A New Approach to Optimization under Monotonic Constraint

Journal of Global Optimization

Volumn 18, Issue 1, 2000, Pages 1-15

  Tuy, Hoang ^a   Luc, Le Tu ^a  

^a INSTITUTE OF MATHEMATICS   (Viet Nam)

Author keywords

Convex multiplicative constraint; Monotonic constraint; Polyblock outer approximation; Rank k reverse convex programs

Indexed keywords

EID: 0347372730     PISSN: 09255001     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008321216723     Document Type: Article

References (11)

1. Horst, R. and Tuy, H. (1996), Global Optimization: Deterministic Approaches, Springer, 3rd edition.
2. Konno, H., Thach, P.T. and Tuy, H. (1997), Optimization on Low Rank Nonconvex Structures, Kluwer.
3. Kuno, T., Konno, H. and Yamomoto, Y. (1992), A parametric successive underestimation method for convex programming problems with an additional convex multiplicative constraint, Journal of the Operations Research Society of Japan 35: 290-299.
4. Kuno, T., Yajima, Y., Yamamoto, Y and Konno, H. (1994), Convex programs with an additional constraint on the product of several convex functions, European Journal of Operational Research 77: 314-324.
5. Kuno, T. and Yamamoto, Y (1998), A finite algorithm for globally optimizing a class of rank-two reverse convex constraints, Journal of Global Optimization 12: 247-265.
6. Pferschy, U. and Tuy, H. (1994), Linear programs with an additional rank two reverse convex constraint, Journal of Global Optimization 4: 441-454.
7. Thach, P.T., Burkard, R. and Oettli, W. (1991), Mathematical programs with a two dimensional reverse convex constraint, Journal of Global Optimization 1: 145-154.
8. Rubinov, A., Tuy, H. and Mays, H. (1998), Algorithm for a Monotonic Global Optimization Problem. Preprint, SIMS, University of Ballarat, Australia. To appear in Optimization.
9. Tuy, H. (1998), Convex Analysis and Global Optimization, Kluwer.
10. Tuy, H. (1999), Monotonic Optimization: Problems and Solution Approaches. Preprint, Institute of Mathematics, Hanoi. To appear in SIAM Journal on Optimization.
11. Tuy, H. and Nghia, N.D. Decomposition algorithms for reverse convex programs. To appear in Vietnam Journal of Mathematics (Springer-Verlag).