Related papers: Accelerated primal-dual methods with enlarged step…

This work presents a universal accelerated first-order primal-dual method for affinely constrained convex optimization problems. It can handle both Lipschitz and H\"{o}lder gradients but does not need to know the smoothness level of the…

We propose an extended primal-dual algorithm framework for solving a general nonconvex optimization model. This work is motivated by image reconstruction problems in a class of nonlinear imaging, where the forward operator can be formulated…

We propose a novel type of nonlinear solver acceleration for systems of nonlinear partial differential equations (PDEs) that is based on online/adaptive learning. It is applied in the context of multiphase flow in porous media. The proposed…

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…

Many important problems in science and engineering require solving the so-called parametric partial differential equations (PDEs), i.e., PDEs with different physical parameters, boundary conditions, shapes of computational domains, etc.…

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…

As the dimension of a system increases, traditional methods for control and differential games rapidly become intractable, making the design of safe autonomous agents challenging in complex or team settings. Deep-learning approaches avoid…

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…

Neural networks have been applied to control problems, typically by combining data, differential equation residuals, and objective costs in the training loss or by incorporating auxiliary architectural components. Instead, we propose a…

We propose a primal--dual technique that applies to infinite dimensional equality constrained problems, in particular those arising from optimal control. As an application of our general framework, we solve a control-constrained double…

Recent work has shown a variety of ways in which machine learning can be used to accelerate the solution of constrained optimization problems. Increasing demand for real-time decision-making capabilities in applications such as artificial…

We consider convex-concave saddle point problems with a separable structure and non-strongly convex functions. We propose an efficient stochastic block coordinate descent method using adaptive primal-dual updates, which enables flexible…

In this paper we consider a class of optimization problems with a strongly convex objective function and the feasible set given by an intersection of a simple convex set with a set given by a number of linear equality and inequality…

Binary optimization is a powerful tool for modeling combinatorial problems, yet scalable and theoretically sound solution methods remain elusive. Conventional solvers often rely on heuristic strategies with weak guarantees or struggle with…

Primal-dual methods for solving convex optimization problems with functional constraints often exhibit a distinct two-stage behavior. Initially, they converge towards a solution at a sublinear rate. Then, after a certain point, the method…

Composite optimization problems, formulated as the minimization of three functions, are ubiquitous in large-scale machine learning and signal processing. While state-of-the-art splitting methods such as Condat-V\~{u} (CV) [Condat, 2013,…

We consider a class of multi-agent cooperative consensus optimization problems with local nonlinear convex constraints where only those agents connected by an edge can directly communicate, hence, the optimal consensus decision lies in the…

Real-world systems are often formulated as constrained optimization problems. Techniques to incorporate constraints into Neural Networks (NN), such as Neural Ordinary Differential Equations (Neural ODEs), have been used. However, these…

The modeling and control of complex physical systems are essential in real-world problems. We propose a novel framework that is generally applicable to solving PDE-constrained optimal control problems by introducing surrogate models for PDE…

In this paper, we consider optimizing a smooth, convex, lower semicontinuous function in Riemannian space with constraints. To solve the problem, we first convert it to a dual problem and then propose a general primal-dual algorithm to…