A semi-smooth Newton method for a special piecewise linear system with application to positively constrained convex quadratic programming
Provides a theoretically grounded and efficient solver for large-scale convex quadratic programs with positivity constraints, a common problem in optimization.
The paper studies a semi-smooth Newton method for a piecewise linear system, proving linear convergence and boundedness of the sequence. Applied to positively constrained convex quadratic programming, the method achieves accurate solutions for large-scale problems in few iterations.
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.