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Approximate invariant subspaces and quasi-newton optimization methods

机译:近似不变子空间和拟牛顿优化方法

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New approximate secant equations are shown to result from the knowledge of (problem dependent) invariant subspace information, which in turn suggests improvements in quasi-Newton methods for unconstrained minimization. A new limited-memory Broyden-Fletcher-Goldfarb-Shanno using approximate secant equations is then derived and its encouraging behaviour illustrated on a small collection of multilevel optimization examples. The smoothing properties of this algorithm are considered next, and automatic generation of approximate eigenvalue information demonstrated. The use of this information for improving algorithmic performance is finally investigated on the same multilevel examples.View full textDownload full textKeywordslarge-scale optimization, quasi-Newton methods, limited memory algorithms, discretized problems, multilevel optimizationRelated var addthis_config = { ui_cobrand: "Taylor & Francis Online", services_compact: "citeulike,netvibes,twitter,technorati,delicious,linkedin,facebook,stumbleupon,digg,google,more", pubid: "ra-4dff56cd6bb1830b" }; Add to shortlist Link Permalink http://dx.doi.org/10.1080/10556780902992746
机译:新的近似割线方程表明是由(依赖于问题的)不变子空间信息的知识产生的,这反过来又暗示了拟牛顿方法的改进,以实现无约束最小化。然后,推导了使用近似割线方程的新的有限内存Broyden-Fletcher-Goldfarb-Shanno,并在少量多级优化示例中说明了其令人鼓舞的行为。接下来考虑该算法的平滑特性,并演示自动生成近似特征值信息。最终,在相同的多级示例上研究了如何使用这些信息来提高算法性能。查看全文下载全文关键字大规模优化,拟牛顿法,有限内存算法,离散化问题,多级优化相关var addthis_config = {ui_cobrand:“ Taylor&弗朗西斯在线”,services_compact:“ citeulike,netvibes,twitter,technorati,美味,linkedin,facebook,stumbleupon,digg,google,更多”,发布号:“ ra-4dff56cd6bb1830b”};添加到候选列表链接永久链接http://dx.doi.org/10.1080/10556780902992746

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