Applying term consistency to an equality constrained...

Data processing: artificial intelligence – Neural network – Learning task

Reexamination Certificate

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C706S012000, C706S014000, C706S046000, C708S446000, C708S493000, C708S495000, C708S496000, C712S222000

Reexamination Certificate

active

07099851

ABSTRACT:
One embodiment of the present invention provides a system that solves a global optimization problem specified by a function ƒ and a set of equality constraints q1(x)=0 (i=1, . . . , r), wherein ƒ is a scalar function of a vector x=(x1, x2, x3, . . . xn). During operation, the system receives a representation of the function ƒ and the set of equality constraints and stores the representation in a memory within a computer system. Next, the system and performs an interval global optimization process to compute guaranteed bounds on a globally minimum value of the function ƒ(x) subject to the set of equality constraints. Performing this interval global optimization process involves, applying term consistency to the set of equality constraints over a subbox X, and excluding portions of the subbox X that violate the set of equality constraints.

REFERENCES:
patent: 3900723 (1975-08-01), Bethany et al.
patent: 4622650 (1986-11-01), Kulisch
patent: 5253327 (1993-10-01), Yoshihara
patent: 6049865 (2000-04-01), Smith
patent: 6718289 (2004-04-01), Suzuki et al.
patent: 2002/0184283 (2002-12-01), Steele, Jr.
Schulte, M.J.; Swartzlander E.E., Jr., “A variable-precision interval arithmetic processor” Application Specific Array Processors 1994. Proceedings., International Conference on Aug. 22-24, 1994 pp. 248-258.
M. J. Schulte, K. C. Bickerstaff, and E. E. Swartzlander, Jr., “Hardware Interval Multipliers,” Journal of Theoretical and Applied Informatics, vol. 3, No. 2, pp. 73-90, 1996.
C. Bliek et al., “COCONUT Deliverable D1 Algorithms for Solving Nonlinear Constrained and Optimization Problems: The State of The Art”, published on http://www.mat.univie.ac.at/˜neum/ms/StArt.pdf, Nov. 2001.
Pascal Van Hentenryck, Laurent Michel, “Newton: Constraint Programming over Nonlinear Real Constraints”, Science of Programming, 1997.
F. Benhamou, F. Gouland, L. Granvilliers, “Revising hull and box consistency”, In Proceedings of International Conference on Logic Programming, Las Cruses, USA, 1999.
H. Collavizza, F. Delobel, and M. Rueher. “Comparing Partial Consistencies”. Reliable Computing, 5(3):213-228, 1999.
Pascal Van Hentenryck, Vijay Saraswat and Yves Deville, “Design, Implementation, and Evaluation of the Constraint Language cc (FD),” Elsevier Science, Inc., 1998.
E.R. Hansen, “Global Optimization Using Interval Analysis,” Marcel Dekker, Inc., New York, NY, 1992.
R.B. Kearfott, “A Fortran 90 Environment for Research and Prototyping of Enclosure Algorithms for Nonlinear Equations and Global Optimization,” ACM Transactions on Mathematical Software, vol. 21, No. 1, Mar. 1995, pp. 63-78 http://interval.louisiana.edu/preprints.html.
R. B. Kearfott, Algorithm 763: Interval Arithmetic: A Fortran 90 Module for an Interval Data Type, ACM Trans. Math. Software, 22, vol. 4, 1996, pp. 385-392. http://interval.louisiana.edu/preprints.html.
R. B. Kearfott and M. Novoa III, “Algorithm 681: INTBIS, A portable interval Newton/bisection package”, ACM Trans. Math Software, vol. 16, No. 2, pp. 152-147. http://www.netlib.org/toms/681.
R. B. Kearfott, M. Dawande, K.S. Du, and C. Hu, “Algorithm 737: INTLIB: A Portable Fortran 737 Interval Standard Function Library,” ACM Trans. Math. Sofware, 20, vol. 4, Dec. 1994, pp. 447-458.
R. B. Kearfott and G. W. Walster, “On Stopping Criteria in Verified Nonlinear Systems or Optimization Algorithms,” ACM Trans. Math. Software, 26, vol. 3, Sep. 2000, pp. 323-351. The Publication itself says Received: Jul. 1999; revised: Mar. 2000; accepted: Mar. 2000. http://interval.louisiana.edu/preprints.html.
R.E. Moore and S.T. Jones “Safe Starting Regions for Iterative Methods”, SIAM Journal on Numerical Analysis, vol. 14, No. 6 (Dec. 1977), pp. 1051-1065.
A. Neumaier, “The Enclosure of Solutions of Parameter-Dependent Systems of Euqations,” Cambridge University Press, Cambridge, 1990, ISBN: 0-12-505630-3, Reliability in Computing pp. 269-286.
S.M. Rump, “Verification Methods for Dense and Sparse Systems of Equations,” in Topics in Validated Computations: Proceedings of the IMACS-GAMM International Workshop on Validated Computations, University of Oldenburg, J. Herzberger, ed., Elsevier Studies in Computational Mathematics, Elsevier, 1994, pp. 63-136.

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