一类闭凸锥上投影算子的计算

Computation of the metric projection over a class of closed convex cones

在凸优化问题的求解过程中,通常会转换为求解优化问题的KKT条件,而在求解其KKT条件时往往会涉及到某个闭凸锥上投影算子的计算。提出并详细阐述了某类凸锥上投影算子显示表达式的计算方法,数值结果表明了算法的有效性。研究结果为加权l1范数、加权l∞范数上图锥投影算子方向导数、广义微分的研究提供了一定的理论基础。

Solution to convex optimization problems is usually converted to solve the KKT conditions, to which the computation of the metric projections over some convex cones is often crucial. This paper proposes an algorithm to compute the explicit formula of the metric projection over a class of closed convex cones. The reported numerical results show that our algorithm is effective. The results obtained in this paper can serve as the theoretic foundation to study the directional derivative and the generalized differential of the metric projections over the epigraph of the weighted lI and l∞ norms.