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Journal of Global Optimization (297)
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Hansen, P., & Jaumard, B. (1992). Reduction of indefinite quadratic programs to bilinear programs. Journal of Global Optimization, 2(1), 41–60.

Authors 2
  1. Pierre Hansen (first)
  2. Brigitte Jaumard (additional)
References 48 Referenced 25
  1. Al-Khayyal, F. A. (1990), Generalized Bilinear Programming: Part I. Models, Applications, and Linear Programming Relaxation, Research Report, Georgia Institute of Technology.
  2. Al-Khayyal, F. A. and J. E., Falk (1983), Jointly Constrained Biconvex Programming, Mathematics of Operations Research 8 (2), 273?286. (10.1287/moor.8.2.273) / Mathematics of Operations Research by F. A. Al-Khayyal (1983)
  3. Al-Khayyal, F., R. Horst, and P. Pardalos (1991), Global Optimization of Concave Functions Subject to Separable Quadratic Constraints and of All-Quadratic Separable Problems, Annals of Operations Research. (10.1007/BF02098176)
  4. Avriel, M., W. E., Diernert, S., Schaible, and I., Zang (1988), Generalized Concavity, New York: Plenum Press. (10.1007/978-1-4684-7600-2) / Generalized Concavity by M. Avriel (1988)
  5. Avriel, M. and A. C., Williams (1971), An Extension of Geometric Programming with Applications in Engineering Optimization, Journal of Engineering Mathematics 5 (3), 187?194. (10.1007/BF01535411) / Journal of Engineering Mathematics by M. Avriel (1971)
  6. Balas, E. and C. S., Yu (1986), Finding a Maximum Clique in an Arbitrary Graph, SIAM Journal on Computing 15, 1054?1068. (10.1137/0215075) / SIAM Journal on Computing by E. Balas (1986)
  7. Baron, D. P. (1972), Quadratic Programming with Quadratic Constraints, Naval Research Logistics Quarterly 19, 253?260. (10.1002/nav.3800190204) / Naval Research Logistics Quarterly by D. P. Baron (1972)
  8. Bartholomew-Biggs, M. C. (1976), A Numerical Comparison between Two Approaches to Nonlinear Programming Problems, Technical Report #77, Numerical Optimization Center, Hatfield, England. / A Numerical Comparison between Two Approaches to Nonlinear Programming Problems / Technical Report by M. C. Bartholomew-Biggs (1976)
  9. Benacer, R. and T., Pham Dinh (1986), Global Maximization of a Nondefinite Quardatic Function over a Convex Polyhedron, pp. 65?76 in J.-B., Hirriart-Urruty (ed.), Fermat Days 1985: Mathematics for Optimization, Amsterdam: North-Holland. (10.1016/S0304-0208(08)72394-6) / Fermat Days 1985: Mathematics for Optimization by R. Benacer (1986)
  10. Berge, C. (1983), Graphes, 3rd ed., Paris: Gauthier-Villars. / Graphes by C. Berge (1983)
  11. Berge, C. (1987), Hypergraphes, Paris, Gauthier-Villars. / Hypergraphes by C. Berge (1987)
  12. Bernard, J. C. and J. A., Ferland (1989), Convergence of Interval-Type Algorithms for Generalized Fractional Programming, Mathematical Programming 43, 349?363. (10.1007/BF01582298) / Mathematical Programming by J. C. Bernard (1989)
  13. Carraghan, R. and P. M., Pardalos (1990), An Exact Algorithm for the Maximum Clique Problem, Operations Research Letters 9, 375?382. (10.1016/0167-6377(90)90057-C) / Operations Research Letters by R. Carraghan (1990)
  14. Colville, A. R. (1986), A Comparative Study on Nonlinear Programming Codes, IBM Scientific Center Report 320-2949, New York.
