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Volumn 11, Issue 2, 2000, Pages 464-494

Monotonic optimization: Problems and solution approaches *

Author keywords

Difference of increasing functions; Distance geometry; Global optimization; Increasing functions; Monotonicity; Multiplicative programming; Nonconvex quadratic programming; Normal sets; Polyblock approximation algorithms; Polynomial programming

Indexed keywords


EID: 0034353741     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1052623499359828     Document Type: Article
Times cited : (275)

References (37)
  • 1
    • 0007469398 scopus 로고
    • Normal sets and monotone functions and their applications
    • in Russian
    • T.M. ABASOV, Normal sets and monotone functions and their applications, J. Comput. Math. Math. Phys., 3 (1993), pp. 1004-1011 (in Russian).
    • (1993) J. Comput. Math. Math. Phys. , vol.3 , pp. 1004-1011
    • Abasov, T.M.1
  • 4
    • 0026853797 scopus 로고
    • Optimization over the efficiency set
    • H.P. BENSON, Optimization over the efficiency set, J. Optim. Theory Appl., 73 (1992), pp. 47-64.
    • (1992) J. Optim. Theory Appl. , vol.73 , pp. 47-64
    • Benson, H.P.1
  • 5
    • 0001560001 scopus 로고
    • Equilibrium configurations of N equal charges on a sphere
    • T. ERBER AND G.M. HOCKNEY, Equilibrium configurations of N equal charges on a sphere, J. Phys. A: Math. Gen., 24 (1991), pp. L1369-L1377.
    • (1991) J. Phys. A: Math. Gen. , vol.24
    • Erber, T.1    Hockney, G.M.2
  • 6
    • 0001889476 scopus 로고
    • Solving bi-criterion mathematical programs
    • A.M. GEOFFRION, Solving bi-criterion mathematical programs, Oper. Res., 15 (1967), pp. 38-54.
    • (1967) Oper. Res. , vol.15 , pp. 38-54
    • Geoffrion, A.M.1
  • 8
    • 17444449584 scopus 로고
    • A general approach to constrained optimal design based on symbolic mathematics
    • Computer Graphics and Expert Systems, S.S. Rao, ed., ASME, Fairfield, NJ
    • C.R. HAMMOND AND G.E. JOHNSON, A general approach to constrained optimal design based on symbolic mathematics, in Advances in Design Automation - Design methods, Computer Graphics and Expert Systems, S.S. Rao, ed., ASME, Fairfield, NJ, 1987, pp. 31-40.
    • (1987) Advances in Design Automation - Design Methods , pp. 31-40
    • Hammond, C.R.1    Johnson, G.E.2
  • 12
    • 0002574382 scopus 로고
    • Multiplicative programming problems
    • R. Horst and P. Pardalos, eds., Kluwer Academic Publishers, Dordrecht, Boston, London
    • H. KONNO AND T. KUNO, Multiplicative programming problems, in Handbook of Global Optimization, R. Horst and P. Pardalos, eds., Kluwer Academic Publishers, Dordrecht, Boston, London, 1995, pp. 369-405.
    • (1995) Handbook of Global Optimization , pp. 369-405
    • Konno, H.1    Kuno, T.2
  • 13
    • 0028768509 scopus 로고
    • Convex programs with an additional constraint on the product of several convex functions
    • H. KUNO, Y. YAJIMA, Y. YAMAMOTO, AND H. KONNO, Convex programs with an additional constraint on the product of several convex functions, European J. Oper. Res., 77 (1991), pp. 314-324.
    • (1991) European J. Oper. Res. , vol.77 , pp. 314-324
    • Kuno, H.1    Yajima, Y.2    Yamamoto, Y.3    Konno, H.4
  • 16
    • 84923717420 scopus 로고    scopus 로고
    • Polyblock approximation approach for optimization over the weakly efficient and efficient sets
    • to appear
    • L.T. LUC, Polyblock approximation approach for optimization over the weakly efficient and efficient Sets, Acta Math. Vietnam., to appear.
    • Acta Math. Vietnam.
    • Luc, L.T.1
  • 18
    • 0000230999 scopus 로고
    • Maxima for graphs and a new proof of a theorem of Turan
    • T.S. MOTZKIN AND E.G. STRAUSS, Maxima for graphs and a new proof of a theorem of Turan, Canad. J. Math. 17 (1965), pp. 533-540.
    • (1965) Canad. J. Math. , vol.17 , pp. 533-540
    • Motzkin, T.S.1    Strauss, E.G.2
  • 21
    • 0007469057 scopus 로고
    • Global solutions of mathematical programs with intrinsically concave functions
    • M. Avriel, ed., Plenum Press, New York
    • U. PASSY, Global solutions of mathematical programs with intrinsically concave functions, in Advances in Geometric Programming, M. Avriel, ed., Plenum Press, New York, 1980, pp. 355-373.
    • (1980) Advances in Geometric Programming , pp. 355-373
    • Passy, U.1
  • 22
    • 0033316870 scopus 로고    scopus 로고
    • Lipschitz programming via increasing convex-along-rays functions
    • A. RUBINOV AND M. ANDRAMONOV, Lipschitz programming via increasing convex-along-rays functions, Optim. Methods Softw., 10 (1999), pp. 763-781.
    • (1999) Optim. Methods Softw. , vol.10 , pp. 763-781
    • Rubinov, A.1    Andramonov, M.2
  • 23
    • 0001694150 scopus 로고    scopus 로고
