26 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…
Haoqian Li
This paper consists of four general parts: convex sets; convex functions; convex optimization; and the interior point algorithm. I will start by introducing the definition of convex sets and give three common convex set examples which will be used later in this paper, then prove the significant separating and…
Anjali Parashar, Priyank Srivastava, Anuradha M. Annaswamy, Biswadip Dey + 1 more
'Biswadip Dey' 'Amit Chakraborty'] Abstract— This paper presents a framework to solve constrained optimization problems in an accelerated manner based on High-Order Tuners (HT). Our approach is based on reformulating the original constrained problem as the unconstrained optimization of a loss function. We start with…
A. Enis Çetin, Alican Bozkurt, Osman Günay, Y. Hakan Habiboǧlu + 4 more
'Kıvanç Köse' 'İbrahim Onaran' 'Mohammad Tofighi' 'R. Akin Sevimli'] Two new optimization techniques based on projections onto convex space (POCS) framework for solving convex and some non-convex optimization problems are presented. The dimension of the minimization problem is lifted by one and sets corresponding to…
Nikita Doikov, Yurii Nesterov
In this paper, we study the iteration complexity of cubic regularization of Newton method for solving composite minimization problems with uniformly convex objective. We introduce the notion of second-order condition number of a certain degree and justify the linear rate of convergence in a nondegenerate case for the…
Radu Ioan Boţ, Axel Böhm
We investigate the convergence properties of incremental mirror descent type subgradient algorithms for minimizing the sum of convex functions. In each step, we only evaluate the subgradient of a single component function and mirror it back to the feasible domain, which makes iterations very cheap to compute. The…
Kushal K. Dey, Rahul Mazumder
Genes with correlated expression across individuals in multiple tissues are potentially informative for systemic genetic activity spanning these tissues. In this context, the tissue-level gene expression data across multiple subjects from the Genotype Tissue Expression (GTEx) Project is a valuable analytical resource.…
Anjali Parashar, Priyank Srivastava, Anuradha M. Annaswamy
— Convex optimization with equality and inequality constraints is a ubiquitous problem in several optimization and control problems in large-scale systems. Recently there has been a lot of interest in establishing accelerated convergence of the loss function. A class of high-order tuners was recently proposed in an…
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…
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…
Tianbao Yang, Qihang Lin, Lijun Zhang
This paper focuses on convex constrained optimization problems, where the solution is subject to a convex inequality constraint. In particular, we aim at challenging problems for which both projection into the constrained domain and a linear optimization under the inequality constraint are time-consuming, which render…
Yurii Nesterov
In this paper, we suggest a new framework for analyzing primal subgradient methods for nonsmooth convex optimization problems. We show that the classical step-size rules, based on normalization of subgradient, or on knowledge of the optimal value of the objective function, need corrections when they are applied to…
Gang Liu, Ting-Zhu Huang, Jun Liu, Xiao-Guang Lv + 1 more
The total variation (TV) regularization method is an effective method for image deblurring in preserving edges. However, the TV based solutions usually have some staircase effects. In order to alleviate the staircase effects, we propose a new model for restoring blurred images under impulse noise. The model consists of…
Abbas Kazemipour, Behtash Babadi, Min Wu, Kaspar Podgorski + 1 more
We consider the problem of optimizing general convex objective functions with nonnegativity constraints. Using the Karush-Kuhn-Tucker (KKT) conditions for the nonnegativity constraints we will derive fast multiplicative update rules for several problems of interest in signal processing, including non-negative…
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…
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…
Peter L. Bartlett, Chris Junchi Li, Jingfeng Wu, Bin Yu
In the field of optimization, developing accelerated methods for solving minimax and fixed-point problems remains a fundamental challenge. This paper presents a novel family of dual accelerated algorithms that achieve optimal convergence rates for both minimax and fixed-point problems. By exploring new anchoring…
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…
Authors not listed
With the ever-increasing demand for atomistic structures representative of real-life systems as well as the ad-vent of exascale computers, it has now become necessary and possible to use advanced global optimization (GO) techniques to intelligently sample the potential energy surface (PES). Given the previous studies…
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…
Lucian Chan, Geoffrey Hutchison, Garrett Morris
Generating low-energy molecular conformers is a key task for many areas of computational chemistry, molecular modeling and cheminformatics. Most current conformer generation methods primarily focus on generating geometrically diverse conformers rather than finding the most probable or energetically lowest minima. Here…
Lucian Chan, Geoffrey Hutchison, Garrett Morris
Generating low-energy molecular conformers is a key task for many areas of computational chemistry, molecular modeling and cheminformatics. Most current conformer generation methods primarily focus on generating geometrically diverse conformers rather than finding the most probable or energetically lowest minima. Here…
Fabian Fröhlich, Peter K. Sorger
Ordinary differential equation (ODE) models are widely used to describe biochemical processes, since they effectively represent mass action kinetics. Optimization-based calibration of ODE models on experimental data can be challenging, even for low-dimensional problems. However, reliable model calibration is a…
Riley Hickman, Priyansh Parakh, Austin Cheng, Qianxiang Ai + 3 more
Experiment planning algorithms are a required component of autonomous platforms for scientific discovery. Selecting a suitable optimization algorithm for a novel application is an important yet difficult choice a researcher has to make based on past empirical performance on similar tasks. To facilitate the evaluation…
Michael Hutcheon, Andrew Teale
Algorithms are presented for performing a topological analysis of an arbitrary function, evaluated on an arbitrary grid of points. These algorithms work strictly by post-processing the data and require no additional function evaluations. This is achieved by connecting the grid points with a neighbourhood graph…
Riley Hickman, Matteo Aldeghi, Alán Aspuru-Guzik
Model-based optimization strategies, such as Bayesian optimization (BO), have been deployed across the natural sciences in design and discovery campaigns due to their sample efficiency and flexibility. The combination of such strategies with automated laboratory equipment and/or high-performance computing in a…