  15. Dembo, R. S. (1972), Solution of Complementary Geometric Programming Problems, M.Sc. Thesis, Technion, Haifa.
  16. Dembo, R. S. (1976), A Set of Geometric Programming Test Problems and Their Solutions, Mathematical Programming 10, 192?213. (10.1007/BF01580667) / Mathematical Programming by R. S. Dembo (1976)
  17. Duffin, R. J., E. L., Peterson, and C., Zener (1967), Geometric Programming: Theory and Applications, New York: Wiley. / Geometric Programming: Theory and Applications by R. J. Duffin (1967)
  18. Ecker, J. G. and R. D., Niemi (1975), A Dual Method for Quadratic Programs with Quadratic Constraints, SIAM Journal on Applied Mathematics 28, 568?576. (10.1137/0128046) / SIAM Journal on Applied Mathematics by J. G. Ecker (1975)
  19. Evans, D. H. (1963), Modular Design?A Special Case in Nonlinear Programming, Operations Research 11, 637?647. (10.1287/opre.11.4.637) / Operations Research by D. H. Evans (1963)
  20. Flippo, O. E. (1989), Stability, Duality and Decomposition in General Mathematical Programming, Rotterdam: Erasmus University Press. / Stability, Duality and Decomposition in General Mathematical Programming by O. E. Flippo (1989)
  21. Floudas, C. A., A., Aggarwal, and A. R., Ciric (1989), Global Optimum Search for Nonconvex NLP and MINLP Problems, Computers and Chemical Engineering 13 (10), 1117?1132. (10.1016/0098-1354(89)87016-4) / Computers and Chemical Engineering by C. A. Floudas (1989)
  22. Floudas, C. A. and P., Pardalos (1990), A Collection of Test Problems for Constrained Global Optimization, Lecture Notes in Computer Science, 455, Berlin: Springer-Verlag. (10.1007/3-540-53032-0) / A Collection of Test Problems for Constrained Global Optimization / Lecture Notes in Computer Science by C. A. Floudas (1990)
  23. Floudas, C. A. and V., Visweswaran (1990), A Global Optimization Algorithm (GOP) for Certain Classes of Nonconvex NLPs?I. Theory, Computers and Chemical Engineering 14 (12), 1397?1417. (10.1016/0098-1354(90)80020-C) / Computers and Chemical Engineering by C. A. Floudas (1990)
  24. Friden, C., A., Hertz, and D.de, Werra (1990), Tabaris: An Exact Algorithm Based on Tabu Search for Finding a Maximum Independent Set in a Graph, Computers and Operations Research 17 (5), 437?445. (10.1016/0305-0548(90)90048-C) / Computers and Operations Research by C. Friden (1990)
  25. Garey, M. R., D. S., Johnson, and L., Stockmeyer (1976), Some Simplified NP-Complete Graph Problems, Theoretical Computer Science 1, 237?267. (10.1016/0304-3975(76)90059-1) / Theoretical Computer Science by M. R. Garey (1976)
  26. Geoffrion, A. M. (1972), Generalized Benders Decomposition, Journal of Optimization Theory and Its Applications 10, 237?260. (10.1007/BF00934810) / Journal of Optimization Theory and Its Applications by A. M. Geoffrion (1972)
  27. Gochet, W. and Y., Smeers (1979), A Branch and Bound Method for Reversed Geometric Programming, Operations Research 27, 982?996. (10.1287/opre.27.5.982) / Operations Research by W. Gochet (1979)
  28. Hock, W. and K., Schittkowski (1981), Test Examples for Nonlinear Programming Codes, Lecture Notes in Economics and Mathematical Systems #187, Berlin: Springer-Verlag. (10.1007/978-3-642-48320-2) / Test Examples for Nonlinear Programming Codes / Lecture Notes in Economics and Mathematical Systems by W. Hock (1981)
  29. Horst, R. and H., Tuy (1990), Global Optimization, Deterministic Approaches, Berlin: Springer-Verlag. (10.1007/978-3-662-02598-7) / Global Optimization, Deterministic Approaches by R. Horst (1990)
  30. Konno, H. (1976), Maximizing a Convex Quadratic Function Subject to Linear Constraints Mathematical Programming 11, 117?127. (10.1007/BF01580380) / Mathematical Programming by H. Konno (1976)
