Optimization Letters最新文献_第2页

Complexity bound of a Levenberg–Marquardt algorithm based on probabilistic Jacobian models 基于概率雅各布模型的 Levenberg-Marquardt 算法的复杂性约束

IF 1.6 4区数学

Optimization Letters Pub Date : 2024-07-18 DOI: 10.1007/s11590-024-02140-x

Ruixue Zhao

引用次数: 0

Stability approach to CDC truck scheduling problem under uncertainty 不确定条件下 CDC 卡车调度问题的稳定性方法

IF 1.6 4区数学

Optimization Letters Pub Date : 2024-07-09 DOI: 10.1007/s11590-024-02137-6

Gabriela B. Fonseca, Thiago H. Nogueira, Martín G. Ravetti

引用次数: 0

A faster heuristic for the traveling salesman problem with drone 有无人机的旅行推销员问题的快速启发式

IF 1.6 4区数学

Optimization Letters Pub Date : 2024-07-08 DOI: 10.1007/s11590-024-02134-9

Pedro Henrique Del Bianco Hokama, Carla Negri Lintzmayer, Mário César San Felice

{"title":"A faster heuristic for the traveling salesman problem with drone","authors":"Pedro Henrique Del Bianco Hokama, Carla Negri Lintzmayer, Mário César San Felice","doi":"10.1007/s11590-024-02134-9","DOIUrl":"https://doi.org/10.1007/s11590-024-02134-9","url":null,"abstract":"The Flying Sidekick Traveling Salesman Problem (FSTSP) consists of using one truck and one drone to perform deliveries to a set of customers. The drone is limited to delivering to one customer at a time, after which it returns to the truck, from where it can be launched again. The goal is to minimize the time required to service all customers and return both vehicles to the depot. In the literature, we can find heuristics for this problem that follow the order-first split-second approach: find a Hamiltonian cycle h with all customers, and then remove some customers to be handled by the drone while deciding from where the drone will be launched and where it will be retrieved. Indeed, they optimally solve the h-FSTSP, which is a variation that consists of solving the FSTSP while respecting a given initial cycle h. We present the Lazy Drone Property, which guarantees that only some combinations of nodes for the launch and retrieval of the drone need to be considered by algorithms for the h-FSTSP. We also present an algorithm that uses the property, and we show experimental results which corroborate its effectiveness in decreasing the running time of such algorithms. Our algorithm was shown to be more than 84 times faster than the previously best-known ones over the literature benchmark. Moreover, on average, it considered an amount of launch and retrieval pairs that is linear on the number of customers, indicating that the algorithm’s performance should be sustainable for larger instances.\u0000","PeriodicalId":49720,"journal":{"name":"Optimization Letters","volume":"29 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141572383","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Improved randomized approaches to the location of a conservative hyperplane 保守超平面位置的改进随机方法

IF 1.6 4区数学

Optimization Letters Pub Date : 2024-07-06 DOI: 10.1007/s11590-024-02136-7

Xiaosong Ding, Jun Ma, Xiuming Li, Xi Chen

引用次数: 0

The modified second APG method for a class of nonconvex nonsmooth problems 一类非凸非光滑问题的修正第二 APG 方法

IF 1.6 4区数学

Optimization Letters Pub Date : 2024-07-06 DOI: 10.1007/s11590-024-02132-x

Kexin Ren, Chunguang Liu, Lumiao Wang

引用次数: 0

A limited memory subspace minimization conjugate gradient algorithm for unconstrained optimization 用于无约束优化的有限内存子空间最小化共轭梯度算法

IF 1.6 4区数学

Optimization Letters Pub Date : 2024-07-02 DOI: 10.1007/s11590-024-02131-y

Zexian Liu, Yu-Hong Dai, Hongwei Liu

{"title":"A limited memory subspace minimization conjugate gradient algorithm for unconstrained optimization","authors":"Zexian Liu, Yu-Hong Dai, Hongwei Liu","doi":"10.1007/s11590-024-02131-y","DOIUrl":"https://doi.org/10.1007/s11590-024-02131-y","url":null,"abstract":"Subspace minimization conjugate gradient (SMCG) methods are a class of quite efficient iterative methods for unconstrained optimization. The orthogonality is an important property of linear conjugate gradient method. It is however observed that the orthogonality of the gradients in linear conjugate gradient method is often lost, which usually causes slow convergence. Based on SMCG(_)BB (Liu and Liu in J Optim Theory Appl 180(3):879–906, 2019), we combine subspace minimization conjugate gradient method with the limited memory technique and present a limited memory subspace minimization conjugate gradient algorithm for unconstrained optimization. The proposed method includes two types of iterations: SMCG iteration and quasi-Newton (QN) iteration. In the SMCG iteration, the search direction is determined by solving a quadratic approximation problem, in which the important parameter is estimated based on some properties of the objective function at the current iterative point. In the QN iteration, a modified quasi-Newton method in the subspace is proposed to improve the orthogonality. Additionally, a modified strategy for choosing the initial stepsize is exploited. The global convergence of the proposed method is established under weak conditions. Some numerical results indicate that, for the tested functions in the CUTEr library, the proposed method has a great improvement over SMCG(_)BB, and it is comparable to the latest limited memory conjugate gradient software package CG(_)DESCENT (6.8) (Hager and Zhang in SIAM J Optim 23(4):2150–2168, 2013) and is also superior to the famous limited memory BFGS (L-BFGS) method.","PeriodicalId":49720,"journal":{"name":"Optimization Letters","volume":"21 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141501395","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

