George
Bernard Dantzig was born in 8 November 1914 in Portland, Oregon, USA. His
father was Mathematics' professor, who left leaving his job as Boss of
Matemáticas's Apartment in the University of Maryland just after Second World
War. His mother was a linguist specialized in Slavic idioms.
Dantzig
studied his course at the University of Maryland, where he tooks a degree in
1936. Next year, he took a studies of postgrade at the Mathematics School of
the University of Michigan. However, it seemed him that courses was too
abstract; So abstract, that he only desired a thing: abandoning his postgrado's
studies and getting a job.
In 1937, Dantzig left Michigan to
work as employee in Statistics at Bureau of Labor Satistics. Two years later,
he enrolled in Berkeley, to study a Statistics' Doctorate.
During his first year in Berkeley,
he enrolled at Statistics' course that was giving the famous professor, Jerzy
Neymann. This professor used to writing on the blackboard a couple of exercises
when his classrooms began in order to, like task for the home, be resolved for
his pupils and delivered at the following classroom. In an occasion, Dantzig
reached later to Neymann's classrooms, and noticed that on the blackboard was
written two problems. He supposed that problems were homeworks and, logically,
he copied and resolved them, even though they seemed him "a little harder
than the ordinary problems". A few days later he delivered them to
Neymann, apologizing to have delayed so much. Approximately six weeks after, a
Sunday's morning at 8:00, Neymann came beating Dantzig's door explaining him
that he wrotten an introduction to one of Dantzig's goods and he was wanting
and that he read it in order to be able to send the article for his
publication. The two problems of task that Dantzig had resolved were, in
reality, two famous problems non resolved of Statistics. The solutions of these
problems became his doctoral thesis, to Neymann's suggestion.
Nevertheless,
Dantzig finished off his doctorate to 1946. Just after the beginning of Second
World War he joined to United States Air Force and worked with ombat Analysis
Branch of Statistical Control. After receiving his Doctorate, he returned to
Air Force like Mathematicas' adviser of the U. A. Air Force Controller. Was in
that work where he found the problems wich took him to do his big discoveries.
Air Force needed a faster way to calculate the duration time of the stages of a
program of display, workout and logistic supply.
The
professor Dantzig basically centered his scientific developments,
chronologically, in the RAND Corporation and Berkeley's and Stanford's
universities in California, with temporary assignments in another centers like
the IIASA in Vienna. (The anecdote that he tells like the principal reason to
move from Berkeley to Stanford, the guilty is a parking for professors just in
front of his new Department door, with such bad luck that this parking had
disappeared when he became incorporated to Stanford).
Dantzig's
work generalized the made for the economist, winner of the Nobel Prize, Wassily
Leontief. Early, Dantzig noticed that the problems of planning wich he against
with them were too much complexes for 1947 fastest computers (and even for the
ones belonging to the present time).
Once
established the general problem of Linear Programming was necessary to find
solutions in a reasonable time.Here Dantzig's geometric intuition yielded
results : "I began noticing that the feasible region is a convex body,
that is, a polyhedral set.Therefore, the process would be able to be improved
if the movements were maded along the borders from one extreme point toward the
following. However, this procedure seemed to be too inefficient. In three
dimensions, the region could be visualized like a diamond with faces, edges and
vertex. In the cases of many borders, the process would take an a journey along
them before the diamond's point optimal corner would be reached".
This
intuition carried the first formulation of the Simplex Method in the summer of
1947. The first practical problem that got worked out with this method was one
of nutrition.
The
October 3 l947 Dantzig visited the Institute for Advanced Study where meet for
first time to John Von Neumann, who ,at that time, was considerate for a lot of
people like the best Mathematician of the world. Von Neumann chatted with
Dantzig about the work that he was realizing with Oscar Morgenstern about game
theory.That moment went when Dantzig knew about the important theorem of
duality for the first time.
Another
one of his grand achievements is the theory of duality, dreamt up together with
Fulkerson and Johnson in 1954 to resolve the Traveling Salesman's paradigmatic
problem (resolving then problems with 49 cities when, nowadays problems get
worked out, by means of modern implementations of the method, with several
thousands of cities and even one million nodes) is the predecessor of useful
todays Branch-and-Cut methods so utilized in entire programming to resolve
problems of grand dimensions.
A
precision about terminology: One simplex is an especial polyhedral convex
united type. More concretely, be P1, P2,. . . , Pn +1 n +1 points ( or vectors
) in R. It is said that vectors have related independence if them n vectors P1
P2, P1 P3,. . . , P1 Pn, P1 are P independent lineally. If points have related
independence, then the convex smaller set that he contains the n+1 points in is
named n-simplex. In R, three points have related independence if not they are
colinear. The convex smaller set that no contains three points colinear a
triangle with these points as like vertex. Therefore, a 2-simplex is a
triangle. In R, four points have related independence if they are no
"co-plane". The convex smaller set that contains four of such points
is a tetrahedron. This is the 3-simplex. Triangles and tetrahedrons are united
polyhedral convex, regardless of that convex polyhedral sets are not
necessarily simplex. The Simplex Method was called thus by George Dantzig,
although it is not clear why he elected that name. It should be more suitable
call it "Set Polyhedral Convex Method".
Finally,
but no the last thing, he is important to depict the programming mathematical
application than the professor Dantzig went developing to long of years for
various industrial sectors and of Administration, highlighting for example the
project PILOT, for a better planning of the energetic sector and, therefore, a
bigger energetic saving.
May
13, 2004, George Bernard Dantzig, he died to the age of 90 years at his house
of Stanford due to complications with diabetes and problems cardiovasculars.
Bibliography:
"George Bernard
Dantzig Biography." George Bernard Dantzig's Biography. Web. 19 Feb. 2012.
<http://www.phpsimplex.com/en/Dantzig_biography.htm>.
