Book Review
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MathSciNet review:
1566960
Full text of review:
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Book Information:
Author:
Magnus R. Hestenes
Title:
Optimization theory, the finite dimensional case
Additional book information:
John Wiley and Sons, New York, London, Sydney, Toronto, 1975, xiii + 447 pp., $24.95.
K. J. Arrow, F. J. Gould, and S. M. Howe, A general saddle point result for constrained optimization, Math. Programming 5 (1973), 225–234. MR 329641, DOI 10.1007/BF01580123
Kenneth J. Arrow, Leonid Hurwicz, and Hirofumi Uzawa, Studies in linear and non-linear programming, Stanford Mathematical Studies in the Social Sciences, II, Stanford University Press, Stanford, Calif., 1958. With contributions by H. B. Chenery, S. M. Johnson, S. Karlin, T. Marschak, R. M. Solow. MR 0108399
R. J. Duffin, Linearizing geometric programs, SIAM Rev. 12 (1970), 211–227. MR 286493, DOI 10.1137/1012043
Richard J. Duffin, Elmor L. Peterson, and Clarence Zener, Geometric programming: Theory and application, John Wiley & Sons, Inc., New York-London-Sydney, 1967. MR 0214374
B. Curtis Eaves and Herbert Scarf, The solution of systems of piecewise linear equations, Math. Oper. Res. 1 (1976), no. 1, 1–27. MR 445792, DOI 10.1287/moor.1.1.1
Hugh Everett III, Generalized Lagrange multiplier method for solving problems of optimum allocation of resources, Operations Res. 11 (1963), 399–417. MR 152360, DOI 10.1287/opre.11.3.399
Anthony V. Fiacco and Garth P. McCormick, Nonlinear programming: Sequential unconstrained minimization techniques, John Wiley & Sons, Inc., New York-London-Sydney, 1968. MR 0243831
F. J. Gould, Extensions of Lagrange multipliers in nonlinear programming, SIAM J. Appl. Math. 17 (1969), 1280–1297. MR 263426, DOI 10.1137/0117120
F. J. Gould and Jon W. Tolle, A necessary and sufficient qualification for constrained optimization, SIAM J. Appl. Math. 20 (1971), 164–172. MR 303954, DOI 10.1137/0120021
F. J. Gould and J. W. Tolle, A unified approach to complementarity in optimization, Discrete Math. 7 (1974), 225–271. MR 334926, DOI 10.1016/0012-365X(74)90037-5
P. C. Haarhoff and J. D. Buys, A new method for the optimization of a nonlinear function subject to nonlinear constraints, Comput. J. 13 (1970), 178–184. MR 277095, DOI 10.1093/comjnl/13.2.178
Magnus R. Hestenes, Multiplier and gradient methods, Computing Methods in Optimization Problems, 2 (Proc. Conf., San Remo, 1968) Academic Press, New York, 1969, pp. 143–163. MR 0262903
Magnus R. Hestenes, Multiplier and gradient methods, J. Optim. Theory Appl. 4 (1969), 303–320. MR 271809, DOI 10.1007/BF00927673
T. L. Magnanti, Fenchel and Lagrange duality are equivalent, Math. Programming 7 (1974), 253–258. MR 368771, DOI 10.1007/BF01585523
O. L. Mangasarian, Unconstrained Lagrangians in nonlinear programming, SIAM J. Control 13 (1975), 772–791. MR 0373626
16. O. L. Mangasarian, Nonlinear programming theory and computation, Handbook of Operations Research, Chapter 6 (Elmaghraby and Moder, editors), van Nostrand Reinhold, New York, 1973.
E. Blum and W. Oettli, Mathematische Optimierung, Ökonometrie und Unternehmensforschung, Band XX, Springer-Verlag, Berlin-New York, 1975. Grundlagen und Verfahren; Mit einem Anhang “Bibliographie zur Nichtlinearer Programmierung”. MR 0418921
J. M. Ortega and W. C. Rheinboldt, Iterative solution of nonlinear equations in several variables, Academic Press, New York-London, 1970. MR 0273810
M. J. D. Powell, A method for nonlinear constraints in minimization problems, Optimization (Sympos., Univ. Keele, Keele, 1968) Academic Press, London, 1969, pp. 283–298. MR 0272403
M. J. D. Powell, A view of unconstrained optimization, Optimization in action (Proc. Conf., Univ. Bristol, Bristol, 1975) Academic Press, London, 1976, pp. 117–152. MR 0431680
R. Tyrrell Rockafellar, Convex analysis, Princeton Mathematical Series, No. 28, Princeton University Press, Princeton, N.J., 1970. MR 0274683
R. Tyrrell Rockafellar, Augmented Lagrange multiplier functions and duality in nonconvex programming, SIAM J. Control 12 (1974), 268–285. Collection of articles dedicated to the memory of Lucien W. Neustadt. MR 0384163
R. Tyrrell Rockafellar, A dual approach to solving nonlinear programming problems by unconstrained optimization, Math. Programming 5 (1973), 354–373. MR 371416, DOI 10.1007/BF01580138
Josef Stoer and Christoph Witzgall, Convexity and optimization in finite dimensions. I, Die Grundlehren der mathematischen Wissenschaften, Band 163, Springer-Verlag, New York-Berlin, 1970. MR 0286498
Philip Wolfe, A method of conjugate subgradients for minimizing nondifferentiable functions, Math. Programming Stud. 3 (1975), 145–173. Nondifferentiable optimization. MR 448896, DOI 10.1007/bfb0120703
- 1.
