Mathematical Programming with Data Perturbations

ISBN-13: 9780824700591 / Angielski / Miękka / 1997 / 464 str.

Anthony V. Fiacco;Fiacco; Anthony V. Fiacco

Opis

Presents research contributions and tutorial expositions on current methodologies for sensitivity, stability and approximation analyses of mathematical programming and related problem structures involving parameters. The text features up-to-date findings on important topics, covering such areas as the effect of perturbations on the performance of algorithms, approximation techniques for optimal control problems, and global error bounds for convex inequalities.

Spis treści

Discretization and mesh-independent of Newton's method for generalized differentiability of optimal solutions in non-linear parametric optimization; characterisations of Lipschitzian stability in nonlinear programming; on second order sufficient conditions for structured nonlinear programs in infinite-dimensional function spaces; algorithmic stability analysis for certain trust region methods; a note on using linear knowledge to solve efficiency linear programs specified with approximate data; on the role of the Mangasarian-Fromovitz constraint qualification for penalty-, exact penalty-, and Lagrange multiplier methods; Hoffman's error bound for systems of convex functions and applications to nonlinear optimization; on well-posedness and stability analysis optimization; convergence of approximations to nonlinear optimal control problems; a perturbation-based duality classification for max-flow min-cut problems of Strang and Iri; central and peripheral results in the study of marginal and performance functions; topological stability of feasible sets in semi-infinite optimization - a tutorial; solution existence for infinite quadratic programming; sensitivity analysis of nonlinear programming problems via minimax functions; parametric linear complementary problems; sufficient conditions for weak sharp minima of order two and directional derivatives of the value function.

O autorze

ANTHONY V. FIACCO is Professor Emeritus of Operations Research and Applied Science at George Washington University, Washington, D.C. From 1960 to 1971, Dr. Fiacco was an Operations Analyst for the Research Analysis Corporation in McLean, Virginia, where he was Project Chairman of a study that pioneered several breakthroughs in nonlinear programming (NLP) methodology. He is the author or coauthor of numerous papers on NLP theory and applications, the coauthor with Garth P. McCormick in 1968 of a Lanchester prize-winning book on barrier and penalty function methodology, and the editor of several books, including Mathematical Programming with Data Perturbations I and II (both titles, Marcel Dekker, Inc.). A prominent contributor to the development of computable methods for sensitivity and stability analysis, Dr. Fiacco received the Ph.D. degree 1967 in applied mathematics from Northwestern University, Evanston, Illinois. Since 1979, he has organized, at the George Washington University, the only annual conference completely devoted to sensitivity and stability issues.