13 papers · ranked by Valyu relevance
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…
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…
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…
Alfonso Landeros, Oscar Hernan Madrid Padilla, Hua Zhou, Kenneth Lange
'Kenneth Lange'] The current paper studies the problem of minimizing a loss f(x) subject to constraints of the form Dx ∈ S, where S is a closed set, convex or not, and D is a matrix that fuses parameters. Fusion constraints can capture smoothness, sparsity, or more general constraint patterns. To tackle this generic…
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…
Omar M. Sleem, M.E. Ashour, N. S. Aybat, Constantino M. Lagoa
Sparsity finds applications in diverse areas such as statistics, machine learning, and signal processing. Computations over sparse structures are less complex compared to their dense counterparts and need less storage. This paper proposes a heuristic method for retrieving sparse approximate solutions of optimization…
Rafal Zdunek, Andrzej Cichocki
Recently, a considerable growth of interest in projected gradient (PG) methods has been observed due to their high efficiency in solving large-scale convex minimization problems subject to linear constraints. Since the minimization problems underlying nonnegative matrix factorization (NMF) of large matrices well…
Junjie Xia, Hoang Van Phan, Luke Vistain, Mengjie Chen + 3 more
'Savaş Tay' 'Shihua Zhang'] Proximity sequencing (Prox-seq) simultaneously measures gene expression, protein expression and protein complexes on single cells. Using information from dual-antibody binding events, Prox-seq infers surface protein dimers at the single-cell level. Prox-seq provides multi-dimensional…
C. B. Scott, Eric Mjolsness, Gabriele Oliva
We define a new family of similarity and distance measures on graphs, and explore their theoretical properties in comparison to conventional distance metrics. These measures are defined by the solution(s) to an optimization problem which attempts find a map minimizing the discrepancy between two graph Laplacian…
Josep M. Porta, Aleix Rull, Federico Thomas, Leonhard M. Reindl
The sensor localization problem can be formalized using distance and orientation constraints, typically in 3D. Local methods can be used to refine an initial location estimation, but in many cases such estimation is not available and a method able to determine all the feasible solutions from scratch is necessary.…
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…
Oliver Serang, Jérémie Bourdon
Linear programming (LP) problems are commonly used in analysis and resource allocation, frequently surfacing as approximations to more difficult problems. Existing approaches to LP have been dominated by a small group of methods, and randomized algorithms have not enjoyed popularity in practice. This paper introduces a…
Marco Bertini, Francesco Ferrante, Laura Gueci, Antonio Prestianni + 3 more
Perspectives on CO/H 2 PROX over MnO 2 Composite Catalysts Authors: ['Marco Bertini' 'Francesco Ferrante' 'Laura Gueci' 'Antonio Prestianni' 'Dario Duca' 'Francesco Arena' 'Dmitry Yu. Murzin'] This study presents a graph-based approach to investigate the steady-state kinetics of the preferential CO oxidation process in…