An accelerated lyapunov function for Polyak’s Heavy-ball on convex quadratics 凸四边形上波利克重球的加速拉普诺夫函数

IF 1.6 4区数学

Optimization Letters Pub Date : 2024-06-25 DOI: 10.1007/s11590-024-02119-8

Antonio Orvieto

{"title":"An accelerated lyapunov function for Polyak’s Heavy-ball on convex quadratics","authors":"Antonio Orvieto","doi":"10.1007/s11590-024-02119-8","DOIUrl":"https://doi.org/10.1007/s11590-024-02119-8","url":null,"abstract":"In 1964, Polyak showed that the Heavy-ball method, the simplest momentum technique, accelerates convergence of strongly-convex problems in the vicinity of the solution. While Nesterov later developed a globally accelerated version, Polyak’s original algorithm remains simpler and more widely used in applications such as deep learning. Despite this popularity, the question of whether Heavy-ball is also globally accelerated or not has not been fully answered yet, and no convincing counterexample has been provided. This is largely due to the difficulty in finding an effective Lyapunov function: indeed, most proofs of Heavy-ball acceleration in the strongly-convex quadratic setting rely on eigenvalue arguments. Our work adopts a different approach: studying momentum through the lens of quadratic invariants of simple harmonic oscillators. By utilizing the modified Hamiltonian of Störmer-Verlet integrators, we are able to construct a Lyapunov function that demonstrates an (O(1/k^2)) rate for Heavy-ball in the case of convex quadratic problems. Our novel proof technique, though restricted to linear regression, is found to work well empirically also on non-quadratic convex problems, and thus provides insights on the structure of Lyapunov functions to be used in the general convex case. As such, our paper makes a promising first step towards potentially proving the acceleration of Polyak’s momentum method and we hope it inspires further research around this question.","PeriodicalId":49720,"journal":{"name":"Optimization Letters","volume":"24 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141501227","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Benchmark-based deviation and drawdown measures in portfolio optimization 投资组合优化中基于基准的偏差和缩减测量方法

IF 1.6 4区数学

Optimization Letters Pub Date : 2024-06-25 DOI: 10.1007/s11590-024-02124-x

Michael Zabarankin, Bogdan Grechuk, Dawei Hao

引用次数: 0

Strategy investments in zero-sum games 零和博弈中的战略投资

IF 1.6 4区数学

Optimization Letters Pub Date : 2024-06-24 DOI: 10.1007/s11590-024-02130-z

Raul Garcia, Seyedmohammadhossein Hosseinian, Mallesh Pai, Andrew J. Schaefer

引用次数: 0

On the linear convergence rate of Riemannian proximal gradient method 论黎曼近似梯度法的线性收敛速率

IF 1.6 4区数学

Optimization Letters Pub Date : 2024-06-19 DOI: 10.1007/s11590-024-02129-6

Woocheol Choi, Changbum Chun, Yoon Mo Jung, Sangwoon Yun

{"title":"On the linear convergence rate of Riemannian proximal gradient method","authors":"Woocheol Choi, Changbum Chun, Yoon Mo Jung, Sangwoon Yun","doi":"10.1007/s11590-024-02129-6","DOIUrl":"https://doi.org/10.1007/s11590-024-02129-6","url":null,"abstract":"Composite optimization problems on Riemannian manifolds arise in applications such as sparse principal component analysis and dictionary learning. Recently, Huang and Wei introduced a Riemannian proximal gradient method (Huang and Wei in MP 194:371–413, 2022) and an inexact Riemannian proximal gradient method (Wen and Ke in COA 85:1–32, 2023), utilizing the retraction mapping to address these challenges. They established the sublinear convergence rate of the Riemannian proximal gradient method under the retraction convexity and a geometric condition on retractions, as well as the local linear convergence rate of the inexact Riemannian proximal gradient method under the Riemannian Kurdyka-Lojasiewicz property. In this paper, we demonstrate the linear convergence rate of the Riemannian proximal gradient method and the linear convergence rate of the proximal gradient method proposed in Chen et al. (SIAM J Opt 30:210–239, 2020) under strong retraction convexity. Additionally, we provide a counterexample that violates the geometric condition on retractions, which is crucial for establishing the sublinear convergence rate of the Riemannian proximal gradient method.","PeriodicalId":49720,"journal":{"name":"Optimization Letters","volume":"5 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141501230","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0