检索结果-内蒙古大学图书馆

A Projected Variable Smoothing for Weakly Convex optimization and Supremum Functions

学校读者我要写书评

暂无评论

arXiv 2025年

作者： López-Rivera, Sergio Pérez-Aros, Pedro Vilches, Emilio Departamento de Ingeniería Matemática Universidad de Chile Santiago Chile Instituto de Ciencias de la Ingeniería Universidad de O’Higgins Rancagua Chile

In this paper, we address two main topics. First, we study the problem of minimizing the sum of a smooth function and the composition of a weakly convex function with a linear operator on a closed vector subspace. For this problem, we propose a projected variable smoothing algorithm and establish a complexity bound of Opϵ´3q to achieve an ϵ-approximate solution. Second, we investigate the Moreau envelope and the proximity operator of functions defined as the supremum of weakly convex functions, and we compute the proximity operator in two important cases. In addition, we apply the proposed algorithm for solving a distributionally robust optimization problem, the LASSO with linear constraints, and the max dispersion problem. We illustrate numerical results for the max dispersion *** Codes 90C2, 49J52, 65K05 © 2025, CC BY.

关键词： optimization algorithms

Stochastic Gradient Descent for Constrained optimization based on Adaptive Relaxed Barrier Functions

学校读者我要写书评

暂无评论

arXiv 2025年

作者： Dimitrieski, Naum Cao, Jing Ebenbauer, Christian Chair of Intelligent Control Systems RWTH Aachen University Aachen52062 Germany

This paper presents a novel stochastic gradient descent algorithm for constrained optimization. The proposed algorithm randomly samples constraints and components of the finite sum objective function and relies on a relaxed logarithmic barrier function that is appropriately adapted in each optimization iteration. For a strongly convex objective function and affine inequality constraints, step-size rules and barrier adaptation rules are established that guarantee asymptotic convergence with probability one. The theoretical results in the paper are complemented by numerical studies which highlight potential advantages of the proposed algorithm for optimization problems with a large number of constraints. Copyright © 2025, The Authors. All rights reserved.

关键词： optimization algorithms

Fig Tree-Wasp Symbiotic Coevolutionary optimization Algorithm

学校读者我要写书评

暂无评论

arXiv 2025年

作者： Kulkarni, Anand J. Purnapatre, Isha Shastri, Apoorva S. Institute of Artificial Intelligence Dr Vishwanath Karad MIT World Peace University 124 Paud Road Kothrud MH Pune411038 India Department of Computer Engineering Cummins College of Engineering for Women Karvenagar MH Pune411052 India

The nature inspired algorithms are becoming popular due to their simplicity and wider applicability. In the recent past several such algorithms have been developed. They are mainly bio-inspired, swarm based, physics based and socio-inspired;however, the domain based on symbiotic relation between creatures is still to be explored. A novel metaheuristic optimization algorithm referred to as Fig Tree-Wasp Symbiotic Coevolutionary (FWSC) algorithm is proposed. It models the symbiotic coevolutionary relationship between fig trees and wasps. More specifically, the mating of wasps, pollinating the figs, searching for new trees for pollination and wind effect drifting of wasps are modeled in the algorithm. These phenomena help in balancing the two important aspects of exploring the search space efficiently as well as exploit the promising regions. The algorithm is successfully tested on a variety of test problems. The results are compared with existing methods and algorithms. The Wilcoxon Signed Rank Test and Friedman Test are applied for the statistical validation of the algorithm performance. The algorithm is also further applied to solve the real-world engineering problems. The performance of the FWSC underscored that the algorithm can be applied to wider variety of real-world problems. © 2025, CC BY.

关键词： optimization algorithms

Alternating direction method of multipliers for polynomial optimization

学校读者我要写书评

暂无评论

arXiv 2025年

作者： Cerone, V. Fosson, S.M. Pirrera, S. Regruto, D. Dipartimento di Automatica e Informatica Politecnico di Torino corso Duca degli Abruzzi 24 Torino10129 Italy

Multivariate polynomial optimization is a prevalent model for a number of engineering problems. From a mathematical viewpoint, polynomial optimization is challenging because it is non-convex. The Lasserre’s theory, based on semidefinite relaxations, provides an effective tool to overcome this issue and to achieve the global optimum. However, this approach can be computationally complex for medium and large scale problems. For this motivation, in this work, we investigate a local minimization approach, based on the alternating direction method of multipliers, which is low-complex, straightforward to implement, and prone to decentralization. The core of the work is the development of the algorithm tailored to polynomial optimization, along with the proof of its convergence. Through a numerical example we show a practical implementation and test the effectiveness of the proposed algorithm with respect to state-of-the-art methodologies. © 2025, CC BY-NC-ND.

关键词： optimization algorithms

BILBO: BILevel Bayesian optimization

学校读者我要写书评

暂无评论

arXiv 2025年

作者： Chew, Ruth Wan Theng Nguyen, Quoc Phong Low, Bryan Kian Hsiang Institute of Data Science National University of Singapore Singapore Applied Artificial Intelligence Institute Deakin University Australia Department of Computer Science National University of Singapore Singapore

Bilevel optimization is characterized by a two-level optimization structure, where the upper-level problem is constrained by optimal lower-level solutions, and such structures are prevalent in real-world problems. The constraint by optimal lower-level solutions poses significant challenges, especially in noisy, constrained, and derivative-free settings, as repeating lower-level optimizations is sample inefficient and predicted lower-level solutions may be suboptimal. We present BILevel Bayesian optimization (BILBO), a novel Bayesian optimization algorithm for general bilevel problems with blackbox functions, which optimizes both upper- and lower-level problems simultaneously, without the repeated lower-level optimization required by existing methods. BILBO samples from confidence-bounds based trusted sets, which bounds the suboptimality on the lower level. Moreover, BILBO selects only one function query per iteration, where the function query selection strategy incorporates the uncertainty of estimated lower-level solutions and includes a conditional reassignment of the query to encourage exploration of the lower-level objective. The performance of BILBO is theoretically guaranteed with a sublinear regret bound for commonly used kernels and is empirically evaluated on several synthetic and real-world problems. © 2025, CC BY.

