English
Related papers

Related papers: Analysis of Convergence for the IPA-AC Method

200 papers

We propose a new algorithm for finite sum optimization which we call the curvature-aided incremental aggregated gradient (CIAG) method. Motivated by the problem of training a classifier for a d-dimensional problem, where the number of…

Machine Learning · Statistics 2017-10-26 Hoi-To Wai , Wei Shi , Angelia Nedic , Anna Scaglione

Minimax optimization has become a central tool in machine learning with applications in robust optimization, reinforcement learning, GANs, etc. These applications are often nonconvex-nonconcave, but the existing theory is unable to identify…

Optimization and Control · Mathematics 2021-04-02 Benjamin Grimmer , Haihao Lu , Pratik Worah , Vahab Mirrokni

The Method of Alternating Projections (MAP), a classical algorithm for solving feasibility prob- lems, has recently been intensely studied for nonconvex sets. However, intrinsically available are only local convergence results: convergence…

Optimization and Control · Mathematics 2013-05-21 Heinz H. Bauschke , Hung M. Phan , Xianfu Wang

Modern robotic systems are required to operate in challenging environments, which demand reliable localization under challenging conditions. LiDAR-based localization methods, such as the Iterative Closest Point (ICP) algorithm, can suffer…

Robotics · Computer Science 2024-02-20 Turcan Tuna , Julian Nubert , Yoshua Nava , Shehryar Khattak , Marco Hutter

The "Inertial Forward-Backward algorithm" (IFB) is a powerful tool for convex nonsmooth minimization problems, it gives the well known "fast iterative shrinkage-thresholding algorithm " (FISTA), which enjoys $O\left( {\frac{1}{{{k^2}}}}…

Optimization and Control · Mathematics 2022-02-25 Hongwei Liu , Ting Wang , Zexian Liu

Principal component analysis (PCA) is a classical and ubiquitous method for reducing data dimensionality, but it is suboptimal for heterogeneous data that are increasingly common in modern applications. PCA treats all samples uniformly so…

Statistics Theory · Mathematics 2021-12-02 David Hong , Kyle Gilman , Laura Balzano , Jeffrey A. Fessler

It is well known that Principal Component Analysis (PCA) is strongly affected by outliers and a lot of effort has been put into robustification of PCA. In this paper we present a new algorithm for robust PCA minimizing the trimmed…

Machine Learning · Statistics 2015-06-02 Anastasia Podosinnikova , Simon Setzer , Matthias Hein

In this paper, we study a new approach related to the convergence analysis of Ishikawa-type iterative models to a common fixed point of two non-expansive mappings in Banach spaces. The main novelty of our contribution lies in the so-called…

Solving convex Semi-Infinite Programming (SIP) problems is challenging when the separation problem, i.e., the problem of finding the most violated constraint, is computationally hard. We propose to tackle this difficulty by solving the…

Optimization and Control · Mathematics 2025-06-11 Antoine Oustry , Martina Cerulli

Primal-dual algorithm (PDA) is a classic and popular scheme for convex-concave saddle point problems. It is universally acknowledged that the proximal terms in the subproblems about the primal and dual variables are crucial to the…

Optimization and Control · Mathematics 2025-04-24 Shuning Liu , Zexian Liu

We discuss adaptive mesh point selection for the solution of scalar IVPs. We consider a method that is optimal in the sense of the speed of convergence, and aim at minimizing the local errors. Although the speed of convergence cannot be…

Numerical Analysis · Mathematics 2018-01-09 Boleslaw Kacewicz

We analyse the convergence of an approximate, fully inexact, ADMM algorithm under additive, deterministic and probabilistic error models. We consider the generalized ADMM scheme that is derived from generalized Lagrangian penalty with…

Optimization and Control · Mathematics 2022-10-06 Anis Hamadouche , Yun Wu , Andrew M. Wallace , Joao F. C. Mota

Primal-Dual Interior-Point methods are capable of solving constrained convex optimization problems to tight tolerances in a fast and robust manner. The derivatives of the primal-dual solution with respect to the problem matrices can be…

Optimization and Control · Mathematics 2024-06-21 Kevin Tracy , Zachary Manchester

In this paper we study proximal conditional-gradient (CG) and proximal gradient-projection type algorithms for a block-structured constrained nonconvex optimization model, which arises naturally from tensor data analysis. First, we…

Optimization and Control · Mathematics 2014-10-16 Bo Jiang , Shuzhong Zhang

We consider a difference-of-convex formulation where one of the terms is allowed to be hypoconvex (or weakly convex). We first examine the precise behavior of a single iteration of the Difference-of-Convex algorithm (DCA), giving a tight…

Optimization and Control · Mathematics 2024-03-26 Teodor Rotaru , Panagiotis Patrinos , François Glineur

We study a stochastic primal-dual method for constrained optimization over Riemannian manifolds with bounded sectional curvature. We prove non-asymptotic convergence to the optimal objective value. More precisely, for the class of…

Optimization and Control · Mathematics 2017-03-24 Masoud Badiei Khuzani , Na Li

This paper proposes an infeasible interior-point algorithm for the convex optimization problem using arc-search techniques. The proposed algorithm simultaneously selects the centering parameter and the step size, aiming at optimizing the…

Optimization and Control · Mathematics 2024-03-12 Yaguang Yang

Principal Component Analysis (PCA) is one of the most important methods to handle high dimensional data. However, most of the studies on PCA aim to minimize the loss after projection, which usually measures the Euclidean distance, though in…

Machine Learning · Computer Science 2019-03-19 Kai Liu , Qiuwei Li , Hua Wang , Gongguo Tang

This paper describes and establishes the iteration-complexity of a doubly accelerated inexact proximal point (D-AIPP) method for solving the nonconvex composite minimization problem whose objective function is of the form $f+h$ where $f$ is…

Optimization and Control · Mathematics 2018-12-20 Jiaming Liang , Renato D. C. Monteiro

Alternating structure-adapted proximal (ASAP) gradient algorithm (M. Nikolova and P. Tan, SIAM J Optim, 29:2053-2078, 2019) has drawn much attention due to its efficiency in solving nonconvex nonsmooth optimization problems. However, the…

Optimization and Control · Mathematics 2024-06-26 Ying Gao , Chunfeng Cui , Wenxing Zhang , Deren Han
‹ Prev 1 8 9 10 Next ›