A Catalyst acceleration for coordinate descent applied to aircraft assembly simulation

Abstract Although a variety of QP solvers are applicable to quadratic programming problems arising in aircraft assembly simulation, computation time -- for both problem-specific and general-purpose solvers -- remains a significant bottleneck. Addressing this issue, the paper considers a first-order solver based on Catalyst acceleration for coordinate descent. The Catalyst acceleration algorithm and the formulation of a coordinate-descent inner solver for the targeted proximal subproblems in the context of assembly simulation are stated. An analysis of the coordinate descent convergence and complexity is conducted. The invariance of coordinate descent with respect to diagonal scaling has led to a modification of Nesterov's a priori functional gap. A new approach to step control for Catalyst acceleration based on online zero-order minimization of the overall Catalyst complexity is developed. Numerical experiments with medium-sized and large-sized assembly models of real aircraft joints are conducted and presented in comparison to other types of QP solvers. Quadratic scalability with respect to problem dimension on a series of fuselage panel assembly models with an increasing number of stringers is experimentally shown. The results of solving contact problems within a full-scale fuselage section mating model confirm the high performance of the presented solver for large-sized contact problems with a bounded condition number.