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Nonlinear programming: sequential unconstrained minimization techniques. Unabridged, corrected republication. (English) Zbl 0713.90043
Classics in Applied Mathematics, 4. Philadelphia, PA: SIAM, Society for Industrial and Applied Mathematics. xvi, 210 p. $ 26.50 (1990).
This is an unabridged, corrected republication of the book which was first published more than twenty years ago and has long been out of print. A review of the 1968 first edition was written by this reviewer (cf. Zbl 0193.188). Since then, the development of the whole area of mathematical programming has shown all of the values of the methods and techniques presented in the book. Several questions which started being studied in the book, like: relationship of penalty function theory to duality theory, use of directions of nonpositive curvature to modify Newton’s method when the Hessian is indefinite, sensitivity analysis, etc... have developed into important areas of research during the last two decades. The most unexpected fact is that a number of techniques such as interior point unconstrained minimization, the use of logarithmic penalty functions (i.e. “barrier functions”, as they are now commonly called), trajectory analysis,..., which were discussed in the book for the primary purpose of nonlinear programming have now become of central interest even in linear programming in connection with Karamarkar’s algorithm and related methods (affine scaling, path following, primal- dual methods).
Therefore, the reedition of the book in the series “Classics in Applied Mathematics” seems to be very opportune, and should be welcome by anybody involved with mathematical programming theory or computations. The revision differs from the original editin only in some corrections to make the proofs of certain theorems more accurate.
Reviewer: H.Tuy

90C30 Nonlinear programming
90-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to operations research and mathematical programming
90C31 Sensitivity, stability, parametric optimization
49M30 Other numerical methods in calculus of variations (MSC2010)