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In this paper, a centralized two-block separable optimization is considered for which a fully parallel primal-dual discrete-time algorithm with fixed step size is derived based on monotone operator splitting method. In this algorithm, the…
Stochastic dual dynamic programming (SDDP) is a state-of-the-art method for solving multi-stage stochastic optimization, widely used for modeling real-world process optimization tasks. Unfortunately, SDDP has a worst-case complexity that…
In this paper, a projected primal-dual gradient flow of augmented Lagrangian is presented to solve convex optimization problems that are not necessarily strictly convex. The optimization variables are restricted by a convex set with…
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 studies distributed convex optimization with both affine equality and nonlinear inequality couplings through the duality analysis. We first formulate the dual of the coupling-constraint problem and reformulate it as a consensus…
We consider a generic convex-concave saddle point problem with separable structure, a form that covers a wide-ranged machine learning applications. Under this problem structure, we follow the framework of primal-dual updates for saddle…
Semidefinite programming (SDP) is widely acknowledged as one of the most effective methods for deriving the tightest lower bounds of the optimal power flow (OPF) problems. In this paper, an enhanced semidefinite relaxation model that…
Block coordinate descent (BCD) methods and their variants have been widely used in coping with large-scale nonconstrained optimization problems in many fields such as imaging processing, machine learning, compress sensing and so on. For…
With the unprecedented growth of signal processing and machine learning application domains, there has been a tremendous expansion of interest in distributed optimization methods to cope with the underlying large-scale problems.…
Trajectory optimization is an efficient approach for solving optimal control problems for complex robotic systems. It relies on two key components: first the transcription into a sparse nonlinear program, and second the corresponding solver…
Many large-scale constrained optimization problems can be formulated as bilevel distributed optimization tasks over undirected networks, where agents collaborate to minimize a global cost function while adhering to constraints, relying only…
The paper studies a distributed constrained optimization problem, where multiple agents connected in a network collectively minimize the sum of individual objective functions subject to a global constraint being an intersection of the local…
In many operations management problems, we need to make decisions sequentially to minimize the cost while satisfying certain constraints. One modeling approach to study such problems is constrained Markov decision process (CMDP). When…
The proliferation of distributed energy resources has heightened the interactions between transmission and distribution (T&D) systems, necessitating novel analyses for the reliable operation and planning of interconnected T&D networks. A…
In this paper, we propose a new decomposition approach named the proximal primal dual algorithm (Prox-PDA) for smooth nonconvex linearly constrained optimization problems. The proposed approach is primal-dual based, where the primal step…
We propose decentralized primal-dual methods for cooperative multi-agent consensus optimization problems over both static and time-varying communication networks, where only local communications are allowed. The objective is to minimize the…
This paper studies a constrained optimization problem over networked systems with an undirected and connected communication topology. The algorithm proposed in this work utilizes singular perturbation, dynamic average consensus, and saddle…
We introduce an extension of Dual Dynamic Programming (DDP) to solve linear dynamic programming equations. We call this extension IDDP-LP which applies to situations where some or all primal and dual subproblems to be solved along the…
The Survivable Network Design problem (SNDP) is a well-studied problem, motivated by the design of networks that are robust to faults under the assumption that any subset of edges up to a specific number can fail. We consider non-uniform…
Decentralized optimization is a common paradigm used in distributed signal processing and sensing as well as privacy-preserving and large-scale machine learning. It is assumed that several computational entities locally hold objective…