An elementary proof of the Fritz-John and Karush-Kuhn-Tucker conditions in nonlinear programming

European Journal of Operational Research

Volumn 180, Issue 1, 2007, Pages 479-484

  Birbil, Ş I ^a   Frenk, J B G ^b   Still, G J ^c  

^a SABANCI UNIVERSITY   (Turkey)

^b ERASMUS UNIVERSITY ROTTERDAM   (Netherlands)

^c UNIVERSITY OF TWENTE   (Netherlands)

Author keywords

Fritz John conditions; Karush Kuhn Tucker conditions; Nonlinear programming

Indexed keywords

CONSTRAINT THEORY; OPERATIONS RESEARCH; PROBLEM SOLVING; SET THEORY; THEOREM PROVING;

ELEMENTARY PROOF; FINITE DIMENSIONAL PROGRAMMING; FRITZ JOHN CONDITIONS; INEQUALITY CONSTRAINTS; KARUSH KUHN TUCKER CONDITIONS;

NONLINEAR PROGRAMMING;

EID: 33846318540     PISSN: 03772217     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ejor.2006.04.012     Document Type: Article

References (11)

1. Avriel M., Diewert W.E., Schaible S., and Zang I. Generalized Concavity. Mathematical Concepts and Methods in Science and Engineering vol. 36 (1988), Pleneum Press, New York
2. Bazaraa M.S., Sherali H.D., and Shetty C.M. Nonlinear Programming: Theory and Algorithms. second ed. Wiley-Interscience Series in Discrete Mathematics and Optimization (1993), Wiley, New York
3. Bertsekas D.P. Nonlinear Programming (1995), Athena Scientific, Massachusetts
4. Chvátal V. Linear Programming (1999), W.H. Freeman and Company, New York
5. Faigle U., Kern K., and Still G. Algorithmic Principles to Mathematical Programming (2002), Kluwer Academic publishers., Dordrecht
6. Farkas J. Theorie der einfachen Ungleichungen. Journal für die reine und angewandte Mathematic 124 (1902) 1-27
7. John F. Extremum problems with inequalities as side conditions. In: Friedrichs K.O., Neugebauer O.E., and Stoker J.J. (Eds). Studies and Essays, Courant Anniversary Volume (1948), Wiley-Interscience
8. W. Karush, Minima of functions of several variables with inequalities as side conditions. Master's thesis, Department of Mathematics, University of Chicago, 1939.
9. Kuhn H.W., and Tucker A.W. Nonlinear programming. In: Neyman J. (Ed). Proceedings of Second Berkeley Symposium on Mathematical Statistics and Probability (1951), University of California Press
10. McShane E.J. The Lagrange multiplier rule. The American Mathematical Monthly 80 8 (1973) 922-925
11. Rudin W. Principles of Mathematical Analysis. third ed. (1976), McGraw-Hill, New York