Proximal Optimization

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14 papers2 papers in the last four weeks, against 1 the four weeks before. 0.0% of all new papers.

Anchored Extra-Proximal Methods: Optimal Higher-Order Methods for Monotone Inclusion Problems
Sep 24, 2026Ruichen Jiang, TaeHo YoonOracle Complexity Second-Order Optimization
Google Research · Johns Hopkins University
Complexities of Weak Proximal Oracle Methods for Composite Convex Optimization
Sep 21, 2026Dan GarberOracle Complexity Optimization Convergence Analysis
Faculty of Data and Decision Sciences Technion - Israel Institute of Technology
Convex Optimization with Nested Evolving Feasible Sets (CONES) under Time-Varying Loss Functions
Sep 10, 2026Rahul VazeOnline Convex Optimization Proximal Optimization
Adaptive Bregman Proximal Stochastic Gradient with a Stabilized Barzilai--Borwein Step Size
Aug 12, 2026Chenhan Jin, Shengze Xu, Binghui Xie +4Nonconvex Stochastic Optimization Adaptive Gradient Methods
1The Chinese University of Hong Kong · University of Utah · 3Beijing Normal-Hong Kong Baptist University +1
An Inertial Block Proximal Linearized Method with Adaptive Momentum for Nonconvex and Nonsmooth Optimization
Aug 6, 2026Weifeng YangMomentum Methods Nonconvex Optimization
Yunnan Earthquake Administration, Kunming 650224, China
Online Optimization of Difference-of-Convex Compositions with Smooth Mappings
Jul 21, 2026Jingwei Ji, Jong-Shi Pang, Renyuan XuNonconvex Optimization Constrained Optimization
Management Science and Engineering, Stanford University · The Daniel J. Epstein Department of Industrial and Systems Engineering, University of Southern California
LCPNet: Latent Consistent Proximal Unfolding Network for Infrared Small Target Detection
Jul 6, 2026Tianfang Zhang, Lei Li, Chang Liu +3Remote Sensing Small Object Detection Proximal Optimization
Department of Automation, Tsinghua University, Beijing, 100190, China. · School of Artificial Intelligence, Beijing Institute of Technology, Beijing, 100081, China. · School of Information and Communication Engineering and the Laboratory of Imaging Detection and Intelligent Perception, University of Electronic Science and Technology of China, Chengdu, 610054, China.
Trajectory Constraints for Imaging Inverse Problems
May 27, 2026Chaoyan Huang, Haijie Yuan, Bharath Subramanian +1Proximal Optimization Image Reconstruction
Department of Computational Mathematics, Science, & Engineering, Michigan State University · Department of Electrical Engineering and Computer Science, University of Michigan · Department of Biomedical Engineering, Michigan State University
Proximal basin hopping: global optimization with guarantees
May 18, 2026Guillaume Lauga, Cesare Molinari, Samuel VaiterProximal Optimization Global Optimization
LJAD · LJAD Université Côte d’Azur France · MaLGA +3
Task Switching Without Forgetting via Proximal Decoupling
Apr 20, 2026Pourya Shamsolmoali, Masoumeh Zareapoor, Eric Granger +2Proximal Optimization Continual Learning
Department of Computer Science, University of York, UK · SEIEE, Shanghai Jiao Tong University, China · LIVIA, Dept. of Systems Engineering, ETS Montreal, Canada +1
Score-Guided Proximal Projection: A Unified Geometric Framework for Rectified Flow Editing
Mar 5, 2026Vansh Bansal, James G ScottProximal Optimization Rectified Flow
Department of Statistics and Data Sciences, UT Austin
General Proximal Flow Networks
Feb 28, 2026Alexander Strunk, Roland AssamProximal Optimization Generative Modeling
Evercot AI
Beyond SGD, Without SVD: Proximal Subspace Iteration LoRA with Diagonal Fractional K-FAC
Feb 18, 2026Abdulla Jasem Almansoori, Maria Ivanova, Andrey Veprikov +3Proximal Optimization Kronecker-Factored Approximation
MBZUAI, Abu Dhabi, UAE · Yandex School of Data Analysis, Moscow, Russia · SB AI Lab, Moscow, Russia +2
Neural Operators Which Certifiably Simultaneously Solve Infinitely Many Convex Programs using Logarithmic Rank and Linear Complexity
Aug 20, 2025Anastasis Kratsios, Ariel Neufeld, Philipp SchmockerNeural Operators Operator Learning
Department of Mathematics, McMaster University and the Vector Institute, Canada · Division of Mathematical Sciences, Nanyang Technological University, Singapore

Sep 24, 2026J/K move · Enter open · S save

Anchored Extra-Proximal Methods: Optimal Higher-Order Methods for Monotone Inclusion Problems

Ruichen Jiang, TaeHo Yoon

Google Research · Johns Hopkins University

Oracle Complexity Second-Order Optimization Extragradient Methods Proximal Optimization

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We study the deterministic oracle complexity of finding approximate solutions to composite monotone inclusion problems, formed by the sum of a smooth single-valued monotone operator and a maximally monotone set-valued operator, under the tangent-residual criterion. We introduce the Anchored Extra-Proximal (AEP) framework, which combines an anchored extrapolation step with an inexact anchored proximal update satisfying a relative-error condition. The framework recovers the composite Fast Extragradient method in the first-order setting and yields natural second- and higher-order extensions by replacing the operator in the implicit update with its Taylor approximation at the extrapolated point. For every

p\geq 2

, assuming that the

(p-1)

th derivative of the single-valued operator is Lipschitz continuous, we combine this construction with a bisection line search to obtain a

p

th-order method that finds a point with tangent residual at most

\varepsilon

\widetilde{O}(\varepsilon^{-2/(3p-1)})

oracle calls. This improves all prior upper bounds for

p

th-order methods: in particular, it improves the previous best-known

\widetilde{O}(\varepsilon^{-1/p})

tangent-residual complexity as well as the classical

O(\varepsilon^{-2/(p+1)})

bound of higher-order hybrid proximal extragradient methods under the weaker duality-gap criterion. We complement this result with a worst-case lower bound of

Ω(\varepsilon^{-2/(3p-1)})

for every deterministic algorithm in the

p

th-order oracle model, without restricting the algorithm to tensor steps or any other prescribed update structure. Thus, the proposed method attains the optimal dependence on

\varepsilon

, up to logarithmic factors, for all

p\geq2