This user-friendly text offers a thorough introduction to the part of optimization theory that lies between approximation theory and mathematical programming, both linear and nonlinear. Written by two distinguished mathematicians, the expert treatment covers the essentials, incorporating important background materials, examples, and extensive notes. Geared toward advanced undergraduate and graduate students of mathematical programming, the text explores best approximation by algebraic polynomials in both discrete and continuous cases; the discrete problem, with and without constraints; the generalized problem of nonlinear programming; and the continuous minimax problem. Several appendixes discuss algebraic interpolation, convex sets and functions, and other topics. 1974 edition.