A new optimization algorithm, which can efficiently solve large-scale constrained non-linear optimization problems and leverage parallel computing, is designed and studied. The new algorithm, referred to herein as LASO or LArge Scale Optimizer, combines the best features of various algorithms to create a computationally efficient algorithm with strong convergence properties. Numerous algorithms were implemented and tested in its creation. Bound-constrained, step-size, and constrained algorithms have been designed that push the state-of-the-art. Along the way, five novel discoveries have been made: (1) a more efficient and robust method for obtaining second order Lagrange multiplier updates in Augmented Lagrangian algorithms, (2) a method for directly identifying the active constraint set at each iteration, (3) a simplified formulation of the penalty parameter sub-problem, (4) an efficient backtracking line-search procedure, (5) a novel hybrid line-search trust-region step-size calculation method. The broader impact of these contributions is that, for the first time, an Augmented Lagrangian algorithm is made to be competitive with state-of-the-art Sequential Quadratic Programming and Interior Point algorithms.
The present work concludes by showing the applicability of the LASO algorithm to simulate one step of digital human walking and to accelerate the optimization process using parallel computing.