메뉴 건너뛰기




Volumn 104, Issue 2, 2000, Pages 255-279

Monotone variable-metric algorithm for linearly constrained nonlinear programming

Author keywords

Differential equations; Nonlinear programming; Path following methods; Projective algorithms

Indexed keywords

NONLINEAR EQUATIONS; NUMERICAL METHODS; ORDINARY DIFFERENTIAL EQUATIONS;

EID: 0034134704     PISSN: 00223239     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1004645328197     Document Type: Article
Times cited : (8)

References (28)
  • 1
    • 51249181779 scopus 로고
    • A new polynomial time algorithm in linear programming
    • 1. KARMARKAR, N., A New Polynomial Time Algorithm in Linear Programming, Combinatorica, Vol. 4, pp. 373-395, 1984.
    • (1984) Combinatorica , vol.4 , pp. 373-395
    • Karmarkar, N.1
  • 2
    • 0022956879 scopus 로고
    • A modification of Karmarkar's linear programming algorithm
    • 2. VANDERBEI, R. J., MEKETON, M. S., and FREEDMAN, B. A., A Modification of Karmarkar's Linear Programming Algorithm, Algorithmica, Vol. 1, pp. 395-407, 1986.
    • (1986) Algorithmica , vol.1 , pp. 395-407
    • Vanderbei, R.J.1    Meketon, M.S.2    Freedman, B.A.3
  • 4
    • 0003333494 scopus 로고
    • Mathematical developments arising from linear programming
    • American Mathematical Society, Providence, Rhode Island
    • 4. LAGARIAS, J. C., and TODD, M. J., Editors, Mathematical Developments Arising from Linear Programming, Contemporary Mathematics, American Mathematical Society, Providence, Rhode Island, Vol. 114, 1990.
    • (1990) Contemporary Mathematics , vol.114
    • Lagarias, J.C.1    Todd, M.J.2
  • 5
    • 0024683802 scopus 로고
    • An extension of Karmarkar's projective algorithm for convex quadratic programming
    • 5. YE, Y., and TSE, E., An Extension of Karmarkar's Projective Algorithm for Convex Quadratic Programming, Mathematical Programming, Vol. 44, pp. 157-179, 1989.
    • (1989) Mathematical Programming , vol.44 , pp. 157-179
    • Ye, Y.1    Tse, E.2
  • 6
    • 0027540470 scopus 로고
    • Projective transformation for interior-point algorithms and a superly-convergent algorithm for the W-center problem
    • 6. FREUND, R. M., Projective Transformation for Interior-Point Algorithms and a Superly-Convergent Algorithm for the W-Center Problem, Mathematical Programming, Vol. 58, pp. 385-414, 1993.
    • (1993) Mathematical Programming , vol.58 , pp. 385-414
    • Freund, R.M.1
  • 9
    • 0001665505 scopus 로고
    • Global convergence of a long-step affine scaling algorithm for degenerate linear programming
    • 9. TSUCHIYA, R. T., and MURAMATSU, M., Global Convergence of a Long-Step Affine Scaling Algorithm for Degenerate Linear Programming, SIAM Journal on Optimization, Vol. 5, pp. 525-551, 1995.
    • (1995) SIAM Journal on Optimization , vol.5 , pp. 525-551
    • Tsuchiya, R.T.1    Muramatsu, M.2
  • 10
    • 0024665752 scopus 로고
    • Interior path-following primal-dual algorithms, part I: Linear programming, part 2: Convex quadratic programming
    • 10. MONTEIRO, R. C., and ADLER, I., Interior Path-Following Primal-Dual Algorithms, Part I: Linear Programming, Part 2: Convex Quadratic Programming, Mathematical Programming, Vol. 44, pp. 27-66, 1989.
    • (1989) Mathematical Programming , vol.44 , pp. 27-66
    • Monteiro, R.C.1    Adler, I.2
  • 13
    • 0002521591 scopus 로고
    • The use of ordinary differential equations in the solution of nonlinear systems of equations
    • Edited by M. T. D. Powell, Academic Press, New York, NY
