Modified lagrangians and monotone maps in optimization - Gol'shteĭn, E. G. (Evgeniĭ Grigor'evich) (Wiley-Interscience series in discrete mathematics and optimization, 1996)
This translation of the important Russian text covers the theory and computational methods of modified Lagrangian functions (MLFs)--a new branch of mathematical programming used to solve optimization problems. Providing a thorough analysis for both traditional convex programming and monotone maps, the book shows the advantages of MLFs over classical Lagrangian functions in such practical applications as numerical algorithms, economic modeling, de-composition, and nonconvex local constrained optimization. Following an overview of convex analysis, the authors introduce MLFs through the more general formalism of weak modified Lagrangian functions (WMLFs). They use the two concepts to develop a theory of duality supported by examples of elementary economic models. Also examined are the benefits of MLFs in the application of dual methods in linear programming and in problems with inconsistent constraints.