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Projected proximal gradient trust-region algorithm for nonsmooth optimization

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arXiv 2025年

作者： Dao, Minh N. Phan, Hung M. Roberts, Lindon School of Science RMIT University MelbourneVIC3000 Australia Department of Mathematics and Statistics Kennedy College of Sciences University of Massachusetts Lowell LowellMA01854 United States School of Mathematics and Statistics University of Sydney CamperdownNSW2006 Australia

We consider trust-region methods for solving optimization problems where the objective is the sum of a smooth, nonconvex function and a nonsmooth, convex regularizer. We extend the global convergence theory of such methods to include worst-case complexity bounds in the case of unbounded model Hessian growth, and introduce a new, simple nonsmooth trust-region subproblem solver based on combining several iterations of proximal gradient descent with a single projection into the trust region, which meets the sufficient descent requirements for algorithm convergence and has promising numerical results. Copyright © 2025, The Authors. All rights reserved.

关键词： optimization algorithms

Distributed Variational Quantum Algorithm with Many-qubit for optimization Challenges

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arXiv 2025年

作者： Kim, Seongmin Suh, In-Saeng National Center for Computational Sciences Oak Ridge National Laboratory Oak RidgeTN37830 United States

optimization problems are critical across various domains, yet existing quantum algorithms, despite their great potential, struggle with scalability and accuracy due to excessive reliance on entanglement. To address these limitations, we propose variational quantum optimization algorithm (VQOA), which leverages many-qubit (MQ) operations in an ansatz solely employing quantum superposition, completely avoiding entanglement. This ansatz significantly reduces circuit complexity, enhances noise robustness, mitigates Barren Plateau issues, and enables efficient partitioning for highly complex large-scale optimization. Furthermore, we introduce distributed VQOA (DVQOA), which integrates high-performance computing with quantum computing to achieve superior performance across MQ systems and classical nodes. These features enable a significant acceleration of material optimization tasks (e.g., metamaterial design), achieving more than 50× speedup compared to state-of-the-art optimization algorithms. Additionally, DVQOA efficiently solves quantum chemistry problems and N-ary (N ≥ 2) optimization problems involving higher-order interactions. These advantages establish DVQOA as a highly promising and versatile solver for real-world problems, demonstrating the practical utility of the quantum-classical approach. © 2025, CC BY.

关键词： optimization algorithms

Accelerated Distributed optimization with Compression and Error Feedback

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arXiv 2025年

作者： Gao, Yuan Rodomanov, Anton Rack, Jeremy Stich, Sebastian U. CISPA Helmholtz Center for Information Security Germany Universität des Saarlandes Germany

Modern machine learning tasks often involve massive datasets and models, necessitating distributed optimization algorithms with reduced communication overhead. Communication compression, where clients transmit compressed updates to a central server, has emerged as a key technique to mitigate communication bottlenecks. However, the theoretical understanding of stochastic distributed optimization with contractive compression remains limited, particularly in conjunction with Nesterov acceleration—a cornerstone for achieving faster convergence in optimization. In this paper, we propose a novel algorithm, ADEF (Accelerated Distributed Error Feedback), which integrates Nesterov acceleration, contractive compression, error feedback, and gradient difference compression. We prove that ADEF achieves the first accelerated convergence rate for stochastic distributed optimization with contractive compression in the general convex regime. Numerical experiments validate our theoretical findings and demonstrate the practical efficacy of ADEF in reducing communication costs while maintaining fast convergence. © 2025, CC BY.

关键词： optimization algorithms

Community Membership Hiding via Gradient-based optimization

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arXiv 2025年

作者： Silvestri, Matteo Gabrielli, Edoardo Silvestri, Fabrizio Tolomei, Gabriele Department of Computer Science Sapienza University of Rome Rome Italy Department of Computer Control and Management Engineering Sapienza University of Rome Rome Italy

We tackle the problem of community membership hiding, which involves strategically altering a network’s structure to obscure a target node’s membership in a specific community identified by a detection algorithm. We reformulate the original discrete counterfactual graph objective as a differentiable constrained optimization task. To solve this, we propose ∇- CMH, a gradient-based method that modifies the network’s structure within the feasible bounds for an individual target node, effectively concealing its membership. Experimental results across multiple datasets and community detection algorithms show that our approach surpasses existing baselines, offering a better balance between accuracy and computational efficiency. © 2025, CC BY.

关键词： optimization algorithms

Maximum Independent Set Using Hummingbird optimization 4th

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Maximum Independent Set Using Hummingbird Optimization

4th International Conference on Advanced Network Technologies and Intelligent Computing, ANTIC 2024

作者： Verma, Ritika Mahato, Dharamendra Prasad Department of Computer Science and Engineering National Institute of Technology Hamirpur HP Hamirpur177 005 India

ISBN: (纸本)9783031837821

The Maximum Independent Set problem in distributed systems is an NP-hard problem. This paper uses a soft computing approach to solve this problem. In this paper, we use Hummingbird optimization to solve the problem. We also compare the proposed algorithm with deterministic algorithm, non-deterministic algorithms and other soft computing algorithms. We tested the algorithms on DIMACS benchmark datasets. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： optimization algorithms

Wireless Sensor Network Lifespan optimization with Simple, Rotated, Order and Modified Partially Matched Crossover Genetic algorithms

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IFAC-PapersOnLine 2016年第25期49卷 182-187页

作者： Ahmed, Yousif E.E. Adjallah, Kondo H. Stock, Romuald Babikier, Sharef F. University of Gezira Wadmadani Sudan & LCOMS EA7306 University of Lorraine France LCOMS EA7306 University of Lorraine France University of Khartoum Khartoum Sudan