关键词： optimization algorithms

Theoretical Approach on Assessing the Accuracy of the Shortest Path Non-Optimal Algorithm for 2-Dimensional Grids with Obstacles 24

学校读者我要写书评

暂无评论

Theoretical Approach on Assessing the Accuracy of the Shorte...

8th International Conference on algorithms, Computing and Systems, ICACS 2024

作者： Mo, Chenghao Oyster River High School DurhamNH United States

ISBN: (纸本)9798400718304

In many applications such as urban navigation and robotics, finding the shortest path in a 2D grid is crucial but computationally expensive using traditional optimal algorithms like Floyd-Warshall or Dijkstra. These traditional algorithms guarantee to find the shortest path at the cost of time complexity, leading to a time-consuming computation, particularly for large-scale grids. Non-optimal algorithms that trade accuracy for speed have emerged to address the issue. However, the impact of grid obstacle density on the accuracy of the algorithms has not been well understood. This paper presents a theoretical framework for evaluating the accuracy of two non-optimal algorithms. By integrating theoretical analysis with extensive experimental data, this paper demonstrates how obstacle density influences algorithm performance, and proposes a methodology to select the best non-optimal algorithms based on the grid obstacle density. The theoretical framework has practical implications for applications requiring rapid path finding in complex environments. © 2024 Copyright held by the owner/author(s). Publication rights licensed to ACM.

关键词： optimization algorithms

Fast sparse optimization via adaptive shrinkage

学校读者我要写书评

暂无评论

arXiv 2025年

作者： Cerone, Vito Fosson, Sophie M. Regruto, Diego Department of Control and Computer Engineering Politecnico di Torino Italy

The need for fast sparse optimization is emerging, e.g., to deal with large-dimensional data-driven problems and to track time-varying systems. In the framework of linear sparse optimization, the iterative shrinkage-thresholding algorithm is a valuable method to solve Lasso, which is particularly appreciated for its ease of implementation. Nevertheless, it converges slowly. In this paper, we develop a proximal method, based on logarithmic regularization, which turns out to be an iterative shrinkage-thresholding algorithm with adaptive shrinkage hyperparameter. This adaptivity substantially enhances the trajectory of the algorithm, in a way that yields faster convergence, while keeping the simplicity of the original method. Our contribution is twofold: on the one hand, we derive and analyze the proposed algorithm;on the other hand, we validate its fast convergence via numerical experiments and we discuss the performance with respect to state-of-the-art algorithms. © 2025, CC BY-NC-ND.

关键词： optimization algorithms

Preference-Based Gradient Estimation for ML-Based Approximate Combinatorial optimization

学校读者我要写书评

暂无评论

arXiv 2025年

作者： Mielke, Arman Bauknecht, Uwe Strauss, Thilo Niepert, Mathias ETAS Research Stuttgart Germany Computer Science Department University of Stuttgart Germany Germany Xi’an Jiaotong-Liverpool University School of AI and Advanced Computing China NEC Laboratories Europe Germany

Combinatorial optimization (CO) problems arise in a wide range of fields from medicine to logistics and manufacturing. While exact solutions are often not necessary, many applications require finding high-quality solutions quickly. For this purpose, we propose a data-driven approach to improve existing non-learned approximation algorithms for CO. We parameterize the approximation algorithm and train a graph neural network (GNN) to predict parameter values that lead to the best possible solutions. Our pipeline is trained end-to-end in a self-supervised fashion using gradient estimation, treating the approximation algorithm as a black box. We propose a novel gradient estimation scheme for this purpose, which we call preference-based gradient estimation. Our approach combines the benefits of the neural network and the non-learned approximation algorithm: The GNN leverages the information from the dataset to allow the approximation algorithm to find better solutions, while the approximation algorithm guarantees that the solution is feasible. We validate our approach on two well-known combinatorial optimization problems, the travelling salesman problem and the minimum k-cut problem, and show that our method is competitive with state of the art learned CO solvers. © 2025, CC BY-SA.

关键词： optimization algorithms

FUSE: First-Order and Second-Order Unified SynthEsis in Stochastic optimization

学校读者我要写书评

暂无评论

arXiv 2025年

作者： Jiang, Zhanhong Hasan, Md Zahid Balu, Aditya Waite, Joshua R. Huang, Genyi Sarkar, Soumik Iowa State University United States Oracle United States

Stochastic optimization methods have actively been playing a critical role in modern machine learning algorithms to deliver decent performance. While numerous works have proposed and developed diverse approaches, first-order and second-order methods are in entirely different situations. The former is significantly pivotal and dominating in emerging deep learning but only leads convergence to a stationary point. However, second-order methods are less popular due to their computational intensity in large-dimensional problems. This paper presents a novel method that leverages both the first-order and second-order methods in a unified algorithmic framework, termed FUSE, from which a practical version (PV) is derived accordingly. FUSE-PV stands as a simple yet efficient optimization method involving a switch-over between first and second orders. Additionally, we develop different criteria that determine when to switch. FUSE-PV has provably shown a smaller computational complexity than SGD and Adam. To validate our proposed scheme, we present an ablation study on several simple test functions and show a comparison with baselines for benchmark datasets. Copyright © 2025, The Authors. All rights reserved.

关键词： optimization algorithms