Related papers: Accelerating design optimization using reduced ord…

Engineers learn from every design they create, building intuition that helps them quickly identify promising solutions for new problems. Topology optimization (TO) - a well-established computational method for designing structures with…

This paper addresses a distributed convex optimization problem with a class of coupled constraints, which arise in a multi-agent system composed of multiple communities modeled by cliques. First, we propose a fully distributed…

First-order operator splitting methods are ubiquitous among many fields through science and engineering, such as inverse problems, signal/image processing, statistics, data science and machine learning, to name a few. In this paper, we…

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…

Distributed optimization is the standard way of speeding up machine learning training, and most of the research in the area focuses on distributed first-order, gradient-based methods. Yet, there are settings where some…

In this extended abstract, we report on ongoing work towards an approximate multimodal optimization algorithm with asymptotic guarantees. Multimodal optimization is the problem of finding all local optimal solutions (modes) to a path…

This monograph covers some recent advances in a range of acceleration techniques frequently used in convex optimization. We first use quadratic optimization problems to introduce two key families of methods, namely momentum and nested…

This thesis focuses on developing and analyzing accelerated and inexact first-order methods for solving or finding stationary points of various nonconvex composite optimization (NCO) problems. The main tools mainly come from variational and…

This paper introduces the concept of abstracted model reduction: a framework to improve the tractability of structure-preserving methods for the complexity reduction of interconnected system models. To effectively reduce high-order,…

Accelerated gradient descent iterations are widely used in optimization. It is known that, in the continuous-time limit, these iterations converge to a second-order differential equation which we refer to as the accelerated gradient flow.…

Despite their frequent slow convergence, proximal gradient schemes are widely used in large-scale optimization tasks due to their tremendous stability, scalability, and ease of computation. In this paper, we develop and investigate a…

This contribution describes the implementation of a data--driven shape optimization pipeline in a naval architecture application. We adopt reduced order models (ROMs) in order to improve the efficiency of the overall optimization, keeping a…

In this paper, we propose a unified two-phase scheme to accelerate any high-order regularized tensor approximation approach on the smooth part of a composite convex optimization model. The proposed scheme has the advantage of not needing to…

It is classical that, when the small deformation is assumed, the incremental analysis problem of an elastoplastic structure with a piecewise-linear yield condition and a linear strain hardening model can be formulated as a convex quadratic…

This paper deals with the definition and optimization of augmentation spaces for faster convergence of the conjugate gradient method in the resolution of sequences of linear systems. Using advanced convergence results from the literature,…

High dimensional and/or nonconvex optimization remains a challenging and important problem across a wide range of fields, such as machine learning, data assimilation, and partial differential equation (PDE) constrained optimization. Here we…

The primary focus of this paper is on designing an inexact first-order algorithm for solving constrained nonlinear optimization problems. By controlling the inexactness of the subproblem solution, we can significantly reduce the…

We consider the problem of constructing optimal designs for model discrimination between competing regression models. Various new properties of optimal designs with respect to the popular $T$-optimality criterion are derived, which in many…

Many computer graphics problems require computing geometric shapes subject to certain constraints. This often results in non-linear and non-convex optimization problems with globally coupled variables, which pose great challenge for…

In this paper, we propose a novel, computationally efficient reduced order method to solve linear parabolic inverse source problems. Our approach provides accurate numerical solutions without relying on specific training data. The forward…