Related papers: A Primal-Dual Level Set Method for Computing Geode…
The rapid advancements in high-dimensional statistics and machine learning have increased the use of first-order methods. Many of these methods can be regarded as instances of the proximal point algorithm. Given the importance of the…
Dual decomposition has been successfully employed in a variety of distributed convex optimization problems solved by a network of computing and communicating nodes. Often, when the cost function is separable but the constraints are coupled,…
In this paper, we study triply periodic surfaces with minimal surface area under a constraint in the volume fraction of the regions (phases) that the surface separates. Using a variational level set method formulation, we present a…
The proximal gradient method is a splitting algorithm for the minimization of the sum of two convex functions, one of which is smooth. It has applications in areas such as mechanics, inverse problems, machine learning, image reconstruction,…
An universal primal-dual approach of description equilibriums in large class of hierarchical congestion population games is proposed. At the very core of the approach is hierarchy of enclosed to each other transport networks. In different…
A vertex set $S$ of a graph $G$ is geodetic if every vertex of $G$ lies on a shortest path between two vertices in $S$. Given a graph $G$ and $k \in \mathbb N$, the NP-hard Geodetic Set problem asks whether there is a geodetic set of size…
Classical multidimensional scaling only works well when the noisy distances observed in a high dimensional space can be faithfully represented by Euclidean distances in a low dimensional space. Advanced models such as Maximum Variance…
The Euler scheme is up to date the most important numerical method for ordinary differential inclusions, because the use of the available higher-order methods is prohibited by their enormous complexity after spatial discretization.…
Multilevel optimization has gained renewed interest in machine learning due to its promise in applications such as hyperparameter tuning and continual learning. However, existing methods struggle with the inherent difficulty of efficiently…
In this paper, we consider a nonsmooth convex finite-sum problem with a conic constraint. To overcome the challenge of projecting onto the constraint set and computing the full (sub)gradient, we introduce a primal-dual incremental gradient…
Partial differential equations (PDEs) on surfaces appear in many applications throughout the natural and applied sciences. The classical closest point method (Ruuth and Merriman, J. Comput. Phys. 227(3):1943-1961, [2008]) is an embedding…
Computing geodesic distances on 3D surfaces is fundamental to many tasks in 3D vision and geometry processing, with deep connections to tasks such as shape correspondence. Recent learning-based methods achieve strong performance but rely on…
This paper describes an interdisciplinary approach to geometry modeling of geospatial boundaries. The objective is to extract surfaces from irregular spatial patterns using differential geometry and obtain coherent directional predictions…
We present a general purpose method for solving partial differential equations on a closed surface, based on a technique for discretizing the surface introduced by Wenjun Ying and Wei-Cheng Wang [J. Comput. Phys. 252 (2013), pp. 606-624]…
Geodesic models are known as an efficient tool for solving various image segmentation problems. Most of existing approaches only exploit local pointwise image features to track geodesic paths for delineating the objective boundaries.…
We show that the primal-dual gradient method, also known as the gradient descent ascent method, for solving convex-concave minimax problems can be viewed as an inexact gradient method applied to the primal problem. The gradient, whose exact…
Many geometric machine learning and image analysis applications, require a left-invariant metric on the 5D homogeneous space of 3D positions and orientations SE(3)/SO(2). This is done in Equivariant Neural Networks (G-CNNs), or in PDE-Based…
Primal-dual splitting schemes are a class of powerful algorithms that solve complicated monotone inclusions and convex optimization problems that are built from many simpler pieces. They decompose problems that are built from sums, linear…
Geodesic tracking on the projective line bundle $\R^2 \times P^1 $ has many uses, including the segmentation of objects in images. However, global tracking requires expensive distance map computations. We provide a practical solution to…
We consider simple bilevel optimization problems where the goal is to compute among the optimal solutions of a composite convex optimization problem, one that minimizes a secondary objective function. Our main contribution is threefold. (i)…