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Length-constrained cycle partition with an application to UAV routing* 长度约束周期划分及其在无人机路由中的应用*
Optimization Methods and Software Pub Date : 2022-05-12 DOI: 10.1080/10556788.2022.2053972
Kai Hoppmann-Baum, O. Burdakov, Gioni Mexi, C. J. Casselgren, T. Koch
{"title":"Length-constrained cycle partition with an application to UAV routing*","authors":"Kai Hoppmann-Baum, O. Burdakov, Gioni Mexi, C. J. Casselgren, T. Koch","doi":"10.1080/10556788.2022.2053972","DOIUrl":"https://doi.org/10.1080/10556788.2022.2053972","url":null,"abstract":"This article discusses the Length-Constrained Cycle Partition Problem (LCCP), which constitutes a new generalization of the Travelling Salesperson Problem (TSP). Apart from nonnegative edge weights, the undirected graph in LCCP features a nonnegative critical length parameter for each vertex. A cycle partition, i.e. a vertex-disjoint cycle cover, is a feasible solution for LCCP if the length of each cycle is not greater than the critical length of each vertex contained in it. The goal is to find a feasible partition having a minimum number of cycles. Besides analyzing theoretical properties and developing preprocessing techniques, we propose an elaborate heuristic algorithm that produces solutions of good quality even for large-size instances. Moreover, we present two exact mixed-integer programming formulations (MIPs) for LCCP, which are inspired by well-known modeling approaches for TSP. Further, we introduce the concept of conflict hypergraphs, whose cliques yield valid constraints for the MIP models. We conclude with a discussion on computational experiments that we conducted using (A)TSPLIB-based problem instances. As a motivating example application, we describe a routing problem where a fleet of uncrewed aerial vehicles (UAVs) must patrol a given set of areas.","PeriodicalId":124811,"journal":{"name":"Optimization Methods and Software","volume":"61 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126175239","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Newton-type proximal gradient method for nonlinear multi-objective optimization problems 非线性多目标优化问题的牛顿型近端梯度法
Optimization Methods and Software Pub Date : 2022-05-09 DOI: 10.1080/10556788.2022.2157000
M. A. T. Ansary
{"title":"A Newton-type proximal gradient method for nonlinear multi-objective optimization problems","authors":"M. A. T. Ansary","doi":"10.1080/10556788.2022.2157000","DOIUrl":"https://doi.org/10.1080/10556788.2022.2157000","url":null,"abstract":"In this paper, a globally convergent Newton-type proximal gradient method is developed for composite multi-objective optimization problems where each objective function can be represented as the sum of a smooth function and a nonsmooth function. The proposed method deals with unconstrained convex multi-objective optimization problems. This method is free from any kind of priori chosen parameters or ordering information of objective functions. At every iteration of the proposed method, a subproblem is solved to find a suitable descent direction. The subproblem uses a quadratic approximation of each smooth function. An Armijo type line search is conducted to find a suitable step length. A sequence is generated using the descent direction and the step length. The global convergence of this method is justified under some mild assumptions. The proposed method is verified and compared with some existing methods using a set of test problems.","PeriodicalId":124811,"journal":{"name":"Optimization Methods and Software","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114429442","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
Convergence to a second-order critical point by a primal-dual interior point trust-region method for nonlinear semidefinite programming 非线性半定规划的原对偶内点信赖域法收敛到二阶临界点
Optimization Methods and Software Pub Date : 2022-05-02 DOI: 10.1080/10556788.2022.2060973
Hiroshi Yamashita
{"title":"Convergence to a second-order critical point by a primal-dual interior point trust-region method for nonlinear semidefinite programming","authors":"Hiroshi Yamashita","doi":"10.1080/10556788.2022.2060973","DOIUrl":"https://doi.org/10.1080/10556788.2022.2060973","url":null,"abstract":"In this paper, we propose a primal-dual interior point trust-region method for solving nonlinear semidefinite programming problems, in which the iterates converge to a point that satisfies the first-order and second-order optimality conditions. The method consists of the outer iteration (SDPIP-revised) that finds a Karush-Kuhn-Tucker (KKT) point which satisfies the second-order optimality condition, and the inner iteration (SDPTR-revised) that calculates an approximate barrier KKT point. Algorithm SDPTR-revised uses a commutative class of Newton-like directions within the framework of the trust-region method in the primal-dual space. In addition, we also use a direction of negative curvature when it exists. The proposed algorithm employs a new method that generates negative-curvature directions in the existence of -type penalty term for equality constraints. It is proved that there exists a limit point of the generated sequence which satisfies the second-order optimality condition along with the barrier KKT conditions.","PeriodicalId":124811,"journal":{"name":"Optimization Methods and Software","volume":"74 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127668597","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
