• Bundle Methods
• Convex nondifferentiable optimization
• Unit Commitment
• Lagrangian Relaxation
• Energy Optimization

Efficiently optimizing complex nondifferentiable functions, composed by a sum of a large number of terms the computation of each of which may be costly, is a crucial task in many applications such as energy optimization. The use of HPC architectures may be required to obtain appropriate performances, but the existing parallelisation approaches, mostly based on the standard master-slave paradigm, do not scale well to a large number of cores. This has justified the recent surge of interest in asynchronous approaches that may allow a higher scalability. We propose a very general asynchronous approach that exploits the availability of multiple resources not only for the "oracles" (black-box) that compute the function components, but also for the solution of multiple master problems, ran in parallel, to provide a stream of potential iterates for the oracles. Each of the master problems is in principle a separate algorithm, typically one of the many variants of bundle methods with some specific setting for its (numerous) algorithmic parameters, which would converge towards an (approximate) optimal solution if ran in isolation. We add to the mix a principal entity managing their interaction, thereby obtaining an "ensemble (asynchronous) bundle" approach, and we examine how different underlying algorithms can withstand interventions of the principal entity (such as information sharing, stability centre updates, and "near points" substitutions) aimed at fostering harmonious collaboration between them towards the goal of more efficiently solving the problem while retaining the good convergence properties that they originally had. We show how our approach can work with a very wide selection of the practical nondifferentiable optimization algorithms proposed in the literature. We test the performance of our ensemble bundle approach on a significant industrial application, i.e., Lagrangian relaxations of the Unit Commitment problem.