- K. J. Arrow, F. J. Gould and S. M. Howe, A general saddle point result for constrained optimization, Math. Programming 5 (1973), 225-234. MR 48 #7983. MR 0329641
- 2.
- K. J. Arrow and R. M. Solow, Gradient methods for constrained maxima with weakened assumptions, Studies in Linear and Nonlinear Programming (K. J. Arrow, L. Hurwicz and H. Uzawa, editors), vol. II, Stanford Univ. Press, Stanford, Calif., 1958, pp. 166-176. MR 21 #7115. MR 108399
- 3.
- R. J. Duffin, Linearizing geometric programs, SIAM Rev. 12 (1970), 211-227. MR 44 #3702. MR 286493
- 4.
- R. J. Duffin, E. L. Peterson and C. Zener, Geometric programming: Theory and application, Wiley, New York and London, 1967. MR 35 #5225. MR 214374
- 5.
- B. C. Eaves and H. Scarf, The solution of systems of piecewise linear equations, Mathematics of Operations Research 1 (1976), 1-27. MR 445792
- 6.
- H. Everett III, Generalized Lagrange multiplier method for solving problems of optimum allocation of resources, Operations Res. 11 (1963), 399-417. MR 27 #2340. MR 152360
- 7.
- A. V. Fiacco and G. P. McCormick, Nonlinear programming: Sequential unconstrained minimization techniques, Wiley, New York and London, 1968. MR 39 #5152. MR 243831
- 8.
- F. J. Gould, Extensions of Lagrange multipliers in nonlinear programming, SIAM J. Appl. Math. 17 (1969), 1280-1297. MR 41 #8031. MR 263426
- 9.
- F. J. Gould and J. W. Tolle, A necessary and sufficient qualification for constrained optimization, SIAM J. Appl. Math. 20 (1971), 164-172. MR 46 #3090. MR 303954
- 10.
- F. J. Gould and J. W. Tolle, A unified approach to complementarity in optimization, Report 7312, Graduate School of Business, Univ. of Chicago, February 1973. MR 334926
- 11.
- P. C. Haarhoff and J. D. Buys, A method for the optimization of a nonlinear function subject to nonlinear constraints, Comput. J. 13 (1970), 178-184. MR 43 #2832. MR 277095
- 12.
- M. R. Hestenes, Multiplier and gradient methods, Computing Methods in Optimization Problems, Vol. 2 (Proc. Conf., San Remo, 1968), Academic Press, New York, 1969, pp. 143-163. MR 41 #7508. MR 262903
- 13.
- M. R. Hestenes, Multiplier and gradient methods, J. Optimization Theory Appl. 4 (1969), 303-320. MR 42 #6690. MR 271809
- 14.
- T. L. Magnanti, Fenchel and Lagrange duality are equivalent, Math. Programming 7 (1974), 253-258. MR 51 #5012. MR 368771
- 15.
- O. L. Mangasarian, Unconstrained Lagrangians in nonlinear programming, SIAM J. Control 13 (1975), 772-791. MR 373626
- 16.
- O. L. Mangasarian, Nonlinear programming theory and computation, Handbook of Operations Research, Chapter 6 (Elmaghraby and Moder, editors), van Nostrand Reinhold, New York, 1973.
- 17.
- W. Oettli, Bibliography on nonlinear programming, Mathematische Optimierung-Grundlagen und Verfahren (Blum and Oettli, editors), Springer-Verlag, Berlin and New York, 1975. MR 418921
- 18.
- J. M. Ortega and W. C. Rheinboldt, Iterative solution of nonlinear equations in several variables, Academic Press, New York, 1970. MR 42 #8686. MR 273810
- 19.
- M. J. D. Powell, A method for nonlinear constraints in minimization problems, Optimization (Sympos., Univ. Keele, 1968) (Fletcher, editor), Academic Press, London, 1969, pp. 283-298. MR 42 #7284. MR 272403
- 20.
- M. J. D. Powell, A view of unconstrained optimization, C.S.S. 14, Computer Science and Systems Division, Atomic Energy Research Establishment, Harwell, Oxfordshire, England, January 1975. MR 431680
- 21.
- R. T. Rockafellar, Convex analysis, Princeton Univ. Press, Princeton, N. J., 1970. MR 43 #445. MR 274683
- 22.
- R. T. Rockafellar, Augmented Lagrange multiplier functions and duality in nonconvex programming, SIAM J. Control 12 (1974), 268-285. MR 384163
- 23.
- R. T. Rockafellar, A dual approach to solving nonlinear programming problems by unconstrained optimization, Math. Programming 5 (1973), 354-373. MR 51 #7634. MR 371416
- 24.
- J. Stoer and C. Witzgall, Convexity and optimization in finite dimensions. I, Springer-Verlag, Berlin and New York, 1970. MR 44 #3707. MR 286498
- 25.
- P. Wolfe, A method of conjugate subgradients for minimizing nondifferentiable functions, Mathematical Programming Study, no. 3, Nondifferentiable Optimization, North-Holland, Amsterdam, 1975, pp. 145-173. MR 448896
Review Information:
Reviewer:
Robert G. Jeroslow
Journal:
Bull. Amer. Math. Soc.
83 (1977), 324-335
DOI:
https://doi.org/10.1090/S0002-9904-1977-14252-3