Related papers: A fast and scalable bottom-left-fill algorithm to …
We propose and analyze a numerical algorithm for solving a class of optimal control problems for learning-informed semilinear partial differential equations. The latter is a class of PDEs with constituents that are in principle unknown and…
We extend a primal-dual fixed point algorithm (PDFP) proposed in [5] to solve two kinds of separable multi-block minimization problems, arising in signal processing and imaging science. This work shows the flexibility of applying PDFP…
Dense image matching is a fundamental low-level problem in Computer Vision, which has received tremendous attention from both discrete and continuous optimization communities. The goal of this paper is to combine the advantages of discrete…
Robotic grasping, the ability of robots to reliably secure and manipulate objects of varying shapes, sizes and orientations, is a complex task that requires precise perception and control. Deep neural networks have shown remarkable success…
A central challenge to many fields of science and engineering involves minimizing non-convex error functions over continuous, high dimensional spaces. Gradient descent or quasi-Newton methods are almost ubiquitously used to perform such…
Convex clustering is a modern method with both hierarchical and $k$-means clustering characteristics. Although convex clustering can capture complex clustering structures hidden in data, the existing convex clustering algorithms are not…
We consider distributed optimization methods for problems where forming the Hessian is computationally challenging and communication is a significant bottleneck. We leverage randomized sketches for reducing the problem dimensions as well as…
We introduce and prove convergence of a damped Newton algorithm to approximate solutions of the semi-discrete optimal transport problem with storage fees, corresponding to a problem with hard capacity constraints. This is a variant of the…
We present a new algorithmic paradigm for the decentralized solution of graph-structured optimization problems that arise in the estimation and control of network systems. A key and novel design concept of the proposed approach is that it…
This work studies rearrangement problems involving the sorting of robots or objects in stack-like containers, which can be accessed only from one side. Two scenarios are considered: one where every robot or object needs to reach a…
With the aggressive scaling of VLSI technology, the explosion of layout patterns creates a critical bottleneck for DFM applications like OPC. Pattern clustering is essential to reduce data complexity, yet existing methods struggle with…
A hypergraph ${\cal F}$ is a set family defined on vertex set $V$. The dual of ${\cal F}$ is the set of minimal subsets $H$ of $V$ such that $F\cap H \ne \emptyset$ for any $F\in {\cal F}$. The computation of the dual is equivalent to many…
This paper studies the set cover problem under the semi-streaming model. The underlying set system is formalized in terms of a hypergraph $G = (V, E)$ whose edges arrive one-by-one and the goal is to construct an edge cover $F \subseteq E$…
In this paper, we develop regularized discrete least squares collocation and finite volume methods for solving two-dimensional nonlinear time-dependent partial differential equations on irregular domains. The solution is approximated using…
The matrix completion problem aims to reconstruct a low-rank matrix based on a revealed set of possibly noisy entries. Prior works consider completing the entire matrix with generalization error guarantees. However, the completion accuracy…
This paper concerns a fundamental class of convex matrix optimization problems. It presents the first algorithm that uses optimal storage and provably computes a low-rank approximation of a solution. In particular, when all solutions have…
Problems in scientific computing, such as distributing large sparse matrix operations, have analogous formulations as hypergraph partitioning problems. A hypergraph is a generalization of a traditional graph wherein "hyperedges" may connect…
In this paper, we present several improvements in the parallelization of the in-place merge algorithm, which merges two contiguous sorted arrays into one with an O(T) space complexity (where T is the number of threads). The approach divides…
In this paper, we present an advanced approach to solving the inverse rig problem in blendshape animation, using high-quality corrective blendshapes. Our algorithm introduces novel enhancements in three key areas: ensuring high data…
In this paper, we study temporal splitting algorithms for multiscale problems. The exact fine-grid spatial problems typically require some reduction in degrees of freedom. Multiscale algorithms are designed to represent the fine-scale…