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The book describes methods and algorithms for the numerical solution of problems involving the determination of extrema of functions and functionals encountered in mathematical programming, economics, optimal control theory, and other fields of science and practice. Special attention is paid to algorithms with a fast rate of convergence and those implementable on computers. Methods for unconstrained and constrained minimisation of functions of independent variables are discussed. The book will be useful to specialists in mathematical programming, computational mathematics, and optimal control theory, as well as a broad audience of students and engineers who, in their practical work, need to solve problems related to function minimisation. Translated from the Russian by V. Zhitomirsky, D.Sc. (Eng.)