A Geometric Algorithm for Solving the General Linear Programming Problem
A Geometric Algorithm for Solving the General Linear Programming Problem
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In our eReader you can find the full English version of the book. Read A Geometric Algorithm for Solving the General Linear Programming Problem Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book A Geometric Algorithm for Solving the General Linear Programming Problem
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U * (x) |p| K(x)f since p is the gradient direction for the face F (whether we . , 10 can move in this direction or not) . Thus P '7T = 7^-(P*u' :: '(x))+ -Mp. P) > -^(p'u'^x))* lLEl(p. U*(x)) M |w| |w| |w| |w| = ■, l? |g| r (P«tt*(x)) > ; g +e »P J (p. U*(x)) = p. U*(xK |£u'(x)+ep| 5|u (x) |+e|p| Thus p»(w/|w[) > p«u (x) which contradicts our definition of u (x) (since (w/|w[)£S ). Thus we must conclude that u*(x) = = p/IpI.
Corollary 1 . For x€D-D w, there exists y€D such that y-x = Ap for so...me p and some X > 0. Furthermore for this y, §5. The geometric algorithm .
We now give the algebraic formulation of the algorithm which we described geometrically in Section 3. So suppose we are given the constraints Ax > b and we wish to maximize L(x) = p*x . We further make the assumption that we are given w°£D . Of course this is a strong assumption, but in Section 7, we will illustrate (using this geometric algorithm) how one ob- tains such a w° (if it exists). We of course also know the di- rections p corresponding to the faces F.
What to read after A Geometric Algorithm for Solving the General Linear Programming Problem?
You can find similar books in the "Read Also" column, or choose other free books by James Thurber to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
U * (x) |p| K(x)f since p is the gradient direction for the face F (whether we . , 10 can move in this direction or not) . Thus P '7T = 7^-(P*u' :: '(x))+ -Mp. P) > -^(p'u'^x))* lLEl(p. U*(x)) M |w| |w| |w| |w| = ■, l? |g| r (P«tt*(x)) > ; g +e »P J (p. U*(x)) = p. U*(xK |£u'(x)+ep| 5|u (x) |+e|p| Thus p»(w/|w[) > p«u (x) which contradicts our definition of u (x) (since (w/|w[)£S ). Thus we must conclude that u*(x) = = p/IpI.
Corollary 1 . For x€D-D w, there exists y€D such that y-x = Ap for so...me p and some X > 0. Furthermore for this y, §5. The geometric algorithm .
We now give the algebraic formulation of the algorithm which we described geometrically in Section 3. So suppose we are given the constraints Ax > b and we wish to maximize L(x) = p*x . We further make the assumption that we are given w°£D . Of course this is a strong assumption, but in Section 7, we will illustrate (using this geometric algorithm) how one ob- tains such a w° (if it exists). We of course also know the di- rections p corresponding to the faces F.
What to read after A Geometric Algorithm for Solving the General Linear Programming Problem?
You can find similar books in the "Read Also" column, or choose other free books by James Thurber to read onlineMoreLess
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