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We present a flexible Alternating Direction Method of Multipliers (F-ADMM) algorithm for solving optimization problems involving a strongly convex objective function that is separable into $n \geq 2$ blocks, subject to (non-separable)…
In this paper, we first introduce a preconditioned primal-dual gradient algorithm based on conjugate duality theory. This algorithm is designed to solve composite optimization problem whose objective function consists of two summands: a…
Minimax problems have recently attracted a lot of research interests. A few efforts have been made to solve decentralized nonconvex strongly-concave (NCSC) minimax-structured optimization; however, all of them focus on smooth problems with…
In this paper, we study a constrained minimization problem that arise from materials science to determine the dislocation (line defect) structure of grain boundaries. The problems aims to minimize the energy of the grain boundary with…
In this paper, we develop a self-adaptive ADMM that updates the penalty parameter adaptively. When one part of the objective function is strongly convex i.e., the problem is semi-strongly convex, our algorithm can update the penalty…
In this paper we consider the problem of distributed nonlinear optimisation of a separable convex cost function over a graph subject to cone constraints. We show how to generalise, using convex analysis, monotone operator theory and…
In this paper we study nonconvex and nonsmooth optimization problems with semi-algebraic data, where the variables vector is split into several blocks of variables. The problem consists of one smooth function of the entire variables vector…
Distributed and decentralized optimization are key for the control of networked systems. Application examples include distributed model predictive control and distributed sensing or estimation. Non-linear systems, however, lead to problems…
Alternating structure-adapted proximal (ASAP) gradient algorithm (M. Nikolova and P. Tan, SIAM J Optim, 29:2053-2078, 2019) has drawn much attention due to its efficiency in solving nonconvex nonsmooth optimization problems. However, the…
We present a new algorithm for solving optimization problems with objective functions that are the sum of a smooth function and a (potentially) nonsmooth regularization function, and nonlinear equality constraints. The algorithm may be…
Alternating minimization (AM) procedures are practically efficient in many applications for solving convex and non-convex optimization problems. On the other hand, Nesterov's accelerated gradient is theoretically optimal first-order method…
Recently, many variance reduced stochastic alternating direction method of multipliers (ADMM) methods (e.g.\ SAG-ADMM, SDCA-ADMM and SVRG-ADMM) have made exciting progress such as linear convergence rates for strongly convex problems.…
We propose Dual-Feedback Generalized Proximal Gradient Descent (DFGPGD) as a new, hardware-friendly, operator splitting algorithm. We then establish convergence guarantees under approximate computational errors and we derive theoretical…
Convex quadratic programs (QPs) constitute a fundamental computational primitive across diverse domains including financial optimization, control systems, and machine learning. The alternating direction method of multipliers (ADMM) has…
We introduce two novel primal-dual algorithms for addressing nonconvex, nonconcave, and nonsmooth saddle point problems characterized by the weak Minty Variational Inequality (MVI). The first algorithm, Nonconvex-Nonconcave Primal-Dual…
In this paper, we study the proximal incremental aggregated gradient(PIAG) algorithm for minimizing the sum of L-smooth nonconvex component functions and a proper closed convex function. By exploiting the L-smooth property and with the help…
The alternating direction method with multipliers (ADMM) has been one of most powerful and successful methods for solving various convex or nonconvex composite problems that arise in the fields of image & signal processing and machine…
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…
Based on the idea of randomized coordinate descent of $\alpha$-averaged operators, a randomized primal-dual optimization algorithm is introduced, where a random subset of coordinates is updated at each iteration. The algorithm builds upon a…
In this paper, we study zeroth-order algorithms for nonconvex minimax problems with coupled linear constraints under the deterministic and stochastic settings, which have attracted wide attention in machine learning, signal processing and…