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Applied Set-Valued Analysis and optimization 2025年第1期7卷 111-124页

作者： Anane, Nassima Khaldi, Merzaka Achache, Mohamed Fundamental and Numerical Mathematics Laboratory Ferhat Abbas University Sétif Algeria

In this paper, we presented a full-Newton short-step interior-point algorithm, which is based on a new algebraically equivalent transformation technique, for a linear optimization problem. This technique offers a new type of Newton search direction and a proximity measure for tracing approximately the central-path of the linear optimization problem. We prove, under new defaults, that our algorithm is well-defined and converges to an optimal solution of the linear optimization problem. Moreover, we obtained its currently best known iteration bound, and we presented some numerical results for its evaluation. ©2025 Applied Set-Valued Analysis and optimization.

关键词： optimization algorithms

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Accelerated Successive Convex Approximation for Nonlinear optimization-Based Control

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IEEE Transactions on Automatic Control 2025年

作者： Wu, Jinxian Dai, Li Dou, Songshi Xia, Yuanqing Beijing Institute of Technology School of Automation Beijing100081 China The University of Hong Kong Department of Electrical and Electronic Engineering Hong Kong

The successive convex approximation (SCA) methods stand out as the viable option for nonlinear optimization-based control, as it effectively addresses the challenges posed by nonlinear (potentially non-convex) optimization problems by transforming them into a sequence of strongly convex subproblems. However, the current SCA algorithm exhibits a slow convergence rate, resulting in a relatively poor performance within a limited sample time. In this paper, the process of SCA is retreated as solving a fixed point nonlinear equation. By analyzing the derivative properties of this nonlinear equation, we introduce a Newton-based accelerated SCA (ASCA) algorithm designed to enhance the local convergence rate while inheriting all favorable characteristics of the SCA methods. Specifically, our algorithm offers the following benefits: (i) It is capable of effectively tackling nonlinear optimization-based control problems;(ii) It permits flexible termination with all generated intermediate solutions being feasible for the original nonlinear problem;and (iii) It guarantees convergence with locally superlinear convergence rate to the stationary point of the original nonlinear problem. Finally, we conduct experiments in a multi-agent collision avoidance scenario to show its validity. © 1963-2012 IEEE.

关键词： optimization algorithms

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A Landscape-Aware Differential Evolution for Multimodal optimization Problems

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IEEE Transactions on Evolutionary Computation 2025年

作者： Lin, Guo-Yun Chen, Zong-Gan Liu, Chuanbin Jiang, Yuncheng Kwong, Sam Zhang, Jun Zhan, Zhi-Hui South China Normal University School of Computer Science Guangzhou510631 China Ministry of Education Center for Scientific Research and Development in Higher Education Institutes China Lingnan University Department of Computing and Decision Science Hong Kong Nankai University College of Artificial Intelligence Tianjin300350 China ERICA Hanyang University 15588 Korea Republic of

How to simultaneously locate multiple global peaks and achieve certain accuracy on the found peaks are two key challenges in solving multimodal optimization problems (MMOPs). In this article, a landscape-aware differential evolution (LADE) algorithm is proposed for MMOPs, which utilizes landscape knowledge to maintain sufficient diversity and provide efficient search guidance. In detail, the landscape knowledge is efficiently utilized in the following three aspects. First, a landscape-aware peak exploration helps each individual evolve adaptively to locate a peak and simulates the regions of the found peaks according to search history to avoid an individual re-locating an already found peak. Second, a landscape-aware peak distinction distinguishes whether an individual locates a new global peak, a new local peak, or an already found peak. Accuracy refinement can thus only be conducted on the global peaks to enhance the search efficiency. Third, a landscape-aware reinitialization specifies the initial position of an individual adaptively according to the distribution and distinction of the found peaks, which helps explore more peaks. The experiments are conducted on the widely-used benchmark MMOPs and multimodal nonlinear equation system problems. Experimental results show that LADE obtains generally better or competitive performance compared with seven well-performing recent algorithms and four winner algorithms in the IEEE CEC competitions for multimodal optimization. © 1997-2012 IEEE.

关键词： optimization algorithms

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Multi Objective optimization System for Bridge Design Based on Multi-objective optimization Theory and Improved Ant Colony Algorithm

Informatica (Slovenia)

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Informatica (Slovenia) 2025年第8期49卷 127-140页