A symmetric grouped and ordered multi-secant Quasi-Newton update formula 一个对称分组有序多割线拟牛顿更新公式
Optimization Methods and Software Pub Date : 2022-04-28 DOI: 10.1080/10556788.2022.2053970
Nicolas Boutet, J. Degroote, R. Haelterman
{"title":"A symmetric grouped and ordered multi-secant Quasi-Newton update formula","authors":"Nicolas Boutet, J. Degroote, R. Haelterman","doi":"10.1080/10556788.2022.2053970","DOIUrl":"https://doi.org/10.1080/10556788.2022.2053970","url":null,"abstract":"For Quasi-Newton methods, one of the most important challenges is to find an estimate of the Jacobian matrix as close as possible to the real matrix. While in root-finding problems multi-secant methods are regularly used, in optimization, it is the symmetric methods (in particular BFGS) that are popular. Combining multi-secant and symmetric methods in one single update formula would combine their benefits. However, it can be proved that the symmetry and multi-secant property are generally not compatible. In this paper, we try to work around this impossibility and approach the combination of both properties into a single update formula. The novelty of our method is to group secant equations based on their relative importance and to order those groups. This leads to a generic formulation of a symmetric Quasi-Newton method that is as close as possible to satisfying multiple secant equations. Our new update formula is modular and can be used in different applications where multiple secant equations, coming from different sources, are available. The formulation encompasses also different existing Quasi-Newton symmetric update formulas that try to approach the multi-secant property.","PeriodicalId":124811,"journal":{"name":"Optimization Methods and Software","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131743983","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Tensorial total variation-based image and video restoration with optimized projection methods 基于张量总变分的图像和视频优化投影复原方法
Optimization Methods and Software Pub Date : 2022-04-27 DOI: 10.1080/10556788.2022.2053971
O. Benchettou, A. Bentbib, A. Bouhamidi
{"title":"Tensorial total variation-based image and video restoration with optimized projection methods","authors":"O. Benchettou, A. Bentbib, A. Bouhamidi","doi":"10.1080/10556788.2022.2053971","DOIUrl":"https://doi.org/10.1080/10556788.2022.2053971","url":null,"abstract":"","PeriodicalId":124811,"journal":{"name":"Optimization Methods and Software","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124247459","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Isotonicity of the proximity operator and stochastic optimization problems in Hilbert quasi-lattices endowed with Lorentz cones 具有Lorentz锥的Hilbert拟格中邻近算子的等压性及随机优化问题
Optimization Methods and Software Pub Date : 2022-04-25 DOI: 10.1080/10556788.2022.2064467
Dezhou Kong, Li Sun, Haibin Chen, Yun Wang
{"title":"Isotonicity of the proximity operator and stochastic optimization problems in Hilbert quasi-lattices endowed with Lorentz cones","authors":"Dezhou Kong, Li Sun, Haibin Chen, Yun Wang","doi":"10.1080/10556788.2022.2064467","DOIUrl":"https://doi.org/10.1080/10556788.2022.2064467","url":null,"abstract":"In this paper, we discuss the isotonicity of the proximity operator in Hilbert quasi-lattices endowed with different Lorentz cones. The extended Lorentz cone is first defined by the Minkowski functionals of some subsets. We then establish some sufficient conditions for the isotonicity of the proximity operator concerning one order and two mutually dual orders induced by Lorentz cones, respectively. Similarly, the cases of the extended Lorentz cones and other ordered inequality properties of the proximity operator are analysed. By adopting these characterizations, some solvability and iterative algorithm theorems for the stochastic optimization problem are established by different order approaches. For solvability, the gradient of the mappings does not need to be continuous, and the solutions are optimal with respect to the orders. In the stochastic proximal algorithms, the mappings satisfy inequality conditions just for comparable elements, but the convergence direction and convergence rate are more optimal.","PeriodicalId":124811,"journal":{"name":"Optimization Methods and Software","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115043219","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A penalty decomposition approach for multi-objective cardinality-constrained optimization problems 多目标基数约束优化问题的惩罚分解方法
Optimization Methods and Software Pub Date : 2022-04-21 DOI: 10.1080/10556788.2022.2060972
M. Lapucci
{"title":"A penalty decomposition approach for multi-objective cardinality-constrained optimization problems","authors":"M. Lapucci","doi":"10.1080/10556788.2022.2060972","DOIUrl":"https://doi.org/10.1080/10556788.2022.2060972","url":null,"abstract":"In this manuscript, we consider multi-objective optimization problems with a cardinality constraint on the vector of decision variables and additional linear constraints. For this class of problems, we analyse necessary and sufficient conditions of Pareto optimality. We afterwards propose a Penalty Decomposition type algorithm, exploiting multi-objective descent methods, to tackle the aforementioned family of problems. We conduct a rigorous convergence analysis for the proposed method, where we prove that the produced sequence of points has limit points, each one being feasible and satisfying first-order optimality conditions. Numerical computational experiments, carried out on instances of relevant real-world problems such as sparse mean/variance portfolio selection and sparse regularized logistic regression, in their multi-objective formulation, show that the proposed procedure is effective at finding solutions forming good Pareto sets approximations.","PeriodicalId":124811,"journal":{"name":"Optimization Methods and Software","volume":"181 17","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120885665","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Using first-order information in direct multisearch for multiobjective optimization 基于一阶信息的直接多搜索多目标优化
