A Newton Method for Convex Regression, Data Smoothing, and Quadratic Programming with Bounded Constraints
A Newton Method for Convex Regression, Data Smoothing, and Quadratic Programming with Bounded Constraints
复制标题
用于凸回归、数据平滑和有界约束二次规划的牛顿法
DOI：
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发表时间：
1993
影响因子：
3.1
通讯作者：
J. Swetits
中科院分区：
文献类型：
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作者：
Wu Li;J. Swetits
本文将分段线性方程组公式化，这些方程组是从约束凸优化问题的 Karush-Kuhn-Tucker 条件导出的，作为无约束最小化问题，其中目标函数是多元二次样条。这些公式为开发许多优化问题的有效算法提供了新的方法，例如凸回归问题、最小距离问题、对称单调线性互补问题和有界约束的凸二次规划问题。理论结果、算法及其实现的描述、数值结果以及稳定性分析均被呈现。
This paper formulates systems of piecewise linear equations, derived from the Karush–Kuhn–Tucker conditions for constrained convex optimization problems, as unconstrained minimization problems in which the objective function is a multivariate quadratic spline. Such formulations provide new ways of developing efficient algorithms for many optimization problems, such as the convex regression problem, the least-distance problem, the symmetric monotone linear complementarily problem, and the convex quadratic programming problem with bounded constraints. Theoretical results, a description of an algorithm and its implementation, and numerical results are presented along with a stability analysis.