22 papers · ranked by Valyu relevance
Steven Diamond, Stephen Boyd
CVXPY is a domain-specific language for convex optimization embedded in Python. It allows the user to express convex optimization problems in a natural syntax that follows the math, rather than in the restrictive standard form required by solvers. CVXPY makes it easy to combine convex optimization with high-level…
Madeleine Udell, Karanveer Mohan, David Zeng, Jenny Hong + 2 more
'Steven Diamond' 'Stephen Boyd'] This paper describes Convex1 , a convex optimization modeling framework in Julia. Convex translates problems from a user-friendly functional language into an abstract syntax tree describing the problem. This concise representation of the global structure of the problem allows Convex to…
Xinyue Shen, Steven Diamond, Yuantao Gu, Stephen Boyd
In this paper we introduce disciplined convex-concave programming (DCCP), which combines the ideas of disciplined convex programming (DCP) with convex-concave programming (CCP). Convex-concave programming is an organized heuristic for solving nonconvex problems that involve objective and constraint functions that are a…
Wei Wei
| A | | Basics of Linear and Conic Programs | 7 | | --- | --- | --- | --- | | | A.1 | Basic Notations 8 | | | | | A.1.1 Convex Sets 8 | | | | | A.1.2 Generalized Inequalities 13 | | | | | A.1.3 Dual Cones and Dual Generalized Inequalities 14 | | | | | A.1.4 Convex Function and Epigraph 16 | | | | A.2 | From Linear to…
Alnur Ali, Eric Wong, J. Zico Kolter
We introduce Newton-ADMM, a method for fast conic optimization. The basic idea is to view the residuals of consecutive iterates generated by the alternating direction method of multipliers (ADMM) as a set of fixed point equations, and then use a nonsmooth Newton method to find a solution; we apply the basic idea to the…
Min Sun, Jing Liu
As a first-order method, the augmented Lagrangian method (ALM) is a benchmark solver for linearly constrained convex programming, and in practice some semi-definite proximal terms are often added to its primal variable’s subproblem to make it more implementable. In this paper, we propose an accelerated PALM with…
Ali Ünlü
This paper presents the technical details of the software package SDT in the R computing and graphics environment, implementing a convex quadratic program that was recently proposed in the literature on self-determination theory of human motivation. Three main features are addressed, with their accompanying code for…
Zhenwei Lin, Zikai Xiong, Dongdong Ge, Yinyu Ye
In this paper, we introduce the Primal-Dual Conic Programming Solver (PDCS), a largescale conic programming solver with GPU enhancements. Problems that PDCS currently supports include linear programs, second-order cone programs, convex quadratic programs, and exponential cone programs. PDCS achieves scalability to…
Min Sun, Yiju Wang
The Jacobian decomposition and the Gauss-Seidel decomposition of augmented Lagrangian method (ALM) are two popular methods for separable convex programming. However, their convergence is not guaranteed for three-block separable convex programming. In this paper, we present a modified hybrid decomposition of ALM…
Abdullah Makkeh, Dirk Oliver Theis, Raul Vicente
Makkeh, Theis, and Vicente found that Cone Programming model is the most robust to compute the Bertschinger et al. partial information decomposition (BROJA PID) measure. We developed a production-quality robust software that computes the BROJA PID measure based on the Cone Programming model. In this paper, we prove the…
Sebastian Banert, Radu Ioan Boț
The possibilities of exploiting the special structure of d.c. programs, which consist of optimising the difference of convex functions, are currently more or less limited to variants of the DCA proposed by Pham Dinh Tao and Le Thi Hoai An in 1997. These assume that either the convex or the concave part, or both, are…
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…
Daniel Dadush, Friedrich Eisenbrand, Thomas Rothvoss
Approximate integer programming is the following: For a given convex body $K \subseteq{\mathbb{R}}^n$, either determine whether $K \cap{\mathbb{Z}}^n$ is empty, or find an integer point in the convex body $2\cdot K - c +c$ which is K, scaled by 2 from its center of gravity c. Approximate integer programming can be…
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…
Tanmaya Karmarkar, Yves Lucet
We propose the first linear-time algorithm to compute the conjugate of (nonconvex) bivariate piecewise linear-quadratic (PLQ) functions (bivariate quadratic functions defined on a polyhedral subdivision). Our algorithm starts with computing the convex envelope of each quadratic piece obtaining rational functions…
Hansol X. Ryu, Manoj Srinivasan
Studying how humans perceive patterns in visually presented data is useful for understanding data-based decision-making and potentially understanding visually mediated sensorimotor control. We conducted experiments to examine how human subjects perform the simplest machine learning or statistical estimation tasks…
Authors not listed
Solving optimization problems, especially for nonlinear and constrained systems, is a challenge. Decades of specialized algorithms have been developed for general and special cases of root finding, minimization (including constraints), for parameter estimation, and mapping connected spaces. These approaches typically…
Naoki Kogo, Vicky Froyen
The visual system performs remarkably well to perceive depth order of surfaces without stereo disparity, indicating the importance of figure-ground organization based on pictorial cues. To understand how figure-ground organization emerges, it is essential to investigate how the global configuration of an image is…
Gunnar Schmidtmann, Nicholas Baker, Kevin J. Lande, Filipp Schmidt
Physiological and psychophysical evidence suggests that the visual system represents object outlines using prominent curvature features, particularly regions of extreme curvature (convex maxima and concave minima). These curvature extrema often coincide with points of high informational content (“surprisal”), but this…
Authors not listed
We comment on the work on convex regions of the potential energy surface (PES) of a molecule by M. Gunde; A. Jay; M. Poberˇznik; N. Salles; N. Richard; G. Landa; N. Mousseau; L. Martin-Samos and A. Hemeryck [J. Chem. Phys. 160, 232501 (2024)]. In contrast to the activation-relaxation technique nouveau (ARTn), in the…
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…
Yanjun Sun, Douglas A Nitz, Xiangmin Xu, Lisa M Giocomo
Corners are a cardinal feature of many of the complex environmental geometries found in the natural world but the neural substrates that could underlie the perception of corners remain elusive. Here we show that the dorsal subiculum contains neurons that encode corners across environmental geometries in an allocentric…