Solving Generalized Networks with Nonlinear Objectives

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The two primary research objectives of this project are: (1) to integrate recent algorithmic advances in network optimization and nonlinear programming, and (2) to design efficient solution strategies for an important problem-class falling between these two areas. The focus of attention is on nonlinear networks with generalized arcs (losses/gains) and non-separable convex objectives. This model is capable of representing numerous significant real-world problems, including electrical power generation, stochastic networks, air-traffic routing, financial cashflow, matrix balancing and stratified sampling. These and other algorithm strategies should provide sufficient efficiencies so that larger problems ( 2000 nodes, 40,000 arcs) will be solvable in a reasonable computer budget. A comparison with previous algorithms, truncated-Newton and simplicial decomposition, is being conducted on a battery of real-world examples. In addition, the successive QP algorithm is specialized for solving network problems with nonlinear multipliers.