Variable metric bundle methods: From conceptual to implementable forms

To minimize a convex function, we combine Moreau–Yosida regularizations, quasi-Newton matrices and bundling mechanisms. First we develop conceptual forms using ‘reversal’ quasi-Newton formulae and we state their global and local convergence. Then, to produce implementable versions, we incorporate a bundle strategy together with a ‘curve-search’. No convergence results are given for the implementable versions; however, some numerical illustrations show their good behaviour even for large-scale problems.