Implied constraints and an alternate unified development of nonlinear programming theory

European Journal of Operational Research

Volumn 88, Issue 3, 1996, Pages 537-549

  Johri, Pravin K ^a  

^a LUCENT TECHNOLOGIES   (United States)

Author keywords

Constraint qualification; Duality; Implied constraints; Karush kuhn tucker conditions; Nonlinear programming; Objective qualification; Simplex method

Indexed keywords

ALGORITHMS; CONSTRAINT THEORY; OPERATIONS RESEARCH; OPTIMAL SYSTEMS;

CONSTRAINT QUALIFICATION; DUALITY; IMPLIED CONSTRAINTS; KARUSH-KUHN-TUCKER CONDITIONS; OBJECTIVE QUALIFICATION; SIMPLEX METHOD;

NONLINEAR PROGRAMMING;

EID: 0030574645     PISSN: 03772217     EISSN: None     Source Type: Journal    
DOI: 10.1016/0377-2217(94)00253-3     Document Type: Article

References (22)

1. Avriel, M., Nonlinear Programming Analysis and Methods, Prentice-Hall, Englewood Cliffs, NY, 1976.
2. Bazaraa, M.S., Goode, J.J., and Shetty, C.M., "Constraint qualification revisited", Management Science 18 (1972) 567-573.
3. Bazaraa, M.S., and Shetty, C.M., Nonlinear Programming: and Algorithms, Wiley, New York, 1979.
4. Bellmore, M., Greenberg, H.J., and Jarvis, J.J., "Generalized penalty-function concepts in Mathematical Programming", Operations Research 18 (1970) 229-252.
5. Blair, C., "Two rules for deducing valid inequalities for 0-1 problems". SIAM Journal on Applied Mathematics 31 (1976) 614-617.
6. Dennis, J.E., and Schnabel, R.B., "A view of unconstrained optimization", in: G.L. Nemhauser, A.H.G. Rinnooy Kan and M.J. Todd (eds.), Operations Research and Management and Science, Vol. 1, Optimization, North-Holland, Amsterdam, 1989, 1-72.
7. Fenchel, W., "On conjugate convex functions", Canadian Journal of Mathematics 1 (1949) 73-77.
8. Fiacco, A.V., and McCormick, G.P., Nonlinear Programming: Sequential Unconstrained Minimization Techniques, Classics in Applied Mathematics, SIAM, Philadelphia, PA, 1990.
9. Garfinkel, R.S., and Nemhauser, G.L., Integer Programming, Wiley, New York, 1972.
10. Gill, P.E., Murray, W., Saunders, M.A., and Wright, M.H., "Constrained nonlinear programming", in: G.L. Nemhauser, A.H.G. Rinnooy Kan and M.J. Todd (eds.), Handbooks in Operations Research and Management Science, Vol. I. Optimization, North-Holland, Amsterdam, 1989, 171-210.
11. Glover, F., "Surrogate constraints", Operations Research 16 (1968) 741-749.
12. Gould, F.J., and Tolle, J.W., "A necessary and sufficient qualification for constrained optimization", SIAM Journal on Applied Mathematics 20 (1971) 164-172.
13. Greenberg, H.J., and Pierskalla, W.P., "Surrogate mathematical programming", Operations Research 18 (1970) 924-939.
14. Guignard, M., "Generalized Kuhr-Tucker conditions for mathematical programming in a Banach space", SIAM Journal on Control 7 (1969) 232-241.
15. Johri, P.K., "Implied constraints and a unified theory of duality in linear and nonlinear programming", European Journal of Operational Research 71 (1993) 61-69.
16. Johri, P.K., "Derivation of duality in mathematical programming and optimization theory", European Journal of Operational Research 73 (1994) 547-554.
17. Johri, P.K., "Duality via half spaces", ZOR Methods and Models of Operations Research 39 (1994) 85-92.
18. Kuhn, H.W., and Tucker, A.W., "Nonlinear programming", in: J. Neymen (ed.), Proc. 2nd Berkeley Symp. on Mathematical Stat. and Prob., University of California Press, Berkeley, CA, 1951.
19. Luenberger, D.G., Linear and Nonlinear Programming, Addison-Wesley, Menlo Park, CA, 1984.
20. Luenberger, D.G., Optimization by Vector Space Methods, Wiley, New York, 1969.
21. Rockafellar, R.T., Convex Analysis, Princeton University Press, Princeton, NJ, 1970.
22. Wolfe, P., "A duality theorem for non-linear programming", Quarterly of Applied Mathematics 19 (1961) 239-244.