Applying term consistency to an inequality constrained...

Electrical computers: arithmetic processing and calculating – Electrical digital calculating computer – Particular function performed

Reexamination Certificate

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

Reexamination Certificate

active

07028065

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 inequality constraints pi(x)≦0 (i=1, . . . , m), wherein ƒ and piare scalar functions of a vector x=(x1, x2, x3, . . . xn). The system operates by receiving a representation of the function ƒ and the set of inequality constraints, and then storing the representation in a memory within the computer system. Next, the system performs an interval inequality constrained global optimization process to compute guaranteed bounds on the minimum value of the function ƒ(x) subject to the set of inequality constraints. While performing the interval global optimization process, the system applies term consistency at various places in the process over a subbox X, and excludes any portion of the subbox X that violates term consistency.

REFERENCES:
patent: 4819197 (1989-04-01), Blais
Elijah et al., An algorithm for optimization problems with functional inequality constraints, 1976, IEEE Transactions on automatic ocntrol vol. AC-21, No. 2, pp. 184-193.
Kolev et al., An interval method for global inequality-constraint optimization problems, 2000, IEEE International symposium on circuits and systems, pp. 617-620.
William Walster, Intervals: the connection between computing and the world, 2000, IEEE, pp. 859-864.
Pascal Van Hentenryck, Vijay Saraswat and Yves Deville, “Design, Implementation, and Evaluation of the Constraint Language cc (FD),” Elsevier Science, Inc., 1998, pp. 139-164.
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, “INTLIB: A Portable Fortran 77 Interval Standard Function Library,” ACM Trans. Math. Software, 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 saysReceived: 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.

LandOfFree

Say what you really think

Search LandOfFree.com for the USA inventors and patents. Rate them and share your experience with other people.

Rating

Applying term consistency to an inequality constrained... does not yet have a rating. At this time, there are no reviews or comments for this patent.

If you have personal experience with Applying term consistency to an inequality constrained..., we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Applying term consistency to an inequality constrained... will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFUS-PAI-O-3555653

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.