Related papers: Generalized Dual Decomposition
This paper presents an algorithmic study and complexity analysis for solving distributionally robust multistage convex optimization (DR-MCO). We generalize the usual consecutive dual dynamic programming (DDP) algorithm to DR-MCO and propose…
Asynchronous parallel optimization algorithms for solving large-scale machine learning problems have drawn significant attention from academia to industry recently. This paper proposes a novel algorithm, decoupled asynchronous proximal…
Higher-order tensors are becoming prevalent in many scientific areas such as computer vision, social network analysis, data mining and neuroscience. Traditional tensor decomposition approaches face three major challenges: model selecting,…
We propose a parallel adaptive constraint-tightening approach to solve a linear model predictive control problem for discrete-time systems, based on inexact numerical optimization algorithms and operator splitting methods. The underlying…
We propose a general dual ascent framework for Lagrangean decomposition of combinatorial problems. Although methods of this type have shown their efficiency for a number of problems, so far there was no general algorithm applicable to…
The density matrix renormalization group (DMRG) algorithm is a popular alternating minimization scheme for solving high-dimensional optimization problems in the tensor train format. Classical DMRG, however, is based on sequential…
System performance for networks composed of interconnected subsystems can be increased if the traditionally separated subsystems are jointly optimized. Recently, parallel and distributed optimization methods have emerged as a powerful tool…
A non-intrusive proper generalized decomposition (PGD) strategy, coupled with an overlapping domain decomposition (DD) method, is proposed to efficiently construct surrogate models of parametric linear elliptic problems. A parametric…
In this paper, we consider the decentralized optimization problems with generalized orthogonality constraints, where both the objective function and the constraint exhibit a distributed structure. Such optimization problems, albeit…
Gaussian Mixture Models (GMMs) range among the most frequently used models in machine learning. However, training large, general GMMs becomes computationally prohibitive for datasets that have many data points $N$ of high-dimensionality…
Merging the two cultures of deep and statistical learning provides insights into structured high-dimensional data. Traditional statistical modeling is still a dominant strategy for structured tabular data. Deep learning can be viewed…
The implementation of a vast majority of machine learning (ML) algorithms boils down to solving a numerical optimization problem. In this context, Stochastic Gradient Descent (SGD) methods have long proven to provide good results, both in…
We contribute improvements to a Lagrangian dual solution approach applied to large-scale optimization problems whose objective functions are convex, continuously differentiable and possibly nonlinear, while the non-relaxed constraint set is…
A fundamental challenge for machine learning models is generalizing to out-of-distribution (OOD) data, in part due to spurious correlations. To tackle this challenge, we first formalize the OOD generalization problem as constrained…
Generalized sampling is a recently developed linear framework for sampling and reconstruction in separable Hilbert spaces. It allows one to recover any element in any finite-dimensional subspace given finitely many of its samples with…
Stochastic gradient descent (SGD) algorithm and its variations have been effectively used to optimize neural network models. However, with the rapid growth of big data and deep learning, SGD is no longer the most suitable choice due to its…
This paper considers the decentralized optimization problem of minimizing a finite sum of strongly convex and twice continuously differentiable functions over a fixed-connected undirected network. A fully decentralized primal-dual…
We study a class of aggregate-join queries with multiple aggregation operators evaluated over annotated relations. We show that straightforward extensions of standard multiway join algorithms and generalized hypertree decompositions (GHDs)…
We introduce a unified framework for the study of multilevel mixed integer linear optimization problems and multistage stochastic mixed integer linear optimization problems with recourse. The framework highlights the common mathematical…
In this paper, we aim at developing computationally tractable methods for nonlinear model/controller reduction. Recently, model reduction by generalized differential (GD) balancing has been proposed for nonlinear systems with constant…