作者： Wen, Qiqi Chongqing Leway Civil Engineering Design Co. Ltd China

In the field of bridge design, multi-objective optimization problems have attracted much attention due to their complexity and multiple solutions. The limitations of existing optimization algorithms in dealing with multi-objective problems, especially the trade-off between multiple objectives such as cost, duration, safety and quality. Therefore, in order to achieve the balance and optimization of each optimization objective while satisfying the bridge design constraints, a multi-objective optimization system based on an improved ant colony algorithm is studied and developed. The study is conducted by modeling natural selection and genetic mechanisms to improve the global search capability and diversity of the algorithm. The results showed that the proposed system was significantly superior to the traditional methods in key performance indicators such as optimization speed, objective function value, and robustness. The accuracy, stability, and safety of the proposed system were as high as 92%, 95%, and 91%, respectively, while the corresponding indicators of the traditional system were only about 55%. Specifically, the optimization speed of the proposed system reached 0.95, which was significantly better than that of the traditional system of 0.70, indicating that the proposed system had a significant advantage in convergence speed. The objective function value of the proposed system was 0.92, which was better than 0.75 of the traditional system, indicating that the proposed system could achieve a more optimal solution when solving optimization problems. The proposed system is superior to the traditional system in all evaluation indices, which proves its superior performance in multi-objective optimization of bridge design. The study provides a new optimization strategy for bridge design, which helps to achieve a more efficient, economical and safer bridge design solution. © 2025 Slovene Society Informatika. All rights reserved.

关键词： optimization algorithms

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A Stochastic Gradient Tracking Algorithm for Decentralized optimization With Inexact Communication

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IEEE Transactions on Automatic Control 2025年

作者： Shah, Suhail M. Bollapragada, Raghu University of Texas at Austin Operations Research and Industrial Engineering Program TX78705 United States

Decentralized optimization is typically studied under the assumption of noise-free transmission. However, real-world scenarios often involve the presence of noise due to factors such as additive white Gaussian noise channels or probabilistic quantization of transmitted data. These sources of noise have the potential to degrade the performance of decentralized optimization algorithms if not effectively addressed. In this paper, we focus on the noisy communication setting and propose an algorithm that bridges the performance gap caused by communication noise while also mitigating other challenges like data heterogeneity. We establish theoretical results of the proposed algorithm that quantify the effect of communication noise and gradient noise on the performance of the algorithm. Notably, our algorithm achieves the optimal convergence rate for minimizing strongly convex, smooth functions in the context of inexact communication and stochastic gradients. Finally, we illustrate the superior performance of the proposed algorithm compared to its state-of-the-art counterparts on machine learning problems using MNIST and CIFAR-10 datasets. © 2025 IEEE.

关键词： optimization algorithms

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ADMM-Tracking Gradient for Distributed optimization over Asynchronous and Unreliable Networks

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IEEE Transactions on Automatic Control 2025年

作者： Carnevale, Guido Bastianello, Nicola Notarstefano, Giuseppe Carli, Ruggero Alma Mater Studiorum - Universita' di Bologna Department of Electrical Electronic and Information Engineering Bologna Italy Kth Royal Institute of Technology School of Electrical Engineering and Computer Science and Digital Futures Stockholm Sweden University of Padova Department of Information Engineering Via G. Gradenigo 6/B Padova35131 Italy

In this paper, we propose a novel distributed algorithm for consensus optimization over networks and a robust extension tailored to deal with asynchronous agents and packet losses. Indeed, to robustly achieve dynamic consensus on the solution estimates and the global descent direction, we embed in our algorithms a distributed implementation of the Alternating Direction Method of Multipliers (ADMM). Such a mechanism is suitably interlaced with a local proportional action steering each agent estimate to the solution of the original consensus optimization problem. First, in the case of ideal networks, by using tools from system theory, we prove the linear convergence of the scheme with strongly convex costs. Then, by exploiting the averaging theory, we extend such a first result to prove that the robust extension of our method preserves linear convergence in the case of asynchronous agents and packet losses. Further, by using the notion of Input-to-State Stability, we also guarantee the robustness of the schemes with respect to additional, generic errors affecting the agents' updates. Finally, some numerical simulations confirm our theoretical findings and compare our algorithms with other distributed schemes in terms of speed and robustness. © 2025 IEEE.

关键词： optimization algorithms

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Distributed Event-Triggered Bandit Convex optimization With Time-Varying Constraints

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IEEE Transactions on Control of Network Systems 2025年

作者： Zhang, Kunpeng Yi, Xinlei Wen, Guanghui Cao, Ming Johansson, Karl H. Chai, Tianyou Yang, Tao Northeastern University State Key Laboratory of Synthetical Automation for Process Industries Shenyang110819 China Ministry of Education Shanghai Institute of Intelligent Science and Technology National Key Laboratory of Autonomous Intelligent Unmanned Systems Frontiers Science Center for Intelligent Autonomous Systems Shanghai201210 China Southeast University School of Automation Nanjing210096 China University of Groningen Engineering and Technology Institute Groningen Faculty of Science and Engineering GroningenAG 9747 Netherlands KTH Royal Institute of Technology Division of Decision and Control Systems School of Electrical Engineering and Computer Science Stockholm10044 Sweden KTH Royal Institute of Technology Digital Futures Stockholm10044 Sweden

This paper considers the distributed bandit convex optimization problem with time-varying inequality constraints over a network of agents, where the goal is to minimize network regret and cumulative constraint violation. Existing distributed online algorithms solving this problem require that each agent broadcasts its decision to its neighbors at each iteration. However, communication resources are often limited. To better utilize communication resources, we propose a distributed event-triggered online primal-dual algorithm with two-point bandit feedback. Under several classes of appropriately chosen decreasing parameter sequences and non-increasing event-triggered threshold sequences, we establish dynamic network regret and network cumulative constraint violation bounds. These bounds are comparable to the results achieved by distributed event-triggered online algorithms with full-information feedback. Finally, a numerical example is provided to verify the theoretical results. © 2014 IEEE.

