A Version of Bundle Trust Region Method with Linear Programming

We present a general version of bundle trust region method for minimizing convex functions. The trust region is constructed by generic p -norm with p∈ [1 , + ∞] . In each iteration the algorithm solves a subproblem with a constraint involving p -norm. We show the convergence of the generic bundle trust region algorithm. In implementation, the infinity norm is chosen so that a linear programming subproblem is solved in each iteration. Preliminary numerical experiments show that our algorithm performs comparably with the traditional bundle trust region method and has advantages in solving large-scale problems.