A semi-smooth Newton method for a special piecewise linear system with application to positively constrained convex quadratic programming

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:301

Article

Barrios, J. G.¹  Bello Cruz, J. Y.¹  Ferreira, O. P.¹  Nemeth, S. Z.² 

[1] IME UFG, Ave Esperana S-N,Campus Samambaia, BR-74690900 Goiania, Go, Brazil

[2] Univ Birmingham, Sch Math, Watson Bldg, Birmingham B15 2TT, W Midlands, England

关键词: Piecewise linear system;    Quadratic programming;    Convex set;    Convex cone;    Semi-smooth Newton method;   

DOI  :  10.1016/j.cam.2016.01.040

来源: Elsevier

【 摘 要 】

In this paper a special piecewise linear system is studied. It is shown that, under a mild assumption, the semi-smooth Newton method applied to this system is well defined and the method generates a sequence that converges linearly to a solution. Besides, we also show that the generated sequence is bounded, for any starting point, and a formula for any accumulation point of this sequence is presented. As an application, we study the convex quadratic programming problem under positive constraints. The numerical results suggest that the semi-smooth Newton method achieves accurate solutions to large scale problems in few iterations. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free