Solving Nonlinear Financial Planning ProblemsWith 109 Decision Variables On MassivelyParallel Architectures
Solving Nonlinear Financial Planning ProblemsWith 109 Decision Variables On MassivelyParallel Architectures
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使用大规模并行架构上的 109 个决策变量解决非线性财务规划问题
DOI：
10.2495/cf060101
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
A. Grothey
中科院分区：
文献类型：
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作者：
J. Gondzio;A. Grothey
多阶段随机规划是处理优化模型中的不确定性的流行技术。然而，充分捕获底层分布的需要会导致通常超出通用求解器范围的大问题。存在专用方法，但对其适用的模型类型有限制。并行性使这些问题可能易于处理，但在当今的通用求解器中通常没有被利用。我们将结构利用并行原对偶内点求解器应用于线性、二次和非线性规划问题。求解器有效地利用了这些模型的结构。它的设计依赖于面向对象的编程原理，将问题的每个子结构视为带有其自己专用的线性代数例程的对象。我们证明了它在各种财务规划问题上的有效性，从而产生了线性、二次或非线性公式。此外，粗粒度并行性以一种通用的方式被利用，这种方式在从以太网连接的 PC 到大规模并行计算机的任何并行架构上都很有效。在峰值性能为 6.2 TFlops 的 1280 处理器机器上，我们可以解决超过 10 个决策变量的二次财务规划问题。
Multistage stochastic programming is a popular technique to deal with uncertainty in optimization models. However, the need to adequately capture the underlying distributions leads to large problems that are usually beyond the scope of general purpose solvers. Dedicated methods exist but pose restrictions on the type of model they can be applied to. Parallelism makes these problems potentially tractable, but is generally not exploited in today’s general purpose solvers. We apply a structure-exploiting parallel primal-dual interior-point solver for linear, quadratic and nonlinear programming problems. The solver efficiently exploits the structure of these models. Its design relies on object-oriented programming principles, treating each substructure of the problem as an object carrying its own dedicated linear algebra routines.We demonstrate its effectiveness on a wide range of financial planning problems, resulting in linear, quadratic or non-linear formulations. Also coarse grain parallelism is exploited in a generic way that is efficient on any parallel architecture from ethernet linked PCs to massively parallel computers. On a 1280-processormachine with a peak performance of 6.2 TFlops we can solve a quadratic financial planning problem exceeding 10 decision variables.