    • Duality for increasing positively homogeneous functions and normal sets
    • A. RUBINOV AND B.M. GLOVER, Duality for increasing positively homogeneous functions and normal sets, RAIRO Rech. Opér., 32 (1998), pp. 105-123.
    • (1998) RAIRO Rech. Opér. , vol.32 , pp. 105-123
    • Rubinov, A.1    Glover, B.M.2
  • 24
    • 0346760585 scopus 로고    scopus 로고
    • Algorithm for a monotonic global optimization problem
    • to appear
    • A. RUBINOV, H. TUY, AND H. MAYS, Algorithm for a monotonic global optimization problem, Optimization, to appear.
    • Optimization
    • Rubinov, A.1    Tuy, H.2    Mays, H.3
  • 25
    • 21844484034 scopus 로고
    • Finite algorithm for generalized linear multiplicative programming
    • S. SCHAIBLE AND C. SODINI, Finite algorithm for generalized linear multiplicative programming, J. Optim. Theory Appl., 87 (1995), pp. 441-455.
    • (1995) J. Optim. Theory Appl. , vol.87 , pp. 441-455
    • Schaible, S.1    Sodini, C.2
  • 26
    • 0022794516 scopus 로고
    • C-programming and the minimization of pseudolinear and additive concave functions
    • M. SNIEDOVICH, C-programming and the minimization of pseudolinear and additive concave functions, Oper. Res. Lett., 5 (1986), pp. 185-189.
    • (1986) Oper. Res. Lett. , vol.5 , pp. 185-189
    • Sniedovich, M.1
  • 27
    • 0007469218 scopus 로고
    • The complementary convex structure in global optimization
    • H. TUY, The complementary convex structure in global optimization, J. Global Optim., 2 (1992), pp. 21-40.
    • (1992) J. Global Optim. , vol.2 , pp. 21-40
    • Tuy, H.1
  • 28
    • 0002911084 scopus 로고
    • D. C. optimization: Theory, methods and algorithms
    • R. Horst and P.M. Pardalos, eds., Kluwer Academic Publishers, Dordrecht, Boston, London
    • H. TUY, D. C. optimization: Theory, methods and algorithms, Handbook on Global Optimization, R. Horst and P.M. Pardalos, eds., Kluwer Academic Publishers, Dordrecht, Boston, London, 1995, pp. 149-216.
    • (1995) Handbook on Global Optimization , pp. 149-216
    • Tuy, H.1
  • 29
    • 0007552920 scopus 로고    scopus 로고
    • Normal sets, polyblocks and monotonic optimization
    • H. TUY, Normal sets, polyblocks and monotonic optimization, Vietnam J. Math., 27 (1999) pp. 277-300.
    • (1999) Vietnam J. Math. , vol.27 , pp. 277-300
    • Tuy, H.1
  • 31
    • 84914814847 scopus 로고    scopus 로고
    • Normal branch and bound algorithms for general nonconvex quadratic programming
    • P.M. Pardalos, A. Migdalas, and R. Burkard, eds., World Scientific, River Edge, NJ, to appear
    • H. TUY, Normal branch and bound algorithms for general nonconvex quadratic programming, in Combinatorial and Global Optimization, P.M. Pardalos, A. Migdalas, and R. Burkard, eds., World Scientific, River Edge, NJ, to appear.
    • Combinatorial and Global Optimization
    • Tuy, H.1
  • 32
    • 0007547093 scopus 로고    scopus 로고
    • The MCCNFP with a fixed number of nonlinear arc costs: Complexity and approximation
    • P.M. Pardalos, ed., Kluwer Academic Publishers, Dordrecht, The Netherlands
    • H. TUY, The MCCNFP with a fixed number of nonlinear arc costs: Complexity and approximation, in Approximation and Complexity in Numerical Optimization: Continuous and Discrete Problems, P.M. Pardalos, ed., Kluwer Academic Publishers, Dordrecht, The Netherlands, 2000, pp. 525-549.
    • (2000) Approximation and Complexity in Numerical Optimization: Continuous and Discrete Problems , pp. 525-549
    • Tuy, H.1
  • 33
    • 84923717410 scopus 로고    scopus 로고
    • A new approach to optimization under monotonic constraint
    • to appear
    • H. TUY AND LE TU LUC, A new approach to optimization under monotonic constraint, J. Global Optim., to appear.
    • J. Global Optim.
    • Tuy, H.1    Le, T.L.2
  • 34
    • 23044518721 scopus 로고    scopus 로고
    • On some recent advances and applications of d.C. Optimization
    • Optimization, V.H. Nguyen, J.J. Strodiot, and P. Tossings, eds., Springer-Verlag, New York
    • H. TUY, On some recent advances and applications of d.c. optimization, in Optimization, V.H. Nguyen, J.J. Strodiot, and P. Tossings, eds., Lecture Notes in Econom. and Math. Systems 481, Springer-Verlag, New York, 2000, pp. 473-497.
    • (2000) Lecture Notes in Econom. and Math. Systems , vol.481 , pp. 473-497
    • Tuy, H.1
  • 35
    • 0003090779 scopus 로고    scopus 로고
    • Minimum inter-particle distance at global minimizers of lennard-jones clusters
    • G.L. XUE, Minimum inter-particle distance at global minimizers of Lennard-Jones clusters, J. Global Optim., 11 (1997), pp. 83-90.
    • (1997) J. Global Optim. , vol.11 , pp. 83-90
    • Xue, G.L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.