27 papers · ranked by Valyu relevance
V. S. Mikhalevich, A. M. Gupal, V. I. Norkin
This book is devoted to finite-dimensional problems of non-convex nonsmooth optimization and numerical methods for their solution. The complexity theory of extremal problems states that nonconvex problems as an object of study are very complex, and the complexity of obtaining a guaranteed solution increases…
Buyun Liang, Ju Sun
Optimizing nonconvex (NCVX) problems, especially nonsmooth and constrained ones, is an essential part of machine learning. However, it can be hard to reliably solve such problems without optimization expertise. Existing general-purpose NCVX optimization packages are powerful but typically cannot handle nonsmoothness.…
Daria Ghilli, Karl Kunisch
A general class of nonconvex optimization problems is considered, where the penalty is the composition of a linear operator with a nonsmooth nonconvex mapping, which is concave on the positive real line. The necessary optimality condition of a regularized version of the original problem is solved by means of a…
Rina Foygel Barber, Emil Y. Sidky
Many optimization problems arising in high-dimensional statistics decompose naturally into a sum of several terms, where the individual terms are relatively simple but the composite objective function can only be optimized with iterative algorithms. In this paper, we are interested in optimization problems of the form…
Chunshan Xue, Hongwei Jiao, Jingben Yin, Yongqiang Chen
This paper presents a novel range division and contraction approach for globally solving nonconvex quadratic program with quadratic constraints. By constructing new underestimating linear relaxation functions, we can transform the initial nonconvex quadratic program problem into a linear program relaxation problem. By…
Rina Foygel Barber, Emil Y. Sidky
The alternating direction method of multipliers (ADMM) algorithm is a powerful and flexible tool for complex optimization problems of the form $min{f(x)+g(y):Ax+By=c}$. ADMM exhibits robust empirical performance across a range of challenging settings including nonsmoothness and nonconvexity of the objective functions…
Michael Muehlebach, Michael I. Jordan
We exploit analogies between first-order algorithms for constrained optimization and non-smooth dynamical systems to design a new class of accelerated first-order algorithms for constrained optimization. Unlike Frank-Wolfe or projected gradients, these algorithms avoid optimization over the entire feasible set at each…
Quanming Yao, James T. Kwok
The use of convex regularizers allows for easy optimization, though they often produce biased estimation and inferior prediction performance. Recently, nonconvex regularizers have attracted a lot of attention and outperformed convex ones. However, the resultant optimization problem is much harder. In this paper, for a…
Zhishuai Guo, Yan Yan, Zhuoning Yuan, Tianbao Yang
This paper focuses on stochastic methods for solving smooth non-convex strongly-concave min-max problems, which have received increasing attention due to their potential applications in deep learning (e.g., deep AUC maximization, distributionally robust optimization). However, most of the existing algorithms are slow…
Peiping Shen, Chunfeng Wang
This paper presents a linear decomposition approach for a class of nonconvex programming problems by dividing the input space into polynomially many grids. It shows that under certain assumptions the original problem can be transformed and decomposed into a polynomial number of equivalent linear programming…
Qiegen Liu, Xi Peng, Jianbo Liu, Dingcheng Yang + 1 more
Nonconvex optimization has shown that it needs substantially fewer measurements than l1 minimization for exact recovery under fixed transform/overcomplete dictionary. In this work, two efficient numerical algorithms which are unified by the method named weighted two-level Bregman method with dictionary updating…
Pouria Mahdavinia, Yuyang Deng, Haochuan Li, Mehrdad Mahdavi
Despite the established convergence theory of Optimistic Gradient Descent Ascent (OGDA) and Extragradient (EG) methods for the convex-concave minimax problems, little is known about the theoretical guarantees of these methods in nonconvex settings. To bridge this gap, for the first time, this paper establishes the…
Amrit Singh Bedi, Ketan Rajawat, Vaneet Aggarwal
Optimizing non-convex functions is of primary importance in the vast majority of machine learning algorithms. Even though many gradient descent based algorithms have been studied, successive convex approximation based algorithms have been recently empirically shown to converge faster. However, such successive convex…
Kyongson Jon, Jun Liu, Xiaoguang Lv, Wensheng Zhu + 1 more
The restoration of the Poisson noisy images is an essential task in many imaging applications due to the uncertainty of the number of discrete particles incident on the image sensor. In this paper, we consider utilizing a hybrid regularizer for Poisson noisy image restoration. The proposed regularizer, which combines…
Chris Vogl, Peng Zheng, Stephen P. Seslar, Aleksandr Y. Aravkin
We consider the problem of locating a point-source heart arrhythmia using data from a standard diagnostic procedure, where a reference catheter is placed in the heart, and arrival times from a second diagnostic catheter are recorded as the diagnostic catheter moves around within the heart. We model this situation as a…
Abiy Tasissa, Rongjie Lai, Chunyu Wang
The problem of finding the configuration of points given partial information on pairwise inter-point distances, the Euclidean distance geometry problem, appears in multiple applications. In this paper, we propose an approach that integrates homology modeling and a nonconvex distance geometry algorithm for the protein…
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…
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…
Giulio Tani Raffaelli, Jakub Kislinger, Tomáš Kroupa, Jaroslav Hlinka
Quantifying higher-order statistical dependencies in multivariate biomedical data is essential for understanding collective dynamics in complex systems such as neuronal populations. The connected information framework provides a principled decomposition of the total information content into contributions from…
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…
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…
I. V. Konnov
We suggest a conjugate subgradient type method without any line-search for minimization of convex non differentiable functions. Unlike the custom methods of this class, it does not require monotone decrease of the goal function and reduces the implementation cost of each iteration essentially. At the same time, its…
Akhil Shajan, Madushanka Manathunga, Andreas Goetz, Kenneth Merz
Based on a series of energy minimizations with starting structures obtained from the Baker test set of 30 organic molecules, a comparison is made between various open source geometry optimization codes that are interfaced with the open-source QUantum Interaction Computational Kernel (QUICK) program for gradient and…
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…
Akhil Shajan, Madushanka Manathunga, Andreas Goetz, Kenneth Merz
Based on a series of energy minimizations with starting structures obtained from the Baker test set of 30 organic molecules, a comparison is made between various open- source geometry optimization codes that are interfaced with the open-source QUantum Interaction Computational Kernel (QUICK) program for gradient and…
AKHIL SHAJAN, Madushanka Manathunga, Andreas Goetz, Kenneth Merz
Based on a series of energy minimizations with starting structures obtained from the Baker test set of 30 organic molecules, a comparison is made between various open-source geometry optimization codes that are interfaced with the open-source QUantum Interaction Computational Kernel (QUICK) program for gradient and…