关键词： optimization algorithms

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Technical Note—Improved Sample-Complexity Bounds in Stochastic optimization

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Operations Research 2025年第2期73卷 986-994页

作者： Baveja, Alok Chavan, Amit Nikiforov, Andrei Srinivasan, Aravind Xu, Pan Department of Supply Chain Management Rutgers Business School Rutgers The State University of New Jersey PiscatawayNJ08854 United States Snowflake Inc. San MateoCA94402 United States School of Business Rutgers The State University of New Jersey CamdenNJ08102 United States Department of Computer Science University of Maryland College ParkMD20742 United States Department of Computer Science New Jersey Institute of Technology NewarkNJ07102 United States

Real-world network-optimization problems often involve uncertain parameters during the optimization phase. Stochastic optimization is a key approach introduced in the 1950s to address such uncertainty. This paper presents improved upper bounds on the number of samples required for the sample-average approximation method in stochastic optimization. It enhances the sample complexity of existing approaches in this setting, providing faster approximation algorithms for any method that employs this framework. This work is particularly relevant for solving problems like the stochastic Steiner tree problem. © 2023 INFORMS.

关键词： optimization algorithms

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Coping With a Severely Changing Number of Objectives in Dynamic Multi-Objective optimization

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IEEE Transactions on Evolutionary Computation 2025年

作者： Ruan, Gan Hou, Zhanglu Yao, Xin Lingnan University School of Data Science Hong Kong Xiangtan University Hunan Engineering Research Center of Intelligent System Optimization and Security Hunan Province Xiangtan411105 China

In dynamic multi-objective optimization problems (DMOPs) where the number of objectives changes, the Pareto-optimal set (PS) manifold may expand or contract over time. Knowledge transfer has been utilized to solve DMOPs because it can transfer valuable information from one problem-solving instance (i.e., source) to solving another related problem instance. However, existing transfer approaches suffer from poor diversity and convergence after a severe increase and decrease in the number of objectives, respectively. The reason is that most transfer approaches simply transfer knowledge from the solutions before the change, which causes degeneration in quality of transferred solutions due to dissimilarity between the problem instances before and after the severe change. In this paper, we propose a simple-yet-effective transfer approach, called similarity transfer approach (STA) to tackling a severely changing number of objectives. It selects the historically most similar environment to the current one as the source problem instance and transfers knowledge from that environment. Furthermore, a novel strategy of randomization enhancing transfer diversity is proposed in STA if the transfer from the most similar environment still lacks sufficient diversity when increasing the number of objectives. Comprehensive studies using 13 DMOP benchmarks with a severely changing number of objectives demonstrate that our proposed STA is effective in improving solution quality not only immediately after changes but also after optimization, in comparison to state-of-the-art algorithms. © 1997-2012 IEEE.

关键词： optimization algorithms

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Setwise Coordinate Descent for Dual Asynchronous Decentralized optimization

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IEEE Transactions on Automatic Control 2025年

作者： Costantini, Marina Liakopoulos, Nikolaos Mertikopoulos, Panayotis Spyropoulos, Thrasyvoulos EURECOM Sophia Antipolis Nice06000 France Amazon Luxembourg City1255 Luxembourg Univ. Grenoble Alpes CNRS Inria Grenoble INP LIG Grenoble38000 France The Technical University of Crete EURECOM Chania73100 Greece

In decentralized optimization over networks, synchronizing the updates of all nodes incurs significant communication overhead. For this reason, much of the recent literature has focused on the analysis and design of asynchronous optimization algorithms where nodes can activate anytime and contact a single neighbor to complete an iteration together. However, most works assume that the neighbor selection is done at random based on a fixed probability distribution (e.g., uniform), a choice that ignores the optimization landscape at the moment of activation. Instead, in this work we introduce an optimization-aware selection rule that chooses the neighbor providing the highest dual cost improvement (a quantity related to a dualization of the problem based on consensus). This scheme is related to the coordinate descent (CD) method with the Gauss-Southwell (GS) rule for coordinate updates;in our setting however, only a subset of coordinates is accessible at each iteration (because each node can communicate only with its neighbors), so the existing literature on GS methods does not apply. To overcome this difficulty, we develop a new analytical framework for smooth and strongly convex functions that covers our new class of setwise CD algorithms -a class that applies to both decentralized and parallel distributed computing scenarios- and we show that the proposed setwise GS rule can speed up the convergence in terms of iterations by a factor equal to the size of the largest coordinate set. We analyze extensions of these algorithms that exploit the knowledge of the smoothness constants when available and otherwise propose an algorithm to estimate these constants. Finally, we validate our theoretical results through extensive simulations. © 1963-2012 IEEE.

关键词： optimization algorithms

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