DOI: 10.1007/bf01100238. Calculation of bounds on variables satisfying nonlinear inequality constraints

Calculation of bounds on variables satisfying nonlinear inequality constraints

10.1007/bf01100238

Crossref journal-article

Springer Science and Business Media LLC

Journal of Global Optimization (297)

Bibliography

Hamed, A. S. E.-D., & McCormick, G. P. (1993). Calculation of bounds on variables satisfying nonlinear inequality constraints. Journal of Global Optimization, 3(1), 25â47.

Authors 2

Ammar Salah El -Deen Hamed (first)
Garth Philip McCormick (additional)

References 45 Referenced 15

Avriel, M. (1973), Methods for Solving Signomial and Reverse Convex Programming Problems, in Avrielet al. (eds.),Optimization and Design, Prentice Hall Inc., Englewood Cliffs, NJ 307?320. / Optimization and Design by M. Avriel (1973)
Benson, H. P. (1975), A Finite Algorithm for Concave Minimzation over a Polyhedron,Naval Research Logistics Quarterly 32, 165?177. (10.1002/nav.3800320119) / Naval Research Logistics Quarterly by H. P. Benson (1975)
Benson, H. P. (1982), On the Convergence of Two Branch-and-Bound Algorithms for Nonconvex Programming Problems,Journal of Optimization Theory and Applications,36, 129?134. (10.1007/BF00934342) / Journal of Optimization Theory and Applications by H. P. Benson (1982)
Falk, J. E. and R. M. Soland (1969), An Algorithm for Separable Nonconvex Programming Problems,Management Science 15, 550?569. (10.1287/mnsc.15.9.550) / Management Science by J. E. Falk (1969)
Fiacco, A. V. and G. P. McCormick (1990),Nonlinear Programming: Sequential Unconstrained Minimization Techniques, John Wiley & Sons, New York (1968); reprinted asClassics in Applied Mathematics Vol. 4, SIAM, Philadelphia, PA. (10.1137/1.9781611971316) / Nonlinear Programming: Sequential Unconstrained Minimization Techniques by A. V. Fiacco (1990)
Fourier, J. G. J. (1826),Solution d'une Question Particulliere du Calcul des Inegalities, Oeuvres II, Paris, pp. 317?328.
Gabot, A. V. (1973), Variations on a Cutting Plane Method for Solving Concave Minimization Problems with Linear Constraints,Naval Research Logistics Quarterly 21, 265?274. / Naval Research Logistics Quarterly by A. V. Gabot (1973)
Hamed, A. (1990), Calculation of Bounds on Variables and Underestimating Convex Functions for Nonconvex Functions, D.Sc. Dissertation, Department of Operations Research, George Washington University, Washington, DC. / D.Sc. Dissertation by A. Hamed (1990)
Hamed, A. and G. P. McCormick (1991), Calculation of Bounds on Variables Satisfying Nonlinear Inequality Constraints, Technical Paper T-544/91, Department of Operations Research, George Washington University, Washington, DC. / Technical Paper T-544/91 by A. Hamed (1991)
Hillestad, R. J. and S. E. Jacobsen (1980a), Reverse Convex Programming,Applied Mathematics and Optimization 6, 63?78. (10.1007/BF01442883) / Applied Mathematics and Optimization by R. J. Hillestad (1980)
Hillestad, R. J. and S. E. Jacobsen, (1980b), Linear Programs with an Additional Reverse Convex Constraint,Applied Mathematics and Optimization 6, 257?269. (10.1007/BF01442898) / Applied Mathematics and Optimization by R. J. Hillestad (1980)
Hoffman, K. L. (1981), A Method for Globally Minimizing Concave Functions over Convex Sets,Mathematical Programming 20, 22?32. (10.1007/BF01589330) / Mathematical Programming by K. L. Hoffman (1981)
Horst, R. (1976a), A New Branch and Bound Approach for Concave Minimization Problems,Lecture Notes in Computer Science 41, 330?337. (10.1007/3-540-07623-9_296) / Lecture Notes in Computer Science by R. Horst (1976)
Horst, R. (1976b), An Algorithm for Nonconvex Programming Problems,Mathematical Programming 10, 312?321. (10.1007/BF01580678) / Mathematical Programming by R. Horst (1976)
