Solving Generalized Networks with Nonlinear Objectives

该项目的两个主要研究目标是：(1)整合网络优化和非线性规划方面的最新算法进展，以及(2)为介于这两个领域之间的一个重要问题类设计有效的求解策略。关注的焦点是具有广义圆弧(损失/收益)和不可分离的凸目标的非线性网络。该模型能够描述许多重要的现实问题，包括发电、随机网络、空中交通路线、金融现金流、矩阵平衡和分层抽样。这些和其他算法策略应该提供足够的效率，以便在合理的计算机预算内可以解决更大的问题(2000个节点，40,000条弧线)。与以前的算法--截断牛顿算法和单纯分解算法--进行了比较，并在一系列真实世界的例子上进行了比较。此外，逐次QP算法专门用于求解具有非线性乘子的网络问题。

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.