Accelerated gradient methods and dual decomposition in distributed model predictive control

Abstract

We propose a distributed optimization algorithm for mixed L1/L2-norm optimization based on accelerated gradient methods using dual decomposition. The algorithm achieves convergence rate O(1 k 2), where k is the iteration number, which significantly improves the convergence rates of existing duality-based distributed optimization algorithms that achieve O(1 k). The performance of the developed algorithm is evaluated on randomly generated optimization problems arising in distributed model predictive control (DMPC). The evaluation shows that, when the problem data is sparse and large-scale, our algorithm can outperform current state-of-the-art optimization software CPLEX and MOSEK.

An improved Distributed Dual Newton-CG method for convex quadratic programming problems

“…Observe that the positivity of the slack variables does not need to be enforced. Indeed, it can be easily verified that inequality constraints of the form s i 0 included in (13) would never be strictly active, and can therefore be discarded.…”

“…the authors of [7] propose a coordinate ascent approach to solve constrained matrix problems. In [8], [9], [10], a gradient method, whereas in [11], [12], [13], a fast gradient method is used in order to attain dual optimality. All these methods make use of only first order derivatives to obtain a search direction and thus their theoretical and practical convergence cannot be faster than sublinear.…”

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“…Primal decomposition refers to the decomposition of the original problem, while dual decomposition manipulates the dual formulation. Dual decomposition has been used in distributed MPC algorithms [23], [24], [25], [26] when the cost function is quadratic and separable.…”

Execution time certification for gradient-based optimization in model predictive control

“…The topic of this paper is to provide certificates for the execution time of the optimization algorithm such that for every feasible initial condition the optimization algorithm provides a solution within the sampling time. We consider linear time-invariant systems with polytopic constraints and quadratic cost and a dual accelerated gradient method [6] is used to solve the resulting optimization problem.…”

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