Related papers: A tensor optimization algorithm for computing Lagr…
We present a subgradient method for minimizing non-smooth, non-Lipschitz convex optimization problems. The only structure assumed is that a strictly feasible point is known. We extend the work of Renegar [5] by taking a different…
This paper presents an efficient gradient projection-based method for structural topological optimization problems characterized by a nonlinear objective function which is minimized over a feasible region defined by bilateral bounds and a…
The proximal gradient method is a generic technique introduced to tackle the non-smoothness in optimization problems, wherein the objective function is expressed as the sum of a differentiable convex part and a non-differentiable…
This paper provides a construction method of the nearest graph Laplacian to a matrix identified from measurement data of graph Laplacian dynamics that include biochemical systems, synchronization systems, and multi-agent systems. We…
We consider learning an undirected graphical model from sparse data. While several efficient algorithms have been proposed for graphical lasso (GL), the alternating direction method of multipliers (ADMM) is the main approach taken…
Augmented Lagrangian method (also called as method of multipliers) is an important and powerful optimization method for lots of smooth or nonsmooth variational problems in modern signal processing, imaging, optimal control and so on.…
This work is devoted to the numerical approximation of high-dimensional advection-diffusion equations. It is well-known that classical methods, such as the finite volume method, suffer from the curse of dimensionality, and that their time…
Graph Neural Networks (GNNs) have emerged as a dominant paradigm for graph classification. Specifically, most existing GNNs mainly rely on the message passing strategy between neighbor nodes, where the expressivity is limited by the…
The sparse group Lasso is a widely used statistical model which encourages the sparsity both on a group and within the group level. In this paper, we develop an efficient augmented Lagrangian method for large-scale non-overlapping sparse…
In this work, we propose Natural Hypergradient Descent (NHGD), a new method for solving bilevel optimization problems. To address the computational bottleneck in hypergradient estimation--namely, the need to compute or approximate Hessian…
This paper presents a method for approximate Gaussian process (GP) regression with tensor networks (TNs). A parametric approximation of a GP uses a linear combination of basis functions, where the accuracy of the approximation depends on…
Generating motions for robots interacting with objects of various shapes is a complex challenge, further complicated by the robot geometry and multiple desired behaviors. While current robot programming tools (such as inverse kinematics,…
Graph disaggregation is a technique used to address the high cost of computation for power law graphs on parallel processors. The few high-degree vertices are broken into multiple small-degree vertices, in order to allow for more efficient…
In this paper, we consider numerical approximations for the optimal partition problem using Lagrange multipliers. By rewriting it into constrained gradient flows, three and four steps numerical schemes based on the Lagrange multiplier…
We propose a linear time and constant space algorithm for computing Euclidean projections onto sets on which a normalized sparseness measure attains a constant value. These non-convex target sets can be characterized as intersections of a…
We investigate a generalized framework to estimate a latent low-rank plus sparse tensor, where the low-rank tensor often captures the multi-way principal components and the sparse tensor accounts for potential model mis-specifications or…
Multi-view learning has progressed rapidly in recent years. Although many previous studies assume that each instance appears in all views, it is common in real-world applications for instances to be missing from some views, resulting in…
We suggest a reduction of the combinatorial problem of hypergraph partitioning to a continuous optimization problem.
Nonlinear acceleration methods are powerful techniques to speed up fixed-point iterations. However, many acceleration methods require storing a large number of previous iterates and this can become impractical if computational resources are…
Tensor regression has shown to be advantageous in learning tasks with multi-directional relatedness. Given massive multiway data, traditional methods are often too slow to operate on or suffer from memory bottleneck. In this paper, we…