On convergence of the block Lanczos method for the CDT subproblem

In [L.Q. Song and W.H. Yang, J. Comput. Math., 37 (2019), pp. 240–260], a block Lanczos method for solving large-scale Celis-Dennis-Tapia (CDT) subproblem was proposed. It is an orthogonal projection method that reduces a large-scale CDT subproblem to a small-sized problem for easier solving. Moreover, Song and Yang also provided error bounds for the optimal value and for the optimal solution. However, no convergence analysis for this method was presented by them. In this paper, we develop some upper bounds for the convergence of approximate optimal function objective values, approximate optimal solutions, the KKT error, and approximate Lagrange multipliers.