Related papers: A tensor optimization algorithm for computing Lagr…
We present a novel efficient theoretical and numerical framework for solving global non-convex polynomial optimization problems. We analytically demonstrate that such problems can be efficiently reformulated using a non-linear objective…
Recent research has shown growing interest in modeling hypergraphs, which capture polyadic interactions among entities beyond traditional dyadic relations. However, most existing methodologies for hypergraphs face significant limitations,…
Computational efficiency is a major bottleneck in using classic graph-based approaches for semi-supervised learning on datasets with a large number of unlabeled examples. Known techniques to improve efficiency typically involve an…
We propose two numerical algorithms in the fully nonconvex setting for the minimization of the sum of a smooth function and the composition of a nonsmooth function with a linear operator. The iterative schemes are formulated in the spirit…
Efficient layout of large-scale graphs remains a challenging problem: the force-directed and dimensionality reduction-based methods suffer from high overhead for graph distance and gradient computation. In this paper, we present a new graph…
We propose a nonconvex estimator for joint multivariate regression and precision matrix estimation in the high dimensional regime, under sparsity constraints. A gradient descent algorithm with hard thresholding is developed to solve the…
In graph signal processing, data samples are associated to vertices on a graph, while edge weights represent similarities between those samples. We propose a convex optimization problem to learn sparse well connected graphs from data. We…
Lagrangian Neural Networks (LNNs) can learn arbitrary Lagrangians from trajectory data, but their unusual optimization objective leads to significant training instabilities that limit their application to complex systems. We propose several…
An efficient gradient-based method to solve the volume constrained topology optimization problems is presented. Each iterate of this algorithm is obtained by the projection of a Barzilai-Borwein step onto the feasible set consisting of box…
We study distributed optimization where nodes cooperatively minimize the sum of their individual, locally known, convex costs $f_i(x)$'s, $x \in {\mathbb R}^d$ is global. Distributed augmented Lagrangian (AL) methods have good empirical…
Hamiltonian Monte Carlo is a widely used algorithm for sampling from posterior distributions of complex Bayesian models. It can efficiently explore high-dimensional parameter spaces guided by simulated Hamiltonian flows. However, the…
We consider minimization of the sum of a large number of convex functions, and we propose an incremental aggregated version of the proximal algorithm, which bears similarity to the incremental aggregated gradient and subgradient methods…
The gradient-based optimization method for deep machine learning models suffers from gradient vanishing and exploding problems, particularly when the computational graph becomes deep. In this work, we propose the tangent-space gradient…
Robust tensor recovery plays an instrumental role in robustifying tensor decompositions for multilinear data analysis against outliers, gross corruptions and missing values and has a diverse array of applications. In this paper, we study…
This paper addresses a class of general nonsmooth and nonconvex composite optimization problems subject to nonlinear equality constraints. We assume that a part of the objective function and the functional constraints exhibit local…
Bayesian optimization is a popular and versatile approach that is well suited to solve challenging optimization problems. Their popularity comes from their effective minimization of expensive function evaluations, their capability to…
We consider a variable metric linesearch based proximal gradient method for the minimization of the sum of a smooth, possibly nonconvex function plus a convex, possibly nonsmooth term. We prove convergence of this iterative algorithm to a…
In this paper, we consider a nonconvex optimization problem with nonlinear equality constraints. We assume that both, the objective function and the functional constraints are locally smooth. For solving this problem, we propose a…
Bilevel optimization has been developed for many machine learning tasks with large-scale and high-dimensional data. This paper considers a constrained bilevel optimization problem, where the lower-level optimization problem is convex with…
The systematization of the purely Lagrangean approach to constrained systems in the form of an algorithm involves the iterative construction of a generalized Hessian matrix W taking a rectangular form. This Hessian will exhibit as many left…