Optimization Methods and Software Pub Date : 2022-04-21 DOI: 10.1080/10556788.2022.2060971
R. Andreani, A. Custódio, M. Raydan
{"title":"Using first-order information in direct multisearch for multiobjective optimization","authors":"R. Andreani, A. Custódio, M. Raydan","doi":"10.1080/10556788.2022.2060971","DOIUrl":"https://doi.org/10.1080/10556788.2022.2060971","url":null,"abstract":"Derivatives are an important tool for single-objective optimization. In fact, it is commonly accepted that derivative-based methods present a better performance than derivative-free optimization approaches. In this work, we will show that the same does not always apply to multiobjective derivative-based optimization, when the goal is to compute an approximation to the complete Pareto front of a given problem. The competitiveness of direct multisearch (DMS), a robust and efficient derivative-free optimization algorithm, will be stated for derivative-based multiobjective optimization (MOO) problems, by comparison with MOSQP, a state-of-art derivative-based MOO solver. We will then assess the potential enrichment of adding first-order information to the DMS framework. Derivatives will be used to prune the positive spanning sets considered at the poll step of the algorithm. The role of ascent directions, that conform to the geometry of the nearby feasible region, will then be highlighted.","PeriodicalId":124811,"journal":{"name":"Optimization Methods and Software","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130320554","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Unrestricted Douglas-Rachford algorithms for solving convex feasibility problems in Hilbert space 求解Hilbert空间凸可行性问题的无限制Douglas-Rachford算法
Optimization Methods and Software Pub Date : 2022-04-01 DOI: 10.1080/10556788.2022.2157003
Kay Barshad, A. Gibali, S. Reich
{"title":"Unrestricted Douglas-Rachford algorithms for solving convex feasibility problems in Hilbert space","authors":"Kay Barshad, A. Gibali, S. Reich","doi":"10.1080/10556788.2022.2157003","DOIUrl":"https://doi.org/10.1080/10556788.2022.2157003","url":null,"abstract":"In this work we focus on the convex feasibility problem (CFP) in Hilbert space. A specific method in this area that has gained a lot of interest in recent years is the Douglas-Rachford (DR) algorithm. This algorithm was originally introduced in 1956 for solving stationary and non-stationary heat equations. Then in 1979, Lions and Mercier adjusted and extended the algorithm with the aim of solving CFPs and even more general problems, such as finding zeros of the sum of two maximally monotone operators. Many developments which implement various concepts concerning this algorithm have occurred during the last decade. We introduce an unrestricted DR algorithm, which provides a general framework for such concepts. Using unrestricted products of a finite number of strongly nonexpansive operators, we apply this framework to provide new iterative methods, where, inter alia, such operators may be interlaced between the operators used in the scheme of our unrestricted DR algorithm.","PeriodicalId":124811,"journal":{"name":"Optimization Methods and Software","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116298502","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Using Nemirovski's Mirror-Prox method as basic procedure in Chubanov's method for solving homogeneous feasibility problems 利用Nemirovski的Mirror-Prox方法作为Chubanov方法中求解齐次可行性问题的基本步骤
Optimization Methods and Software Pub Date : 2022-03-04 DOI: 10.1080/10556788.2021.2023523
Zhang Wei, Kees Roos
{"title":"Using Nemirovski's Mirror-Prox method as basic procedure in Chubanov's method for solving homogeneous feasibility problems","authors":"Zhang Wei, Kees Roos","doi":"10.1080/10556788.2021.2023523","DOIUrl":"https://doi.org/10.1080/10556788.2021.2023523","url":null,"abstract":"We introduce a new variant of Chubanov's method for solving linear homogeneous systems with positive variables. In the Basic Procedure we use a recently introduced cut in combination with Nemirovski's Mirror-Prox method. We show that the cut requires at most time, just as Chubanov's cut. In an earlier paper it was shown that the new cuts are at least as sharp as those of Chubanov. Our Modified Main Algorithm is in essence the same as Chubanov's Main Algorithm, except that it uses the new Basic Procedure as a subroutine. The new method has time complexity, where is a suitably defined condition number. As we show, a simplified version of the new Basic Procedure competes well with the Smooth Perceptron Scheme of Peña and Soheili and, when combined with Rescaling, also with two commercial codes for linear optimization.","PeriodicalId":124811,"journal":{"name":"Optimization Methods and Software","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131585495","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
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