Horst, R. (1984), On the Global Minimization of Concave Functions,Operations Research Spektrum 6, 195?205. (10.1007/BF01720068) / Operations Research Spektrum by R. Horst (1984)
Horst, R. (1990a), 'Deterministic Global Optimization; Some Recent Advances and New Fields of Application,Naval Research Logistics Quarterly 37, 433?471. (10.1002/1520-6750(199008)37:4<433::AID-NAV3220370403>3.0.CO;2-2) / Naval Research Logistics Quarterly by R. Horst (1990)
Horst, R. and H. Tuy (1990b),Global Optimization;Deterministic Approaches, Springer-Verlag Berlin-Heidelberg. (10.1007/978-3-662-02598-7) / Global Optimization;Deterministic Approaches by R. Horst (1990)
Horst, R. and N. V. Thoai (1988), Branch-and-Bound Methods for Solving Systems of Nonlinear Equations and Inequalities,Journal of Optimization Theory and Application 58, 139?146. (10.1007/BF00939776) / Journal of Optimization Theory and Application by R. Horst (1988)
Horst, R., N. V. Thoai and H. P. Benson. (1988), Concave Minimization via Conical Partitions and Polyhedral Outer Approximation, Discussion Paper No. 140, Center for Econometrics and Decision Sciences, University of Florida, submitted.
Jones, A. P. and R. M. Soland (1969), A Branch and Bound Algorithm for Multi-Level Fixed Charge Problems,Management Science 16, 67?76. (10.1287/mnsc.16.1.67) / Management Science by A. P. Jones (1969)
Leaver, S. G. (1984), Computing Global Maximum Likelihood Parameter Estimates for Product Models for Frequency Tables Involving Indirect Observations, D.Sc. dissertation, Department of Operations Research, The George Washington University.
Leaver, S. G. and G. P. McCormick. (1984), Formulas for Updating the Generalized Inverse of a Symmetric Rank Two Matrix Composed of Two Nonsymmetric Dyads. Technical Paper Serial T-493/84, Institute for Management Science and Engineering, The George Washington University.
Mancini, L. and G. P. McCormick (1975), Bounding Global Minima,Mathematics of Operations Research 1, 50?53. (10.1287/moor.1.1.50) / Mathematics of Operations Research by L. Mancini (1975)
Mancini, L. and G. P. McCormick (1979), Bounding Global Minima with Interval Arithmetic,Operations Research 27, 743?754. (10.1287/opre.27.4.743) / Operations Research by L. Mancini (1979)
McCormick, G. P. (1976), Computability of Global Solutions to Factorable Nonconvex Programs: Part I -Convex Underestimating Problems,Mathematical Programming 10, 147?175. (10.1007/BF01580665) / Mathematical Programming by G. P. McCormick (1976)
McCormick, G. P. (1980), Locating an Isolated Global Minimizer of a Constrained Nonconvex Program,Mathematics of Operations Research 5, 435?443. (10.1287/moor.5.3.435) / Mathematics of Operations Research by G. P. McCormick (1980)
McCormick, G. P. (1983),Nonlinear Programming: Theory, Algorithms and Applications, John Wiley & Sons, New York. / Nonlinear Programming: Theory, Algorithms and Applications by G. P. McCormick (1983)
McCormick, G. P. (1985),Global Solutions to Factorable Nonlinear Optimzation Problems Using Separable Programming Techniques, NBSIR 85-3206, U.S. Department of Commerce, National Bureau of Standard, Gaithersburg, MD. / NBSIR 85-3206 by G. P. McCormick (1985)
Moore, R. E. (1966),Interval Analysis, Prentice-Hall, Englewood Cliffs. New Jersey. / Interval Analysis by R. E. Moore (1966)
Moore, R. E. (1979),Methods and Applications of Interval Analysis, SIAM, Philadelphia. (10.1137/1.9781611970906) / Methods and Applications of Interval Analysis by R. E. Moore (1979)
Rosen, J. B. (1979), Minimization of a Linearly Constrained Concave Function by Partition of Feasible Domain,Matehmatics of Operations Research 8, 215?230. (10.1287/moor.8.2.215) / Matehmatics of Operations Research by J. B. Rosen (1979)
Sen, S. and H. D. Sherali (1987), Nondifferentiable Reverse Convex Programs and Facial Convexity Cuts via Disjunctive Characterization,Mathematical Programming 37, 169?183. (10.1007/BF02591693) / Mathematical Programming by S. Sen (1987)
