Linear Network Optimization: Algorithms and Codes
Large-scale optimization is becoming increasingly important for students and professionals in electrical and industrial engineering, computer science, management science and operations research, and applied mathematics.
Linear Network Optimization presents a thorough treatment of classical approaches to network problems such as shortest path, max-flow, assignment, transportation, and minimum cost flow problems. It is the first text to clearly explain important recent algorithms such as auction and relaxation, proposed by the author and others for the solution of these problems. Its coverage of both theory and implementations make it particularly useful as a text for a graduate-level course on network optimization as well as a practical guide to state-of-the-art codes in the field.
Bertsekas focuses on the algorithms that have proved successful in practice and provides FORTRAN codes that implement them. The presentation is clear, mathematically rigorous, and economical. Many illustrations, examples, and exercises are included in the text.
Dimitri P. Bertsekas is Professor of Electrical Engineering and Computer Science at MIT.
Contents: Introduction. Simplex Methods. Dual Ascent Methods. Auction Algorithms. Performance and Comparisons. Appendixes.
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algorithm terminates arc flow arc i,j arc lengths artificial arcs assignment problem augmenting path backward arcs Bertsekas binary heap candidate list COMMON computation CONTINUE corresponding cost flow problem destination e-CS condition e-relaxation e-scaling END IF END end node ENDIF Exercise feasible assignment feasible flow vector finite number flow bounds Ford-Fulkerson algorithm forward algorithm forward/reverse go to Step GOTO graph implementation in-arc initial price INTEGER label setting method max-flow problem minimum cost flow multiassignment negative cost Network Flow nonnegative number of arcs number of iterations number of nodes object optimal solution out-arc pair x,p person price rise price vector primal cost primal-dual method problem data problem is infeasible Programming Prop Proposition relaxation method reverse auction satisfying e-CS Section shortest distance shortest path problem Show simple cycle simple path simplex method starting SUPERSOURCE SURPI surplus terminal node unassigned unblocked path zero
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