Related papers: Primal-Dual Method for Optimization Problems with …
Robust optimization (RO) is one of the key paradigms for solving optimization problems affected by uncertainty. Two principal approaches for RO, the robust counterpart method and the adversarial approach, potentially lead to excessively…
A proximal safeguarded augmented Lagrangian method for minimizing the difference of convex (DC) functions over a nonempty, closed and convex set with additional linear equality as well as convex inequality constraints is presented. Thereby,…
The primal-dual method of Chambolle and Pock is a widely used algorithm to solve various optimization problems written as convex-concave saddle point problems. Each update step involves the application of both the forward linear operator…
We propose a primal-dual smoothing framework for finding a near-stationary point of a class of non-smooth non-convex optimization problems with max-structure. We analyze the primal and dual gradient complexities of the framework via two…
This work proposes an accelerated primal-dual dynamical system for affine constrained convex optimization and presents a class of primal-dual methods with nonergodic convergence rates. In continuous level, exponential decay of a novel…
In this paper, we design an inertial accelerated primal-dual algorithm to address the convex-concave saddle point problem, which is formulated as $\min_{x}\max_{y} f(x) + \langle Kx, y \rangle - g(y)$. Remarkably, both functions $f$ and $g$…
A new primal-dual algorithm is presented for solving a class of non-convex minimization problems. This algorithm is based on canonical duality theory such that the original non-convex minimization problem is first reformulated as a…
We propose to solve large instances of the non-convex optimization problems reformulated with canonical duality theory. To this aim we propose an interior point potential reduction algorithm based on the solution of the primal-dual total…
Heterogeneous networks comprise agents with varying capabilities in terms of computation, storage, and communication. In such settings, it is crucial to factor in the operating characteristics in allowing agents to choose appropriate…
We develop a unified theory of augmented Lagrangians for nonconvex optimization problems that encompasses both duality theory and convergence analysis of primal-dual augmented Lagrangian methods in the infinite dimensional setting. Our goal…
This paper studies the distributed optimization problem when the objective functions might be nondifferentiable and subject to heterogeneous set constraints. Unlike existing subgradient methods, we focus on the case when the exact…
Optimization problems with convex quadratic cost and polyhedral constraints are ubiquitous in signal processing, automatic control and decision-making. We consider here an enlarged problem class that allows to encode logical conditions and…
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…
This work investigates the distributed constrained optimization problem under inter-agent communication delays from the perspective of passivity. First, we propose a continuous-time algorithm for distributed constrained optimization with…
We develop primal-dual coordinate methods for solving bilinear saddle-point problems of the form $\min_{x \in \mathcal{X}} \max_{y\in\mathcal{Y}} y^\top A x$ which contain linear programming, classification, and regression as special cases.…
This paper proposes a novel distributed approach for solving a cooperative Constrained Multi-agent Reinforcement Learning (CMARL) problem, where agents seek to minimize a global objective function subject to shared constraints. Unlike…
Bilevel programs are optimization problems where some variables are solutions to optimization problems themselves, and they arise in a variety of control applications, including: control of vehicle traffic networks, inverse reinforcement…
In this paper, we consider a nonconvex optimization problem with nonlinear equality constraints. We assume that both, the objective function and the functional constraints are locally smooth. For solving this problem, we propose a…
In this paper we propose a randomized primal-dual proximal block coordinate updating framework for a general multi-block convex optimization model with coupled objective function and linear constraints. Assuming mere convexity, we establish…
In this paper, we consider a network of agents that jointly aim to minimise the sum of local functions subject to coupling constraints involving all local variables. To solve this problem, we propose a novel solution based on a primal-dual…