23 papers · ranked by Valyu relevance
Hanyang Li, Ying Cui
In nonsmooth optimization, a negative subgradient is not necessarily a descent direction, making the design of convergent descent methods based on zeroth-order and first-order information a challenging task. The well-studied bundle methods and gradient sampling algorithms construct descent directions by aggregating…
Anton Rodomanov, Yurii Nesterov
In this paper, we present a new ellipsoid-type algorithm for solving nonsmooth problems with convex structure. Examples of such problems include nonsmooth convex minimization problems, convex-concave saddle-point problems and variational inequalities with monotone operator. Our algorithm can be seen as a combination of…
Xiao Li, Lei Zhao, Daoli Zhu, Anthony Man–Cho So
The subgradient method is one of the most fundamental algorithmic schemes for nonsmooth optimization. The existing complexity and convergence results for this algorithm are mainly derived for Lipschitz continuous objective functions. In this work, we first extend the typical complexity results for the subgradient…
Moslem Zamani, François Glineur
We first introduce a proof technique that generalizes the standard analysis of subgradient methods. It is based on tracking the distance between the current iterate and a different reference point at each iteration. Using this technique, we obtain the exact worst-case convergence rate for the objective accuracy of the…
Bennet Gebken, Sebastian Peitz
In this article, we present an efficient descent method for locally Lipschitz continuous multiobjective optimization problems (MOPs). The method is realized by combining a theoretical result regarding the computation of descent directions for nonsmooth MOPs with a practical method to approximate the subdifferentials of…
Kazuhiro Hishinuma, Hideaki Iiduka
The existing machine learning algorithms for minimizing the convex function over a closed convex set suffer from slow convergence because their learning rates must be determined before running them. This paper proposes two machine learning algorithms incorporating the line search method, which automatically and…
Yue Tu, Shukuan Lin, Jianzhong Qiao, Peng Zhang + 2 more
'Fabio Baselice'] Alzheimer’s disease (AD), a neuropsychiatric disorder, continually arises in the elderly. To date, no targeted medications have been developed for AD. Early and fast diagnosis of AD plays a pivotal role in identifying potential AD patients, enabling timely medical interventions, and mitigating disease…
Bicheng Ying, Ali H. Sayed
—In this work and the supporting Part II [2], we examine the performance of stochastic sub-gradient learning strategies under weaker conditions than usually considered in the literature. The new conditions are shown to be automatically satisfied by several important cases of interest including SVM, LASSO, and…
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…
Ademir Alves Aguiar, O. P. Ferreira, L. F. Prudente
In this paper, we propose a new inexact version of the projected subgradient method to solve nondifferentiable constrained convex optimization problems. The method combine ǫ-subgradient method with a procedure to obtain a feasible inexact projection onto the constraint set. Asymptotic convergence results and…
Yijie Wang, Xiaoning Qian
Functional module identification in biological networks may provide new insights into the complex interactions among biomolecules for a better understanding of cellular functional organization. Most of existing functional module identification methods are based on the optimization of network modularity and cluster…
Kiyuob Jung, Jehan Oh
Root-Linear Convergence Authors: ['Kiyuob Jung' 'Jehan Oh'] In this paper, we find the special case of the subgradient method minimizing a one-dimensional real-valued function, which we term the specular gradient method, that converges root-linearly without any additional assumptions except the convexity. Furthermore…
Songnian He, Tao Wu
In the setting of Hilbert space, a modified subgradient extragradient method is proposed for solving Lipschitz-continuous and monotone variational inequalities defined on a level set of a convex function. Our iterative process is relaxed and self-adaptive, that is, in each iteration, calculating two metric projections…
Kazunori D Yamada
In the deep learning era, a gradient descent method is the most common method to optimize parameters of neural networks. Among various mathematical optimization methods, a gradient descent method is the most naive method. Although controlling a learning rate of the method is necessary for quick convergence, the…
Frank Dondelinger, Sach Mukherjee
We consider high-dimensional regression over subgroups of observations. Our work is motivated by biomedical problems, where disease subtypes, for example, may differ with respect to underlying regression models, but sample sizes at the subgroup-level may be limited. We focus on the case in which subgroup-specific…
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…
Samuel Schmidgall, Joe Hays
We propose that in order to harness our understanding of neuroscience toward machine learning, we must first have powerful tools for training brain-like models of learning. Although substantial progress has been made toward understanding the dynamics of learning in the brain, neuroscience-derived models of learning…
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…
Ray Zirui Zhang, Christopher E. Miles, Xiaohui Xie, John S. Lowengrub
We propose a new neural network based method for solving inverse problems for partial differential equations (PDEs) by formulating the PDE inverse problem as a bilevel optimization problem. At the upper level, we minimize the data loss with respect to the PDE parameters. At the lower level, we train a neural network to…
Christine H. Lind, Angela J. Yu
Several recent papers have studied the double descent phenomenon: a classic U-shaped empirical risk curve when the number of parameters is smaller or equal to the number of data points, followed by a decrease in empirical risk (referred to as “second descent”) as the number of features is increased past the…
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…
Authors not listed
We present a comprehensive theoretical analysis of quantum subspace diagonalization methods for molecular electronic structure calculations, establishing rigorous complexity bounds and convergence guarantees. Building on recent developments in adaptive quantum algorithms for chemical systems, we formulate a general…