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****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****4.**E. J. McShane,*On multipliers for Lagrange problems*, Amer. J. Math.**61**(1939), 809–819. MR**0000462**, https://doi.org/10.2307/2371626**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****6.**L. S. Pontrjagin, V. G. Boltjanskiĭ, R. V. Gamkrelidze, and E. F. Miščenko,*\cyr Matematicheskaya teoriya optimal′nykh protsessov*, Gosudarstv. Izdat. Fiz.-Mat. Lit., Moscow, 1961 (Russian). MR**0166036**

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 York-London, 1962. MR**0166037**

L. S. Pontrjagin, V. G. Boltjanskij, R. V. Gamkrelidze, and E. F. Misčenko,*Mathematische Theorie optimaler Prozesse*, R. Oldenbourg, Munich-Vienna, 1964 (German). MR**0166038****7.**R. T. Rockafellar,*Extension of Fenchel’s duality theorem for convex functions*, Duke Math. J.**33**(1966), 81–89. MR**0187062****8.**R. Tyrrell Rockafellar,*Duality and stability in extremum problems involving convex functions*, Pacific J. Math.**21**(1967), 167–187. MR**0211759****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**, https://doi.org/10.1016/0022-247X(70)90324-0**10.**R. T. Rockafellar,*Existence and duality theorems for convex problems of Bolza*, Trans. Amer. Math. Soc.**159**(1971), 1–40. MR**0282283**, https://doi.org/10.1090/S0002-9947-1971-0282283-0

Review Information:

Reviewer: Leonard D. Berkovitz

Journal: Bull. Amer. Math. Soc.

**2**(1980), 479-482

DOI: https://doi.org/10.1090/S0273-0979-1980-14776-X