Related papers: Scalable Primal Decomposition Schemes for Large-Sc…
The electrical network reconfiguration problem aims to minimize losses in a distribution system by adjusting switches while ensuring radial topology. The growing use of renewable energy and the complexity of managing modern power grids make…
We present a hierarchical optimization architecture for large-scale power networks that overcomes limitations of fully centralized and fully decentralized architectures. The architecture leverages principles of multigrid computing schemes,…
This paper considers a convex optimization problem with cost and constraints that evolve over time. The function to be minimized is strongly convex and possibly non-differentiable, and variables are coupled through linear constraints. In…
This paper proposes a two-level distributed algorithmic framework for solving the AC optimal power flow (OPF) problem with convergence guarantees. The presence of highly nonconvex constraints in OPF poses significant challenges to…
In contrast with many other convex optimization classes, state-of-the-art semidefinite programming solvers are yet unable to efficiently solve large scale instances. This work aims to reduce this scalability gap by proposing a novel…
We consider the convex-concave saddle point problem $\min_{\mathbf{x}}\max_{\mathbf{y}}\Phi(\mathbf{x},\mathbf{y})$, where the decision variables $\mathbf{x}$ and/or $\mathbf{y}$ subject to a multi-block structure and affine coupling…
We study the problem of minimizing a sum of local objective convex functions over a network of processors/agents. This problem naturally calls for distributed optimization algorithms, in which the agents cooperatively solve the problem…
This paper considers an optimization problem that components of the objective function are available at different nodes of a network and nodes are allowed to only exchange information with their neighbors. The decentralized alternating…
This paper proposes and analyzes a dampened proximal alternating direction method of multipliers (DP.ADMM) for solving linearly-constrained nonconvex optimization problems where the smooth part of the objective function is nonseparable.…
In this paper, we propose a novel trajectory optimization algorithm for mobile manipulators under end-effector path, collision avoidance and various kinematic constraints. Our key contribution lies in showing how this highly non-linear and…
In this paper we combine an infeasible Interior Point Method (IPM) with the Proximal Method of Multipliers (PMM). The resulting algorithm (IP-PMM) is interpreted as a primal-dual regularized IPM, suitable for solving linearly constrained…
Primal-Dual Hybrid Gradient (PDHG) and Alternating Direction Method of Multipliers (ADMM) are two widely-used first-order optimization methods. They reduce a difficult problem to simple subproblems, so they are easy to implement and have…
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…
This paper considers the robust phase retrieval, which can be cast as a nonsmooth and nonconvex composite optimization problem. We propose two first-order algorithms with adaptive step sizes: the subgradient algorithm (AdaSubGrad) and the…
Distributed restoration can harness distributed energy resources (DER) to enhance the resilience of active distribution networks. However, the large number of decision variables, especially the binary decision variables of reconfiguration,…
The semidefinite programming (SDP) relaxation has proven to be extremely strong for many hard discrete optimization problems. This is in particular true for the quadratic assignment problem (QAP), arguably one of the hardest NP-hard…
Trajectory optimization methods provide an efficient and reliable means of computing feasible trajectories in nonconvex solution spaces. However, a well-known limitation of these algorithms is that they are inherently local in nature, and…
The growing demand for solving large-scale, data-intensive linear and conic optimization problems, particularly in applications such as artificial intelligence and machine learning, has highlighted the limitations of classical interior…
We propose both serial and parallel proximal (linearized) alternating direction method of multipliers (ADMM) algorithms for training residual neural networks. In contrast to backpropagation-based approaches, our methods inherently mitigate…
We propose a distributed algorithm, named Distributed Alternating Direction Method of Multipliers (D-ADMM), for solving separable optimization problems in networks of interconnected nodes or agents. In a separable optimization problem there…