- Damped Proximal Augmented Lagrangian Methodology for weakly-Convex Points with Convex Constraints(arXiv)
Author : Hari Dahal, Wei Liu, Yangyang Xu
Abstract : We give a damped proximal augmented Lagrangian methodology (DPALM) for fixing points with a weakly-convex objective and convex linear/nonlinear constraints. Instead of taking a full stepsize, DPALM adopts a damped twin stepsize to verify the boundedness of dual iterates. We current that DPALM can produce a (near) $vareps$-KKT degree inside $O(vareps^{-2})$ outer iterations if each DPALM subproblem is solved to an accurate accuracy. In addition to, we arrange common iteration complexity of DPALM when the goal is each a regularized straightforward carry out or in a regularized compositional sort. For the earlier case, DPALM achieves the complexity of O˜(ε−2.5) to offer an ε-KKT degree by making use of an accelerated proximal gradient (APG) methodology to each DPALM subproblem. For the latter case, the complexity of DPALM is O˜(ε−3) to offer a near ε-KKT degree by using an APG to resolve a Moreau-envelope smoothed mannequin of each subproblem. Our outer iteration complexity and the final complexity each generalize present biggest ones from unconstrained or linear-constrained points to convex-constrained ones, or improve over the best-known outcomes on fixing the same-structured points. Furthermore, numerical experiments on linearly/quadratically constrained non-convex quadratic packages and linear-constrained robust nonlinear least squares are carried out to show the empirical effectivity of the proposed DPALM over quite a few state-of-the paintings methodology
2. Augmented Lagrangian Methods as Layered Administration Architectures(arXiv)
Author : Anusha Srikanthan, Vijay Kumar, Nikolai Matni
Abstract : or optimum administration points that include planning and following a trajectory, two diploma of freedom (2DOF) controllers are a ubiquitously used administration construction that decomposes the difficulty proper right into a trajectory expertise layer and a recommendations administration layer. Nonetheless, whatever the broad use and wise success of this layered administration construction, it stays a design choice that need to be imposed a priori on the administration protection. To deal with this gap, this paper seeks to impress a principled analysis of the design of layered administration architectures, with an preliminary take care of the 2DOF controller. We current that making use of the Alternating Route Methodology of Multipliers (ADMM) algorithm to resolve a strategically rewritten optimum administration draw back ends in choices that are naturally layered, and composed of a trajectory expertise layer and a recommendations administration layer. Furthermore, these layers are coupled by means of Lagrange multipliers that assure dynamic feasibility of the deliberate trajectory. We instantiate this framework throughout the context of deterministic and stochastic linear optimum administration points, and current how our technique mechanically yields a feedforward/feedback-based administration protection that exactly solves the distinctive draw back. We then current that the simplicity of the following controller development suggests pure heuristic algorithms for about fixing nonlinear optimum administration points. We empirically show improved effectivity of these layered nonlinear optimum controllers as compared with iLQR, and highlight their flexibility by incorporating every convex and nonconvex constraints.
