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Introduction to optimization. (Vvedenie v optimizatsiyu). (Russian) Zbl 0652.49002

Moskva: Nauka. 384 p. R. 2.40 (1983).
This extensive tome is a demanding text and handbook on the theory and practice of optimization in finite-dimensional spaces, and is well worth reading. It is written primarily for engineers, economists, statisticians and computer scientists, but can also be recommended for students of mathematics. Besides providing fundamental concepts, theorems, optimality criteria and methods, the author also gives proofs and detailed commentaries. Explanatory illustrations, hints regarding applications and stimulating exercises (without solution) complete the teaching effectiveness of this book, which - except for graph-theoretical aspects - really does not hold back anything that has happened during the last 30 years in the main trends of optimization with regard to procedures; the book is complemented by an extensive bibliography and subject index. The reviewer has one critical comment: the concept of the first variation should not be confused (if only out of regard for Euler and Lagrange) with that of the directional derivative.

MSC:

49-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to calculus of variations and optimal control
49J10 Existence theories for free problems in two or more independent variables
49K10 Optimality conditions for free problems in two or more independent variables
49J05 Existence theories for free problems in one independent variable
49K05 Optimality conditions for free problems in one independent variable
90-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to operations research and mathematical programming
90C30 Nonlinear programming