Book Review
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Book Information
Authors:
V. Barbu and Th. Precupanu
Title:
Convexity and optimization in Banach spaces
Additional book information
Sÿthoff & Noordhoff International Publishers, Alphen aan den Rijn, The Netherlands, 1978, xi + 316 pp.
 1.
Fritz
John, Extremum problems with inequalities as subsidiary
conditions, Studies and Essays Presented to R. Courant on his 60th
Birthday, January 8, 1948, Interscience Publishers, Inc., New York, N. Y.,
1948, pp. 187–204. MR 0030135
(10,719b)
 2.
W. E. Karush, Minima of functions of several variables with inequalities as side conditions, Masters dissertation, University of Chicago, Chicago, December, 1939.
 3.
H.
W. Kuhn and A.
W. Tucker, Nonlinear programming, Proceedings of the Second
Berkeley Symposium on Mathematical Statistics and Probability, 1950,
University of California Press, Berkeley and Los Angeles, 1951,
pp. 481–492. MR 0047303
(13,855f)
 4.
E.
J. McShane, On multipliers for Lagrange problems, Amer. J.
Math. 61 (1939), 809–819. MR 0000462
(1,78a)
 5.
Lucien
W. Neustadt, Optimization, Princeton University Press,
Princeton, N. J., 1976. A theory of necessary conditions; With a chapter by
H. T. Banks. MR
0440440 (55 #13315)
 6.
L.
S. Pontryagin, V.
G. Boltyanskii, R.
V. Gamkrelidze, and E.
F. Mishchenko, The mathematical theory of optimal processes,
Translated from the Russian by K. N. Trirogoff; edited by L. W. Neustadt,
Interscience Publishers John Wiley & Sons, Inc. New YorkLondon, 1962.
MR
0166037 (29 #3316b)
 7.
R.
T. Rockafellar, Extension of Fenchel’s duality theorem for
convex functions, Duke Math. J. 33 (1966),
81–89. MR
0187062 (32 #4517)
 8.
R.
Tyrrell Rockafellar, Duality and stability in extremum problems
involving convex functions, Pacific J. Math. 21
(1967), 167–187. MR 0211759
(35 #2636)
 9.
R.
T. Rockafellar, Conjugate convex functions in optimal control and
the calculus of variations, J. Math. Anal. Appl. 32
(1970), 174–222. MR 0266020
(42 #929)
 10.
R.
T. Rockafellar, Existence and duality theorems for
convex problems of Bolza, Trans. Amer. Math.
Soc. 159 (1971),
1–40. MR
0282283 (43 #7995), http://dx.doi.org/10.1090/S00029947197102822830
 1.
 F. John, Extremum problems with inequalities as side conditions, Studies and Essays, Courant Anniversary Volume (K. O. Friedrichs, O. E. Neugebauer, and J. J. Stoker, editors), Wiley, New York, 1948, pp. 187204. MR 30135
 2.
 W. E. Karush, Minima of functions of several variables with inequalities as side conditions, Masters dissertation, University of Chicago, Chicago, December, 1939.
 3.
 H. W. Kuhn and A. W. Tucker, Nonlinear programming, Proc. Second Berkeley Sympos. on Mathematical Statistics and Probability (J. Neyman, editor), University of California Press, Berkeley, 1951, pp. 481492. MR 47303
 4.
 E. J. McShane, On multipliers for Lagrange problems, Amer. J. Math. 61 (1939), 809819. MR 462
 5.
 L. W. Neustadt, Optimization, a theory of necessary conditions, Princeton Univ. Press, Princeton, N. J., 1976. MR 440440
 6.
 L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze and E. F. Mishchenko, The mathematical theory of optimal processes (Translated by K. N. Trirogoff, L. W. Neustadt, editor) Wiley, New York, 1962. MR 166037
 7.
 R. T. Rockafellar, An extension of Fenchel's duality theorem for convex functions, Duke Math. J. 33 (1966), 8190. MR 187062
 8.
 R. T. Rockafellar, Duality and stability in extremum problems involving convex functions, Pacific J. Math. 21 (1967), 167187. MR 211759
 9.
 R. T. Rockafellar, Conjugate convex functions in optimal control and the calculus of variations, J. Math. Anal. Appl. 32 (1970), 174222. MR 266020
 10.
 R. T. Rockafellar, Existence and duality theorems for convex problems of Bolza, Trans. Amer. Math. Soc. 159 (1971), 140. MR 282283
Review Information
Reviewer:
Leonard D. Berkovitz
Journal:
Bull. Amer. Math. Soc. 2 (1980), 479482
DOI:
http://dx.doi.org/10.1090/S02730979198014776X
PII:
S 02730979(1980)14776X
