-03-29
techie wrote:> ... It is impossible to construct an algorithm that will find a > global minimum for an arbitrary function.It is possible if the range of interest is finite. Jerry -- Engineering is the art of making what you want from things you can get. ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
Reply by ●March 29, 20072007-03-29
Reply by ●March 29, 20072007-03-29
Vladimir Vassilevsky wrote:> > > Jerry Avins wrote: > >> techie wrote: >> >> >>> ... It is impossible to construct an algorithm that will find a >>> global minimum for an arbitrary function. >> >> >> It is possible if the range of interest is finite. > > No, it is not. There could be the infinite number of minimums in the > finite range.If the range is finite and the function is "well behaved". The kind that describe real phenomena. Math tells us that a sphere can be decomposed and the pieces reassembled to make two solid spheres equal in size to the original. I except such objects from serious discussion in an applied field. Jerry -- Engineering is the art of making what you want from things you can get. ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
Reply by ●March 29, 20072007-03-29
Jerry Avins wrote:> techie wrote: > > >> ... It is impossible to construct an algorithm that will find a >> global minimum for an arbitrary function. > > > It is possible if the range of interest is finite.No, it is not. There could be the infinite number of minimums in the finite range. Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com
Reply by ●March 29, 20072007-03-29
Jerry Avins wrote:>>>> ... It is impossible to construct an algorithm that will find a >>>> global minimum for an arbitrary function. >>> >>> It is possible if the range of interest is finite. >> >> No, it is not. There could be the infinite number of minimums in the >> finite range. > > If the range is finite and the function is "well behaved". The kind that > describe real phenomena.Unfortunately, the functions with the infinite number of minimums are happening in the reality, too. A real system can be described by a set of nonlinear equations. One of the brute force methods to deal with that is collapsing all of the equations into one and applying a multidimensional minimization. But this can very well result in a function with the infinite number of local minimums. Math tells us that a sphere can be decomposed> and the pieces reassembled to make two solid spheres equal in size to > the original. I except such objects from serious discussion in an > applied field.I am not the expert in the spherical horses, so I can't add much to it :-) Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com> > Jerry
Reply by ●March 29, 20072007-03-29
On 29 Mar, 15:59, Jerry Avins <j...@ieee.org> wrote:> Vladimir Vassilevsky wrote: > > > Jerry Avins wrote: > > >> techie wrote: > > >>> ... It is impossible to construct an algorithm that will find a > >>> global minimum for an arbitrary function. > > >> It is possible if the range of interest is finite. > > > No, it is not. There could be the infinite number of minimums in the > > finite range. > > If the range is finite and the function is "well behaved". The kind that > describe real phenomena.Define the function f(x,y,z) = x^2 on some finite domain, say, |x| <= 1, |y|<=1. There are infinitely many global minimum points inside the domain. For "real phenomena" one needs to account for noise, which hardly makes the task of finding "a" global minimum very well behaved. Rune
Reply by ●March 29, 20072007-03-29
a global minimum of a function f(x) is a point x* for which f(x*) ? f(x) for all x. Any global minimum is also a local minimum; however, a local minimum need not also be a global minimum. I mathematics, finding the global minimum is the goal of optimization. The above definition can easily be extended to a function of multiple variables. Tom "RUCHI" <ruchikalalit@gmail.com> wrote in message news:1175151555.989144.23870@r56g2000hsd.googlegroups.com...> what is global minium >
Reply by ●March 29, 20072007-03-29
Rune Allnor wrote:> On 29 Mar, 15:59, Jerry Avins <j...@ieee.org> wrote: >> Vladimir Vassilevsky wrote: >> >>> Jerry Avins wrote: >>>> techie wrote: >>>>> ... It is impossible to construct an algorithm that will find a >>>>> global minimum for an arbitrary function. >>>> It is possible if the range of interest is finite. >>> No, it is not. There could be the infinite number of minimums in the >>> finite range. >> If the range is finite and the function is "well behaved". The kind that >> describe real phenomena. > > Define the function > > f(x,y,z) = x^2 > > on some finite domain, say, |x| <= 1, |y|<=1. > > There are infinitely many global minimum points inside > the domain. For "real phenomena" one needs to account for > noise, which hardly makes the task of finding "a" global > minimum very well behaved.I think we have a language problem here. Setting aside the question of whether one can be shown to exist, a global minimum is the smallest of all minima of a function. Other minima are called "local minima". Noise doesn't change the meaning even if it makes the point harder to find. A function can have more than one global minimum if all have the same value. The function f(x) = x^4 - 2*x^2 has two minima that are both local and global. (It has one local maximum (a double root, in fact) and no global maxima.) Jerry -- Engineering is the art of making what you want from things you can get. ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
