95 research outputs found
A faster prediction-correction framework for solving convex optimization problems
He and Yuan's prediction-correction framework [SIAM J. Numer. Anal. 50:
700-709, 2012] is able to provide convergent algorithms for solving convex
optimization problems at a rate of in both ergodic and pointwise
senses. This paper presents a faster prediction-correction framework at a rate
of in the non-ergodic sense and in the pointwise sense,
{\it without any additional assumptions}. Interestingly, it provides a faster
algorithm for solving {\it multi-block} separable convex optimization problems
with linear equality or inequality constraints
Decentralized Proximal Method of Multipliers for Convex Optimization with Coupled Constraints
In this paper, a decentralized proximal method of multipliers (DPMM) is
proposed to solve constrained convex optimization problems over multi-agent
networks, where the local objective of each agent is a general closed convex
function, and the constraints are coupled equalities and inequalities. This
algorithm strategically integrates the dual decomposition method and the
proximal point algorithm. One advantage of DPMM is that subproblems can be
solved inexactly and in parallel by agents at each iteration, which relaxes the
restriction of requiring exact solutions to subproblems in many distributed
constrained optimization algorithms. We show that the first-order optimality
residual of the proposed algorithm decays to at a rate of under
general convexity. Furthermore, if a structural assumption for the considered
optimization problem is satisfied, the sequence generated by DPMM converges
linearly to an optimal solution. In numerical simulations, we compare DPMM with
several existing algorithms using two examples to demonstrate its
effectiveness
Implementation of model predictive control for tracking in embedded systems using a sparse extended ADMM algorithm
This article presents a sparse, low-memory footprint optimization algorithm for the implementation of model predictive control (MPC) for tracking formulation in embedded systems. This MPC formulation has several advantages over standard MPC formulations, such as an increased domain of attraction and guaranteed recursive feasibility even in the event of a sudden reference change. However, this comes at the expense of the addition of a small amount of decision variables to the MPC's optimization problem that complicates the structure of its matrices. We propose a sparse optimization algorithm, based on an extension of the alternating direction method of multipliers, that exploits the structure of this particular MPC formulation. We describe the controller formulation and detail how its structure is exploited by means of the aforementioned optimization algorithm. We show closed-loop simulations comparing the proposed solver against other solvers and approaches from the literature
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