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The Fritz John necessary optimality conditions in the presence of equality and inequality constraints. (English) Zbl 0149.16701


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[1] Kuhn, H. W.; Tucker, A. W., Nonlinear programming, (Neyman, J., Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability (1951), Univ. of Calif. Press: Univ. of Calif. Press Berkeley, Calif), 481-492 · Zbl 0044.05903
[2] John, F., Extremum problems with inequalities as side conditions, (Friedrichs, K. O.; Neugebauer, O. E.; Stoker, J. J., Studies and Essays, Courant Anniversary Volume (1948), Wiley (Interscience): Wiley (Interscience) New York), 187-204
[3] Arrow, K. J.; Hurwicz, L.; Uzawa, H., Constraint qualification in maximization problems, Naval Research Logistics Quarterly, 8, 175-191 (1961) · Zbl 0129.34103
[4] Courant, R., (Differential and Integral Calculus, Vol. II (1936), Wiley (Interscience): Wiley (Interscience) New York), Chapter III · JFM 62.0830.14
[5] Apostol, T. M., Mathematical Analysis, ((1957), Addison-Wesley: Addison-Wesley Reading, Mass), 146-157
[6] Motzkin, T. S., Two consequences of the transposition theorem of linear Inequalities, Econometrica, 19, 184-185 (1951), The first inequality appearing in this paper should be reversed · Zbl 0042.01201
[7] Slater, M. L., A note on Motzkin’s transposition theorem, Econometrica, 19, 185-187 (1951) · Zbl 0042.01202
[8] Tucker, A. W., Dual systems of homogeneous linear relations, (Linear Inequalities and Related Systems. Linear Inequalities and Related Systems, Annals of Mathematics Studies No. 38 (1956), Princeton University Press: Princeton University Press Princeton, New Jersey), 3-18, Corollary 2A · Zbl 0072.37503
[9] Cottle, R. W., A theorem of Fritz John in mathematical programming, RAND Memorandum RM-3858-PR (October, 1963)
[10] Fleming, W. H., Functions of Several Variables, ((1965), Addison-Wesley: Addison-Wesley Reading, Mass), 116-120
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