    • 13. ZIRILLI, F., The Use of Ordinary Differential Equations in the Solution of Nonlinear Systems of Equations, Nonlinear Optimization 1981, Edited by M. T. D. Powell, Academic Press, New York, NY, pp. 39-47, 1982.
    • (1982) Nonlinear Optimization 1981 , pp. 39-47
    • Zirilli, F.1
  • 15
    • 0000302389 scopus 로고
    • Linear fractional functional programming
    • 15. SWARUP, K., Linear Fractional Functional Programming, Operations Research, Vol. 13, pp. 1029-1036, 1965.
    • (1965) Operations Research , vol.13 , pp. 1029-1036
    • Swarup, K.1
  • 16
    • 0001720476 scopus 로고
    • On the convergence of gradient methods under constraints
    • 16. WOLFE, P., On the Convergence of Gradient Methods under Constraints, IBM Journal of Research and Development, Vol. 16, pp. 407-411, 1972.
    • (1972) IBM Journal of Research and Development , vol.16 , pp. 407-411
    • Wolfe, P.1
  • 19
    • 0002283257 scopus 로고
    • A parametric simplex-like algorithm for a quadratic fractional programming problem
    • Edited by P. Mazzoleni, Tecnoprint, Milan, Italy
    • 19. ELLERO, A., and MORETTI, E., A Parametric Simplex-Like Algorithm for a Quadratic Fractional Programming Problem, Optimization of Generalized Convex Problems in Economics, Edited by P. Mazzoleni, Tecnoprint, Milan, Italy, pp. 163-176, 1994.
    • (1994) Optimization of Generalized Convex Problems in Economics , pp. 163-176
    • Ellero, A.1    Moretti, E.2
  • 20
    • 0002168842 scopus 로고
    • Optimizing the sum of linear fractional functions
    • Edited by C. A. Floudas and P. M. Pardalos, Princeton University Press, Princeton, New Jersey
    • 20. FALK, J. E., and POLACSAY, S. W., Optimizing the Sum of Linear Fractional Functions, Recent Advances in Global Optimization, Edited by C. A. Floudas and P. M. Pardalos, Princeton University Press, Princeton, New Jersey, pp. 221-258, 1992.
    • (1992) Recent Advances in Global Optimization , pp. 221-258
    • Falk, J.E.1    Polacsay, S.W.2
  • 23
    • 0002116965 scopus 로고
    • Differential equations and dynamical systems
    • Springer Verlag, New York, NY
    • 23. PERKO, L., Differential Equations and Dynamical Systems, Texts in Applied Mathematics, Springer Verlag, New York, NY, Vol. 7, 1991.
    • (1991) Texts in Applied Mathematics , vol.7
    • Perko, L.1
  • 24
    • 0002101752 scopus 로고
    • Birkhäuser, Boston, Massachusetts
    • 24. KARLOFF, H., Linear Programming, Birkhäuser, Boston, Massachusetts, 1991.
    • (1991) Linear Programming
    • Karloff, H.1
  • 25
    • 0002560431 scopus 로고
    • A class of fractional programming problems
    • 25. ALMOGY, Y., and LEVIN, O., A Class of Fractional Programming Problems, Operations Research, Vol. 19, pp. 57-67, 1971.
    • (1971) Operations Research , vol.19 , pp. 57-67
    • Almogy, Y.1    Levin, O.2
  • 26
    • 0001342416 scopus 로고
    • Nonlinear programming: Counterexamples to two global optimization algorithms
    • 26. ZWART, P. B., Nonlinear Programming: Counterexamples to Two Global Optimization Algorithms, Operations Research, Vol. 21, pp. 1260-1266, 1973.
    • (1973) Operations Research , vol.21 , pp. 1260-1266
    • Zwart, P.B.1
  • 27
    • 0016986845 scopus 로고
    • A successive underestimation method for concave minimization problems
    • 27. FALK, J. E., and HOFFMAN, K. R., A Successive Underestimation Method for Concave Minimization Problems, Mathematics of Operations Research, Vol. 1, pp. 251-259, 1976.
    • (1976) Mathematics of Operations Research , vol.1 , pp. 251-259
    • Falk, J.E.1    Hoffman, K.R.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.