An introduction to structured modeling
Management Science
Nonlinear programming on generalized networks
ACM Transactions on Mathematical Software (TOMS)
Finding embedded network rows in linear programs. I. Extraction heuristics
Management Science
Modeling languages versus matrix generators for linear programming
ACM Transactions on Mathematical Software (TOMS)
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Research in network optimization has reached the stage where large-scale problems-linear or non-linear, pure or generalized-are solved very efficiently with minimal computing resources. Representing such problems for solution on the computer, however, remains a rather cumbersome task. Taking advantage of developments in high-level modeling languages, we design and implement integrated systems to facilitate the representation and solution of network problems. Such systems integrate the flexibility and robustness of modeling languages with the efficiency of network optimizers.We describe two alternative modes for this integration, which can be achieved for linear and nonlinear problems alike. The use of the resulting systems is demonstrated with the solution of large-scale problems from diverse applications and with the implementation of network decomposition algorithms.