Related papers: Conditionally adaptive augmented Lagrangian method…
Shape-constrained convex regression problem deals with fitting a convex function to the observed data, where additional constraints are imposed, such as component-wise monotonicity and uniform Lipschitz continuity. This paper provides a…
Regularizing Deep Neural Networks (DNNs) is essential for improving generalizability and preventing overfitting. Fixed penalty methods, though common, lack adaptability and suffer from hyperparameter sensitivity. In this paper, we propose a…
Many problems in physical sciences are characterized by the prediction of space-time sequences. Such problems range from weather prediction to the analysis of disease propagation and video prediction. Modern techniques for the solution of…
The augmented Lagrange method is employed to address the optimal control problem involving pointwise state constraints in parabolic equations. The strong convergence of the primal variables and the weak convergence of the dual variables are…
The multi-contact nonlinear complementarity problem (NCP) is a naturally arising challenge in robotic simulations. Achieving high performance in terms of both accuracy and efficiency remains a significant challenge, particularly in…
Parametric optimal control problems governed by partial differential equations (PDEs) are widely found in scientific and engineering applications. Traditional grid-based numerical methods for such problems generally require repeated…
In this paper we study decomposition methods based on separable approximations for minimizing the augmented Lagrangian. In particular, we study and compare the Diagonal Quadratic Approximation Method (DQAM) of Mulvey and Ruszczy\'{n}ski and…
Alternating Direction Method of Multipliers (ADMM) has been used successfully in many conventional machine learning applications and is considered to be a useful alternative to Stochastic Gradient Descent (SGD) as a deep learning optimizer.…
Physics-informed neural networks (PINNs) leverage neural-networks to find the solutions of partial differential equation (PDE)-constrained optimization problems with initial conditions and boundary conditions as soft constraints. These soft…
This paper develops an adaptive proximal alternating direction method of multipliers (ADMM) for solving linearly constrained, composite optimization problems under the assumption that the smooth component of the objective is weakly convex,…
This paper studies a class of double-loop (inner-outer) algorithms for convex composite optimization. For unconstrained problems, we develop a restarted accelerated composite gradient method that attains the optimal first-order complexity…
An attractive research direction for future communication systems is the design of new waveforms that can both support high throughputs and present advantageous signal characteristics. Although most modern systems use orthogonal…
A stochastic linear quadratic (LQ) optimal control problem with a pointwise linear equality constraint on the terminal state is considered. A strong Lagrangian duality theorem is proved under a uniform convexity condition on the cost…
"AI for Science" aims to solve fundamental scientific problems using AI techniques. As most physical phenomena can be described as Partial Differential Equations (PDEs) , approximating their solutions using neural networks has evolved as a…
This paper proposes a novel Coordinate-Descent Augmented-Lagrangian (CDAL) solver for linear, possibly parameter-varying, model predictive control (MPC) problems. At each iteration, an augmented Lagrangian (AL) subproblem is solved by…
We present the numerical methods and GPU-accelerated implementation underlying a Total Lagrangian finite element framework for finite-deformation flexible multibody dynamics, introduced in the companion paper [1]. The framework supports…
Deep generative models hold great promise for representing complex physical systems, but their deployment is currently limited by the lack of guarantees on the physical plausibility of the generated outputs. Ensuring that known physical…
This paper is concerned with augmented Lagrangian methods for the treatment of fully convex composite optimization problems. We extend the classical relationship between augmented Lagrangian methods and the proximal point algorithm to the…
The Alternating Direction Method of Multipliers (ADMM) is a widely used method for structured convex optimization, and its practical performance depends strongly on the choice of penalty and relaxation parameters. Motivated by settings such…
We study the Bregman Augmented Lagrangian method (BALM) for solving convex problems with linear constraints. For classical Augmented Lagrangian method, the convergence rate and its relation with the proximal point method is well-understood.…