Related papers: An augmented Lagrangian deep learning method for v…
In this paper, we consider augmented Lagrangian (AL) algorithms for solving large-scale nonlinear optimization problems that execute adaptive strategies for updating the penalty parameter. Our work is motivated by the recently proposed…
Many inverse and parameter estimation problems can be written as PDE-constrained optimization problems. The goal, then, is to infer the parameters, typically coefficients of the PDE, from partial measurements of the solutions of the PDE for…
In this paper, we propose a unified primal-dual algorithm framework based on the augmented Lagrangian function for composite convex problems with conic inequality constraints. The new framework is highly versatile. First, it not only covers…
Mathematical optimization is the workhorse behind several aspects of modern robotics and control. In these applications, the focus is on constrained optimization, and the ability to work on manifolds (such as the classical matrix Lie…
Approximating solutions of ordinary and partial differential equations constitutes a significant challenge. Based on functional expressions that inherently depend on neural networks, neural forms are specifically designed to precisely…
In this paper we apply an augmented Lagrange method to a class of semilinear elliptic optimal control problems with pointwise state constraints. We show strong convergence of subsequences of the primal variables to a local solution of the…
We develop a decomposition method based on the augmented Lagrangian framework to solve a broad family of semidefinite programming problems, possibly with nonlinear objective functions, nonsmooth regularization, and general linear…
In this paper, we study a class of misspecified variational inequalities (VIs) where both the monotone operator and nonlinear convex constraints depend on an unknown parameter learned via a secondary VI. Existing data-driven VI methods…
This paper considers a generic convex minimization template with affine constraints over a compact domain, which covers key semidefinite programming applications. The existing conditional gradient methods either do not apply to our template…
This paper considers stochastic optimization problems with weakly convex objective and constraint functions. We propose Prox-PEP, a proximal method equipped with quadratic subproblems. To handle nonlinear equality constraints, we employ an…
There are many important practical optimization problems whose feasible regions are not known to be nonempty or not, and optimizers of the objective function with the least constraint violation prefer to be found. A natural way for dealing…
In the past years, augmented Lagrangian methods have been successfully applied to several classes of non-convex optimization problems, inspiring new developments in both theory and practice. In this paper we bring most of these recent…
We consider solving equality-constrained nonlinear, nonconvex optimization problems. This class of problems appears widely in a variety of applications in machine learning and engineering, ranging from constrained deep neural networks, to…
Differential Dynamic Programming (DDP) has become a well established method for unconstrained trajectory optimization. Despite its several applications in robotics and controls however, a widely successful constrained version of the…
We present several key advances to the Physics and Equality Constrained Artificial Neural Networks (PECANN) framework, substantially improving its capacity to solve challenging partial differential equations (PDEs). Our enhancements broaden…
We consider the minimization of a sum of a smooth function with a nonsmooth composite function, where the composition is applied on a random linear mapping. This random composite model encompasses many problems, and can especially capture…
We introduce a deep learning-based framework for weakly enforcing boundary conditions in the numerical approximation of partial differential equations. Building on existing physics-informed neural network and deep Ritz methods, we propose…
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…
Variable selection is one of the most important tasks in statistics and machine learning. To incorporate more prior information about the regression coefficients, the constrained Lasso model has been proposed in the literature. In this…
Physics-informed neural networks (PINNs) often struggle with multi-scale PDEs featuring sharp gradients and nontrivial boundary conditions, as the physics residual and boundary enforcement compete during optimization. We present a…