- Damped Proximal Augmented Lagrangian Methodology for weakly-Convex Issues with Convex Constraints(arXiv)
Writer : Hari Dahal, Wei Liu, Yangyang Xu
Summary : We give a damped proximal augmented Lagrangian methodology (DPALM) for fixing issues with a weakly-convex goal and convex linear/nonlinear constraints. As a substitute of taking a full stepsize, DPALM adopts a damped twin stepsize to make sure the boundedness of twin iterates. We present that DPALM can produce a (close to) $vareps$-KKT level inside $O(vareps^{-2})$ outer iterations if every DPALM subproblem is solved to a correct accuracy. As well as, we set up general iteration complexity of DPALM when the target is both a regularized easy perform or in a regularized compositional kind. For the previous case, DPALM achieves the complexity of O˜(ε−2.5) to provide an ε-KKT level by making use of an accelerated proximal gradient (APG) methodology to every DPALM subproblem. For the latter case, the complexity of DPALM is O˜(ε−3) to provide a close to ε-KKT level by utilizing an APG to resolve a Moreau-envelope smoothed model of every subproblem. Our outer iteration complexity and the general complexity both generalize current greatest ones from unconstrained or linear-constrained issues to convex-constrained ones, or enhance over the best-known outcomes on fixing the same-structured issues. Moreover, numerical experiments on linearly/quadratically constrained non-convex quadratic packages and linear-constrained strong nonlinear least squares are performed to display the empirical effectivity of the proposed DPALM over a number of state-of-the artwork methodology
2. Augmented Lagrangian Strategies as Layered Management Architectures(arXiv)
Writer : Anusha Srikanthan, Vijay Kumar, Nikolai Matni
Summary : or optimum management issues that contain planning and following a trajectory, two diploma of freedom (2DOF) controllers are a ubiquitously used management structure that decomposes the issue right into a trajectory technology layer and a suggestions management layer. Nonetheless, regardless of the broad use and sensible success of this layered management structure, it stays a design selection that have to be imposed a priori on the management coverage. To handle this hole, this paper seeks to provoke a principled research of the design of layered management architectures, with an preliminary deal with the 2DOF controller. We present that making use of the Alternating Route Methodology of Multipliers (ADMM) algorithm to resolve a strategically rewritten optimum management downside ends in options which are naturally layered, and composed of a trajectory technology layer and a suggestions management layer. Moreover, these layers are coupled through Lagrange multipliers that guarantee dynamic feasibility of the deliberate trajectory. We instantiate this framework within the context of deterministic and stochastic linear optimum management issues, and present how our strategy mechanically yields a feedforward/feedback-based management coverage that precisely solves the unique downside. We then present that the simplicity of the ensuing controller construction suggests pure heuristic algorithms for about fixing nonlinear optimum management issues. We empirically display improved efficiency of those layered nonlinear optimum controllers as in comparison with iLQR, and spotlight their flexibility by incorporating each convex and nonconvex constraints.