Sisser, F. S. (1982a), Computer-Generated Interval Extensions of Factorable Functions and Their Derivatives,International J. of Computer Math. 10, 327?336. (10.1080/00207168208803291) / International J. of Computer Math. by F. S. Sisser (1982)
Sisser, F. S. (1982b), Inverting an Interval Hessian of a Factorable Function,Computing 29, 63?72. (10.1007/BF02254851) / Computing by F. S. Sisser (1982)
Soland, R. M. (1971), An Algorithm for Separable Nonconvex Programming Problems II: Nonconvex Constraints,Management Science 11, 759?773. (10.1287/mnsc.17.11.759) / Management Science by R. M. Soland (1971)
Taha, H. (1973), Concave Minimization over a Convex Polyhedron,Naval Research Logistics Quarterly 20, 533?548. (10.1002/nav.3800200313) / Naval Research Logistics Quarterly by H. Taha (1973)
Thach, P. T. (1988), The Design Centering Problem as a DC-Programming Problem,Mathematical Programming 41, 229?248. (10.1007/BF01580765) / Mathematical Programming by P. T. Thach (1988)
The Operation Research Society of America and the Institute of Management Science (1990),ORSA/TIMS Bulletin Number 30: of the Joint National Meeting in Philadelphia, Pennsylvania, October 29?31, 1990. Baltimore MD: ORSA and TIMS, 1990. / ORSA/TIMS Bulletin Number 30: of the Joint National Meeting in Philadelphia, Pennsylvania, October 29?31, 1990 by The Operation Research Society of America and the Institute of Management Science (1990)
Thoai, N. V. (1988), A Modified Version of Tuy's Method for Solving DC Programming Problems,Optimization 19, 665?674. (10.1080/02331938808843381) / Optimization by N. V. Thoai (1988)
Tuy, H. (1985), Global Minimization of a Difference of Two Convex Functions, in: Hammer, G. and D. Pallaschke (eds.),Selected Topics in Operations Research and Mathematical Economics, Lecture Notes in Economics and Mathematical Systems,226, 98?118.
Tuy, H. (1987a), Global Minimization of a Difference of Two Convex Functions,Mathematical Programming Study 30, 150?182. (10.1007/BFb0121159) / Mathematical Programming Study by H. Tuy (1987)
Tuy, H. (1987b), Convex Programs with an Additional Reverse Convex Constraint,Journal of Optimization Theory and Applications 52, 463?485. (10.1007/BF00938217) / Journal of Optimization Theory and Applications by H. Tuy (1987)
Tuy, H. and R. Horst (1988), Convergence and Restart in Branch-and-Bound Algorithms for Global Optimization. Application to Concave Minimization and DC-Optimization Problems,Mathematical Programming 41, 161?183. (10.1007/BF01580762) / Mathematical Programming by H. Tuy (1988)
Tuy, H. and N. V. Thuong. (1985), Minimizing a Convex Function over the Complement of a Convex Set,Methods of Operations Research 49, 85?99. / Methods of Operations Research by H. Tuy (1985)
Williams, H. P. (1986), Fourier's Method of Linear Programming and Its Dual,American Mathematical Monthly 93, 681?695. (10.1080/00029890.1986.11971923) / American Mathematical Monthly by H. P. Williams (1986)

Dates

Type	When
Created	20 years, 6 months ago (Feb. 4, 2005, 11:58 p.m.)
Deposited	6 years, 3 months ago (May 1, 2019, 5:07 a.m.)
Indexed	1 month, 3 weeks ago (July 1, 2025, 7:06 a.m.)
Issued	32 years, 7 months ago (Jan. 1, 1993)
Published	32 years, 7 months ago (Jan. 1, 1993)
Published Print	32 years, 7 months ago (Jan. 1, 1993)

Funders 0

None

BibTeX

@article{Hamed_1993, title={Calculation of bounds on variables satisfying nonlinear inequality constraints}, volume={3}, ISSN={1573-2916}, url={http://dx.doi.org/10.1007/bf01100238}, DOI={10.1007/bf01100238}, number={1}, journal={Journal of Global Optimization}, publisher={Springer Science and Business Media LLC}, author={Hamed, Ammar Salah El -Deen and McCormick, Garth Philip}, year={1993}, pages={25–47} }

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