21 papers · ranked by Valyu relevance
Dmitriy Drusvyatskiy, Courtney Paquette
We consider global efficiency of algorithms for minimizing a sum of a convex function and a composition of a Lipschitz convex function with a smooth map. The basic algorithm we rely on is the prox-linear method, which in each iteration solves a regularized subproblem formed by linearizing the smooth map. When the…
Kevin L. Keys, Hua Zhou, Kenneth Lange
Proximal distance algorithms combine the classical penalty method of constrained minimization with distance majorization. If f(x) is the loss function, and C is the constraint set in a constrained minimization problem, then the proximal distance principle mandates minimizing the penalized loss…
Kevin L. Keys, Hua Zhou, Kenneth Lange
Proximal distance algorithms combine the classical penalty method of constrained minimization with distance majorization. If f(x) is the loss function, and C is the constraint set in a constrained minimization problem, then the proximal distance principle mandates minimizing the penalized loss f(x) + ρ 2 dist(x, C) 2…
Sorin-Mihai Grad, Felipe Lara
We introduce and investigate a new generalized convexity notion for functions called prox-convexity. The proximity operator of such a function is single-valued and firmly nonexpansive. We provide examples of (strongly) quasiconvex, weakly convex, and DC (difference of convex) functions that are prox-convex, however…
Ziqiang Shi
In this work, we generalized and unified recent two completely different works of Jascha [9] and Lee [2] respectively into one by proposing the proximal stochastic Newton-type gradient (PROXTONE) method for optimizing the sums of two convex functions: one is the average of a huge number of smooth convex functions, and…
Stanley Osher, Howard Heaton, Samy Wu Fung
Title: Significance Many objective functions do not admit explicit formulas for their proximal operators. Moreover, these operators often cannot be estimated using exact gradients (e.g., when objectives are accessible via an oracle). In this work, we give a formula for accurately approximating proximal operators using…
Clarice Poon, Jingwei Liang, Carola‐Bibiane Schönlieb
Over the past ten years, driven by large scale optimisation problems arising from machine learning, the development of stochastic optimisation methods have witnessed a tremendous growth. However, despite their popularity, the theoretical understandings of these methods are quite limited in contrast to the deterministic…
Niao He, Zaïd Harchaoui
We propose a new first-order optimisation algorithm to solve high-dimensional non-smooth composite minimisation problems. Typical examples of such problems have an objective that decomposes into a non-smooth empirical risk part and a non-smooth regularisation penalty. The proposed algorithm, called Semi-Proximal…
Georg Hahn, Sharon M. Lutz, Nilanjana Laha, Christoph Lange
Penalized linear regression approaches that include an L_1_ term have become an important tool in statistical data analysis. One prominent example is the least absolute shrinkage and selection operator (Lasso), though the class of L_1_ penalized regression operators also includes the fused and graphical Lasso, the…
Anatoli Juditsky, Arkadi Nemirovski
The standard algorithms for solving large-scale convex-concave saddle point problems, or, more generally, variational inequalities with monotone operators, are proximal type algorithms which at every iteration need to compute a prox-mapping, that is, to minimize over problem's domain X the sum of a linear form and the…
Yu Huo, Hongpei Li, Xiao Wang, Xiaochen Du + 1 more
When analysing two-dimensional data sets, scientists are often interested in regions where one variable depends linearly on the other. Typically they use an ad hoc method to do so. Here we develop a statistically rigorous, Bayesian approach to infer the optimal partitioning of a data set into contiguous piece-wise…
Georg Hahn, Sharon M. Lutz, Nilanjana Laha, Michael Cho + 2 more
High dimensional linear regression problems are often fitted using LASSO-type approaches. Although the LASSO objective function is convex, it is not differentiable everywhere, making the use of gradient descent methods for minimization not straightforward. To avoid this technical issue, we apply Nesterov smoothing to…
Junjie Xia, Hoang Van Phan, Luke Vistain, Mengjie Chen + 2 more
Proximity sequencing (Prox-seq) measures gene expression, protein expression, and protein complexes at the single cell level, using information from dual-antibody binding events and a single cell sequencing readout. Prox-seq provides multi-dimensional phenotyping of single cells and was recently used to track the…
Luke Vistain, Hoang Van Phan, Christian Jordi, Mengjie Chen + 2 more
Multiplexed analysis of single-cells enables accurate modeling of cellular behaviors, classification of new cell types, and characterization of their functional states. Here we present proximity-sequencing (Prox-seq), a method for simultaneous measurement of an individual cell’s proteins, protein complexes and mRNA.…
Fuchao Wu, Ming Zhang, Guanghui Wang, Zhanyi Hu + 1 more
Line triangulation, a classical geometric problem in computer vision, is to determine the 3D coordinates of a line based on its 2D image projections from more than two views of cameras with known projection matrices. Compared to point features, line segments are more robust to matching errors, occlusions, and image…
Jan Schröder, Yair Censor, Philipp Süss, Karl-Heinz Küfer
Given a family of linear constraints and a linear objective function one can consider whether to apply a Linear Programming (LP) algorithm or use a Linear Superiorization (LinSup) algorithm on this data. In the LP methodology one aims at finding a point that fulfills the constraints and has the minimal value of the…
Authors not listed
We present a fast, asymptotically linear-scaling implementation of the perturbative quadruples energy correction in coupled-cluster theory using local natural orbitals. Our work follows the domain-based local pair natural orbital (DLPNO) approach previously applied to lower levels of excitations in coupled-cluster…
C.S. Elder, Minh Hoang, Mohsen Ferdosi, Carl Kingsford
The Beltway and Turnpike problems entail the reconstruction of circular and linear one-dimensional point sets from unordered pairwise distances. These problems arise in computational biology when the measurements provide distances but do not associate those distances with the entities that gave rise to them. Such…
Kevin Robben, Christopher Cheatum
We report a comprehensive study of the efficacy of least-squares fitting of multidimensional spectra to generalized Kubo lineshape models and introduce a novel least-squares fitting metric, termed the Scale Invariant Gradient Norm (SIGN), that enables a highly reliable and versatile algorithm. The precision of…
Qianxiang Ai, Joshua Schrier
In a recent paper in this journal (Chem. Mater. 2022, 34, 2545-2552), Twyman et al. studied the environmental stability of crystals by introducing a greedy heuristic algorithm for determining possible oxidation reactions. We show how the problem can be solved exactly, with less code and comparable computational time by…
Eric Hermes, Khachik Sargsyan, Habib Najm, Judit Zádor
We present a new algorithm for the optimization of molecular structures to saddle points on the potential energy surface using a redundant internal coordinate system. This algorithm automates the procedure of defining the internal coordinate system, including the handling of linear bending angles, e.g. through the…