27 research outputs found
On the Convergence of Alternating Direction Lagrangian Methods for Nonconvex Structured Optimization Problems
Nonconvex and structured optimization problems arise in many engineering
applications that demand scalable and distributed solution methods. The study
of the convergence properties of these methods is in general difficult due to
the nonconvexity of the problem. In this paper, two distributed solution
methods that combine the fast convergence properties of augmented
Lagrangian-based methods with the separability properties of alternating
optimization are investigated. The first method is adapted from the classic
quadratic penalty function method and is called the Alternating Direction
Penalty Method (ADPM). Unlike the original quadratic penalty function method,
in which single-step optimizations are adopted, ADPM uses an alternating
optimization, which in turn makes it scalable. The second method is the
well-known Alternating Direction Method of Multipliers (ADMM). It is shown that
ADPM for nonconvex problems asymptotically converges to a primal feasible point
under mild conditions and an additional condition ensuring that it
asymptotically reaches the standard first order necessary conditions for local
optimality are introduced. In the case of the ADMM, novel sufficient conditions
under which the algorithm asymptotically reaches the standard first order
necessary conditions are established. Based on this, complete convergence of
ADMM for a class of low dimensional problems are characterized. Finally, the
results are illustrated by applying ADPM and ADMM to a nonconvex localization
problem in wireless sensor networks.Comment: 13 pages, 6 figure
Efficient MIMO detection for high-order QAM constellations in time dispersive channels
In this paper, we apply a generalized form of the alternating direction method of multipliers (ADMM) and derive a multiple-input multiple-output (MIMO) detection algorithm for single carrier transmissions in time dispersive channels. The proposed algorithm supports different penalty parameters for each individual subcarrier and antenna and also includes a relaxation coefficient in the iterations. Besides evaluating the impact of these parameters, a method is presented for the automatic selection of the penalty. It is shown through simulations that very competitive performances can be obtained with the proposed approach for systems with high-order modulation combined with large antenna settings.info:eu-repo/semantics/acceptedVersio
Online Trajectory Planning Through Combined Trajectory Optimization and Function Approximation: Application to the Exoskeleton Atalante
Autonomous robots require online trajectory planning capability to operate in
the real world. Efficient offline trajectory planning methods already exist,
but are computationally demanding, preventing their use online. In this paper,
we present a novel algorithm called Guided Trajectory Learning that learns a
function approximation of solutions computed through trajectory optimization
while ensuring accurate and reliable predictions. This function approximation
is then used online to generate trajectories. This algorithm is designed to be
easy to implement, and practical since it does not require massive computing
power. It is readily applicable to any robotics systems and effortless to set
up on real hardware since robust control strategies are usually already
available. We demonstrate the computational performance of our algorithm on
flat-foot walking with the self-balanced exoskeleton Atalante