Fundamental Science

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

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  • School of Science, Shenyang Aerospace University, Shenyang 110136

Received date: 2013-07-02

Abstract

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 l1 and l norms.

Cite this article

HAN Ning, LIU Yong-jin, LIU Mei-jiao . Computation of the metric projection over a class of closed convex cones[J]. Journal of Shenyang Aerospace University, 2013 , 30(5) : 88 -91 . DOI: 10.3969/j.issn.2095-1248.2013.05.018

References

[1]SUN D F.The strong second order sufficient condition and constraint nondegeneracy in nonlinear semidefinite programming and their implications[J].Mathematics of Operations Research, 2006, 31(4):761-776.
[2]WANG Y, ZHANG L W.Properties of equation reformulation of the Karush-Kuhn-Tucker condition for nonlinear second order cone optimization problems[J].Mathematical Methods of Operations Research, 2009, 70(2):195-218.
[3]HELGASON R, KENNINGTON J, LALL H.A polynomially bounded algorithm for a singly constrained quadratic program[J].Mathematical Programming, 1980, 18(1):338-343.
[4]PARDALOS P M, KOVOOR N.An algorithm for a singly constrained class of quadratic programs subject to upper and lower bounds[J].Mathematical Programming, 1990, 46(1-3):321-328.
[5]BROOKS J, DULA J H, BOONE E L.A pure L1-norm principal component analysis[J].Computational Statistics and Data Analysis, 2013(61):83-98.
[6]WU B, DING C, SUN D F, et al.On the Moreau-Yoshida regularization of the vector k-norm related function[DB/OL].http://www.math.nus.edu.sg/~matsundf/k-norm-08 Mar 11.pdf, 下载时间:2012-06-27.
[7]王英楠, 修乃华.几类非对称矩阵锥分析 [D].北京:北京交通大学, 2011.
[8]DING C, SUN D F, TOH K-C.An introduction to a class of matrix cone programming[DB/OL].http://www.math.nus.edu.sg/~matsundf/Introduction Mcp-Sep-15.pdf, 下载时间:2012-06-28.
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