Simplex Algorithm

From GM-RKB
Jump to navigation Jump to search

A Simplex Optimization Algorithm is an iterative convex linear programming algorithm that performs successive pivot operations along adjacent vertices to an improved basic feasible solution (pivot element).



References

2012a

  1. Stone, Richard E.; Tovey, Craig A. (1991). "The simplex and projective scaling algorithms as iteratively reweighted least squares methods". SIAM Review 33 (2): 220–237. doi:10.1137/1033049. JSTOR 2031142. MR1124362. 
  2. Stone, Richard E.; Tovey, Craig A. (1991). "Erratum: The simplex and projective scaling algorithms as iteratively reweighted least squares methods". SIAM Review 33 (3): 461. doi:10.1137/1033100. JSTOR 2031443. MR1124362. 
  3. Strang, Gilbert (1 June 1987). "Karmarkar's algorithm and its place in applied mathematics". The Mathematical Intelligencer (New York: Springer) 9 (2): 4–10. doi:10.1007/BF03025891. ISSN 0343-6993. MR883185 '''883185'''. 

2012b

2011

2006

2004

2002

  • (Forsgreen et al., 2002) ⇒ A. Forsgren, P. E. Gill, and M. H. Wright. (2002). “Interior Methods for Nonlinear Optimization.” In: SIAM Rev. 44.

1999

  • Nocedal, J. and Wright, S. J. (1999). “Numerical Optimization." New York: Springer-Verlag.

1972

  • (Klee & Minty, 1972) ⇒ Victor Klee and George Minty. (1972). “How Good is the Simplex Algorithm?". In Shisha, Oved. Inequalities III (Proceedings of the Third Symposium on Inequalities held at the University of California, Los Angeles, Calif., September 1–9, 1969, dedicated to the memory of Theodore S. Motzkin). New York-London: Academic Press..

1965

  • (Nelder & Mead, 1965) ⇒ J. A. Nelder, and R. Mead. (1965). “A Simplex Method for Function Minimization.” In: Comp. J. 7.

1963

  • (Dantzig, 1963) ⇒ G. B. Dantzig. (1963). “Linear Programming and Extensions.” Princeton University Press.