Limited-memory Common-directions Method for Large-scale Optimization: Convergence, Parallelization, and Distributed Optimization

In this paper, we present a limited-memory common-directions method for smooth optimization that interpolates between first- and second- order methods. At each iteration, a subspace of a limited dimension size is constructed using first-order information from previous iterations, and an ef- ficient Newton method is deployed to find an approximate minimizer within this subspace. With … Read more

Convergence properties of a second order augmented Lagrangian method for mathematical programs with complementarity constraints

Mathematical Programs with Complementarity Constraints (MPCCs) are difficult optimization problems that do not satisfy the majority of the usual constraint qualifications (CQs) for standard nonlinear optimization. Despite this fact, classical methods behaves well when applied to MPCCs. Recently, Izmailov, Solodov and Uskov proved that first order augmented Lagrangian methods, under a natural adaption of the … Read more