  31. Konno, H. and T. Kuno (1989), Linear Multiplicative Programming, Preprint IHSS 89-13, Tokyo Institute of Technology.
  32. Kough, P. F. (1979), The Indefinite Quadratic Programming Problem, Operations Research 27, 516?533. (10.1287/opre.27.3.516) / Operations Research by P. F. Kough (1979)
  33. Mladineo, R. H. (1986), An Algorithm for Finding the Global Maximum of a Multimodal, Multivariate Function, Mathematical Programming 34, 188?200. (10.1007/BF01580583) / Mathematical Programming by R. H. Mladineo (1986)
  34. Pardalos, P. M., J. H., Glick, and J. B., Rosen (1987), Global Minimization of Indefinite Quadratic Problems, Computing 39, 281?291. (10.1007/BF02239972) / Computing by P. M. Pardalos (1987)
  35. Pardalos, P. M. and J. B., Rosen (1986), Methods for Global Concave Minimization: A Bibliographic Survey, SIAM Review 28 (3), 367?379. (10.1137/1028106) / SIAM Review by P. M. Pardalos (1986)
  36. Pardalos, P. M. and J. B., Rosen (1987), Constrained Global Optimization: Algorithms and Applications, Lecture Notes in Computer Science #268, Berlin: Springer Verlag. (10.1007/BFb0000035) / Constrained Global Optimization: Algorithms and Applications / Lecture Notes in Computer Science by P. M. Pardalos (1987)
  37. Pham Dinh, T. and S.El, Bernoussi (1989), Numerical Methods for Solving a Class of Global Nonconvex Optimization Problems, International Series of Numerical Mathematics 87, 97?132. / International Series of Numerical Mathematics by T. Pham Dinh (1989)
  38. Phan, H. (1982), Quadratically Constrained Quadratic Programming: Some Applications and a Method of Solution, Zeitschrift für Operations Research 26, 105?119. / Zeitschrift für Operations Research by H. Phan (1982)
  39. Phillips, A. T. and J. B., Rosen, (1990), Guaranteed ?-Approximate Solution to Indefinite Global Optimization, Naval Research Logistics 37, 499?514. (10.1002/1520-6750(199008)37:4<499::AID-NAV3220370405>3.0.CO;2-9) / Naval Research Logistics by A. T. Phillips (1990)
  40. Ragavachari, M. (1989), On Connections between Zero-One Integer Programming and Concave Programming under Linear Constraints, Operations Research 17, 680?684. (10.1287/opre.17.4.680) / Operations Research by M. Ragavachari (1989)
  41. Reeves, G. R. (1975), Global Minimization in Nonconvex All-Quadratic Programming, Management Science 22, 76?86. (10.1287/mnsc.22.1.76) / Management Science by G. R. Reeves (1975)
  42. Sherali, H. and A. Alameddine (1990), A New Reformulation-Linearization Technique for Bilinear Programming Problems, Research Report, Department of Industrial and Systems Engineering, Virginia Polytechnic Institute.
  43. Stephanopoulos, G. and A. W., Westerberg (1975), The Use of Hestenes' Method of Multipliers to Resolve Dual Gaps in Engineering System Optimization, Journal of Optimization Theory and Applications 15, 285?309. (10.1007/BF00933339) / Journal of Optimization Theory and Applications by G. Stephanopoulos (1975)
  44. Simões, L. M. C. (1987), Search for the Global Optimum of Least Volume Trusses, Engineering Optimization 11, 49?67. (10.1080/03052158708941036) / Engineering Optimization by L. M. C. Simões (1987)
  45. Thoai, N. V. (1990), Application of Decomposition Techniques in Global Optimization to the Convex Multiplicative Programming Problem, Paper presented at the Second Workshop on Global Optimization, Sopron, Hungary.
  46. Tuy, H. (1986), A General Deterministic Approach to Global Optimization via d.-c. Programming, pp. 137?162, in J. B., Hirriart-Urruty (ed.), Fermat Days 1985: Mathematics for Optimization, Amsterdam: North-Holland. / Fermat Days 1985: Mathematics for Optimization by H. Tuy (1986)
  47. Visweswaran, V. and C. A., Floudas (1990), A Global Optimization Algorithm (GOP) for Certain Classes of Nonconvex NLPs?II. Application of Theory and Test Problems, Computers and Chemical Engineering 14 (12), 1419?1434. (10.1016/0098-1354(90)80021-3) / Computers and Chemical Engineering by V. Visweswaran (1990)
  48. Wolsey, L. A. (1981), A Resource Decomposition Algorithm for General Mathematical Programs, Mathematical Programming Study 14, 244?257. (10.1007/BFb0120932) / Mathematical Programming Study by L. A. Wolsey (1981)
Dates
Type When
Created 20 years, 10 months ago (Nov. 3, 2004, 10:56 p.m.)
Deposited 2 years, 4 months ago (April 29, 2023, 6:46 p.m.)
Indexed 2 months ago (July 1, 2025, 7:06 a.m.)
Issued 33 years, 8 months ago (Jan. 1, 1992)
Published 33 years, 8 months ago (Jan. 1, 1992)
Published Print 33 years, 8 months ago (Jan. 1, 1992)
Funders 0

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@article{Hansen_1992, title={Reduction of indefinite quadratic programs to bilinear programs}, volume={2}, ISSN={1573-2916}, url={http://dx.doi.org/10.1007/bf00121301}, DOI={10.1007/bf00121301}, number={1}, journal={Journal of Global Optimization}, publisher={Springer Science and Business Media LLC}, author={Hansen, Pierre and Jaumard, Brigitte}, year={1992}, pages={41–60} }