A hybrid algorithm for the two-trust-region subproblem

TL;DR

This paper introduces a hybrid algorithm combining trust-region methods and ADMM to efficiently solve the two-trust-region subproblem, demonstrating improved performance over existing algorithms on various test problems.

Contribution

A novel hybrid algorithm integrating trust-region minimization techniques with ADMM for solving TTRS, with proven convergence properties.

Findings

The proposed algorithm converges to first-order stationary points under certain conditions.

It outperforms Sakaue et al.'s algorithm and Snopt in computational tests.

The method effectively handles large and complex TTRS instances.

Abstract

Two-trust-region subproblem (TTRS), which is the minimization of a general quadratic function over the intersection of two full-dimensional ellipsoids, has been the subject of several recent research. In this paper, to solve TTRS, a hybrid of efficient algorithms for finding global and local-nonglobal minimizers of trust-region subproblem and the alternating direction method of multipliers (ADMM) is proposed. The convergence of the ADMM steps to the first order stationary condition is proved under certain conditions. On several classes of test problems, we compare the new algorithm with the recent algorithm of Sakaue et. al's \cite{SakaueNakat:16} and Snopt software.