An inexact SQP Newton method for convex SC1 minimization problems

Abstract

The convex SC1 minimization problems model many problems as special cases. One particular example is the dual problem of the least squares covariance matrix (LSCM) problems with inequality constraints. The purpose of this thesis is to introduce an efficient inexact SQP Newton method for solving the general convex SC1 minimization problems under realistic assumptions. In Chapter 2, we introduce our method and conduct a complete convergence analysis including the super-linear (quadratic) rate of convergence. Numerical results conducted in Chapter 3 show that our inexact SQP Newton method is competitive when it is applied to the LSCM problems with many lower and upper bounds constraints. We make our final conclusions in Chapter 4.