Optimization theory / by Hubertus Th. Jongen, Klaus Meer, Eberhard Triesch

Includes bibliographical references (pages 427-443) and indexes

Optimality criteria on simple regions -- Constraints, lagrange function, optimality -- Parametric aspects, semi-infinite optimization -- Convex functions, duality, separation theorem -- Linear inequalities, constraint qualifications -- Linear programming : the simplex method -- The ellipsoid method -- Karmarkar's method for linear programming -- Order of convergence, steepest descent -- Conjugate direction, variable metric -- Penalty-, barrier-, multiplier-, IP-methods -- Search methods without derivatives -- One-dimensional minimization -- Graphs and networks -- Flows in networks -- Applications of the max-flow min-cut theorem -- Integer linear programming -- Computability; the turing machine -- Complexity theory -- Reducibility and NP-completeness -- Some NP-completeness results -- The random access machine -- Complexity theory over the real numbers -- Approximating NP-hard problems -- Approximation algorithms for TSP -- Approximation algorithms for bin packing -- A FPTAS for knapsack -- Miscellaneous

"Optimization Theory is becoming a more and more important mathematical as well as interdisciplinary area, especially in the interplay between mathematics and many other sciences like computer science, physics, engineering, operations research, etc." "This volume gives a comprehensive introduction into the theory of (deterministic) optimization on an advanced undergraduate and graduate level." "One main feature is the treatment of both continuous and discrete optimization at the same place. This allows the study of the problems from different points of view, supporting a better understanding of the entire field."

"Audience: The book can be adapted well as an introductory textbook into optimization theory on a basis of a two semester course: however, each of its parts can also be taught separately. Many exercise are included to increase the readers' understanding."--Jacket