This paper proposes a genetic algorithm (GA) with a benchmarking study for optimizing the wireless sensor network (WSN) lifespan. Four crossover operators combined with four mutation operators were developed to enhance the GA efficiency, and thus the performance of the lifespan optimization algorithm. The traditional one-point crossover operator referred as the “simple crossover”, is used to evaluate the modified “partially matched” and the “order” crossovers. Also, a new crossover operator referred as “rotated” crossover is also proposed and evaluated. Different combinations of these crossover operators with the one-point and two-points deterministic and random mutations are used to optimize the WSNs lifespan. The algorithms were coded in C programming language and applied to different instances of WSNs initial configurations. The optimization software tool developed based on the combinatorial operators allows selecting the best solution among 16 through a smart decision making. For illustration, among all the investigated algorithms, the modified partially matched crossover associated with the random two-points mutation has shown the best performances on the studied instance, due to its capability to reach closer to the optimal solution. © 2016

关键词： Wireless sensor networks C (programming language) Decision making Genetic algorithms crossover Initial configuration Life span Mutation operators optimization algorithms optimization software Set cover Two points mutation

Lower Bounds and Accelerated algorithms for Bilevel optimization

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Journal of Machine Learning Research 2023年第1期24卷 1-56页

作者： Ji, Kaiyi Liang, Yingbin Department of Computer Science and Engineering University at Buffalo BuffaloNY14260-2500 United States Department of Electrical and Computer Engineering The Ohio State University ColumbusOH98195-4322 United States

Bilevel optimization has recently attracted growing interests due to its wide applications in modern machine learning problems. Although recent studies have characterized the convergence rate for several such popular algorithms, it is still unclear how much further these convergence rates can be improved. In this paper, we address this fundamental question from two perspectives. First, we provide the first-known lower complexity bounds of (Formula presented) respectively for strongly-convex-strongly-convex and convex-strongly-convex bilevel optimizations. Second, we propose an accelerated bilevel optimizer named AccBiO, for which we provide the first-known complexity bounds without the gradient boundedness assumption (which was made in existing analyses) under the two aforementioned geometries. We also provide significantly tighter upper bounds than the existing complexity when the bounded gradient assumption does hold. We show that AccBiO achieves the optimal results (i.e., the upper and lower bounds match up to logarithmic factors) when the inner-level problem takes a quadratic form with a constant-level condition number. Interestingly, our lower bounds under both geometries are larger than the corresponding optimal complexities of minimax optimization, establishing that bilevel optimization is provably more challenging than minimax optimization. Our theoretical results are validated by numerical experiments. ©2022 Kaiyi Ji and Yingbin Liang.

关键词： optimization algorithms

Design optimization of cam-follower mechanisms using Rao algorithms and their variants

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EVOLUTIONARY INTELLIGENCE 2024年第2期17卷 745-770页

作者： Rao, R., V Pawar, R. B. SV Natl Inst Technol Dept Mech Engn Surat 395007 Gujarat India

This paper presents the design optimization of cam-follower mechanisms (CFM) with eccentric roller type follower using recently developed advanced optimization algorithms, namely Rao, SAMP-Rao, and QO-Rao algorithms. Four types of follower motion law i.e., cycloidal, modified harmonic, 3-4-5 degree polynomial, and 4-5-6-7 degree polynomial motion, are considered. The CFM is optimized to minimize three objectives such as the input torque needed to rotate the cam, the radius of the pitch circle of the cam, and the maximum contact stress. The problem has five continuous design variables, namely the roller radius (R-g), the radius of cam base circle (R-b), the distance between the follower bearing and the center of the cam (q), the eccentricity of the follower (e), and the length of follower bearing (b). Eight design constraints related to the geometry of the cam mechanism, the pressure angle, the efficiency of the mechanism, the curvature radius of the pitch curve, and the maximum contact stress, are considered. The computational results obtained using Rao algorithms and their variants are compared with other advanced optimization algorithms such as the salp swarm algorithm (SSA), ant lion optimizer (ALO), moth-flame optimization (MFO), multi verse optimizer (MVO), evaporation rate water cycle algorithm (ER-WCA), grey wolf optimizer (GWO), and mine blast algorithm (MBA). The comparison of optimization results reveals that the optimum value of a fitness function obtained using Rao algorithms and their variants is superior to GWO, ALO, MFO, SSA, ER-WCA, MBA, and MVO for all four cases considered. The optimum fitness function value of the CFM with case III is reduced by 3.14%, 4.13%, and 7.61% compared to the CFM's fitness function value with the case I, case II, and case IV, respectively. Hence, the 3-4-5 degree polynomial motion of the follower is effective for better performance of the CFM. Also, the average time required for Rao algorithms and their variants is compar

关键词： Rao algorithms optimization algorithms Metaheuristics Engineering design problems Cam-follower mechanism

Dynamic Change of Three-Dimensional Soil in Game Simulators

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Dynamic Change of Three-Dimensional Soil in Game Simulators

International IoT, Electronics and Mechatronics Conference, IEMTRONICS 2024

作者： Belov, Aleksandr Sapozhnikov, Artem Semichasnov, Iliya Departament of the Applied Mathematics National Research University "Higher School of Economics" Moscow Russia

ISBN: (纸本)9789819747832

This article describes the practical usage of mathematical algorithms in a computer game to create realistic soil behavior in contact with external objects. The study uses a set of algorithms to simulate the behavior of soil, specifically contact point detection algorithm, basic deformation algorithm, soil compaction algorithm, displaced mass distribution algorithm, and erosion algorithm. A comparative analysis of several algorithms was conducted, and the most effective algorithms were identified. Based on the results of this analysis, a final simulation was performed to showcase examples of soil types that can be simulated using this approach. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2025.

关键词： optimization algorithms