Journal of Global Optimization最新文献_第7页

Consensus-based optimization for multi-objective problems: a multi-swarm approach 基于共识的多目标问题优化：多群方法

IF 1.8 3区数学

Journal of Global Optimization Pub Date : 2024-02-15 DOI: 10.1007/s10898-024-01369-1

Kathrin Klamroth, Michael Stiglmayr, Claudia Totzeck

引用次数: 0

A method for searching for a globally optimal k-partition of higher-dimensional datasets 搜索高维数据集全局最优 k 分区的方法

IF 1.8 3区数学

Journal of Global Optimization Pub Date : 2024-02-13 DOI: 10.1007/s10898-024-01372-6

{"title":"A method for searching for a globally optimal k-partition of higher-dimensional datasets","authors":"","doi":"10.1007/s10898-024-01372-6","DOIUrl":"https://doi.org/10.1007/s10898-024-01372-6","url":null,"abstract":"<h3>Abstract</h3> The problem of finding a globally optimal k-partition of a set (mathcal {A}) is a very intricate optimization problem for which in general, except in the case of one-dimensional data, i.e., for data with one feature ( (mathcal {A}subset mathbb {R}) ), there is no method to solve. Only in the one-dimensional case, there are efficient methods based on the fact that the search for a globally optimal k-partition is equivalent to solving a global optimization problem for a symmetric Lipschitz-continuous function using the global optimization algorithm DIRECT. In the present paper, we propose a method for finding a globally optimal k-partition in the general case ( (mathcal {A}subset mathbb {R}^n) , (nge 1) ), generalizing an idea for solving the Lipschitz global optimization for symmetric functions. To do this, we propose a method that combines a global optimization algorithm with linear constraints and the k-means algorithm. The first of these two algorithms is used only to find a good initial approximation for the k-means algorithm. The method was tested on a number of artificial datasets and on several examples from the UCI Machine Learning Repository, and an application in spectral clustering for linearly non-separable datasets is also demonstrated. Our proposed method proved to be very efficient. ","PeriodicalId":15961,"journal":{"name":"Journal of Global Optimization","volume":"25 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139759418","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Global solution of quadratic problems using interval methods and convex relaxations 利用区间法和凸松弛法求解二次函数问题的全局方案

IF 1.8 3区数学

Journal of Global Optimization Pub Date : 2024-02-12 DOI: 10.1007/s10898-024-01370-8

Sourour Elloumi, Amélie Lambert, Bertrand Neveu, Gilles Trombettoni

{"title":"Global solution of quadratic problems using interval methods and convex relaxations","authors":"Sourour Elloumi, Amélie Lambert, Bertrand Neveu, Gilles Trombettoni","doi":"10.1007/s10898-024-01370-8","DOIUrl":"https://doi.org/10.1007/s10898-024-01370-8","url":null,"abstract":"Interval branch-and-bound solvers provide reliable algorithms for handling non-convex optimization problems by ensuring the feasibility and the optimality of the computed solutions, i.e. independently from the floating-point rounding errors. Moreover, these solvers deal with a wide variety of mathematical operators. However, these solvers are not dedicated to quadratic optimization and do not exploit nonlinear convex relaxations in their framework. We present an interval branch-and-bound method that can efficiently solve quadratic optimization problems. At each node explored by the algorithm, our solver uses a quadratic convex relaxation which is as strong as a semi-definite programming relaxation, and a variable selection strategy dedicated to quadratic problems. The interval features can then propagate efficiently this information for contracting all variable domains. We also propose to make our algorithm rigorous by certifying firstly the convexity of the objective function of our relaxation, and secondly the validity of the lower bound calculated at each node. In the non-rigorous case, our experiments show significant speedups on general integer quadratic instances, and when reliability is required, our first results show that we are able to handle medium-sized instances in a reasonable running time.","PeriodicalId":15961,"journal":{"name":"Journal of Global Optimization","volume":"16 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139759499","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Efficiency conditions and duality for multiobjective semi-infinite programming problems on Hadamard manifolds 哈达玛流形上多目标半无限编程问题的效率条件和对偶性

IF 1.8 3区数学

Journal of Global Optimization Pub Date : 2024-01-31 DOI: 10.1007/s10898-024-01367-3

Balendu Bhooshan Upadhyay, Arnav Ghosh, Savin Treanţă

引用次数: 0

The appeals of quadratic majorization–minimization 二次大化-最小化的诉求

IF 1.8 3区数学

Journal of Global Optimization Pub Date : 2024-01-28 DOI: 10.1007/s10898-023-01361-1

Marc C. Robini, Lihui Wang, Yuemin Zhu

引用次数: 0

Generalized derivatives of optimal-value functions with parameterized convex programs embedded 嵌入参数化凸程序的最优值函数广义导数

IF 1.8 3区数学

Journal of Global Optimization Pub Date : 2024-01-25 DOI: 10.1007/s10898-023-01359-9

Yingkai Song, Paul I. Barton

{"title":"Generalized derivatives of optimal-value functions with parameterized convex programs embedded","authors":"Yingkai Song, Paul I. Barton","doi":"10.1007/s10898-023-01359-9","DOIUrl":"https://doi.org/10.1007/s10898-023-01359-9","url":null,"abstract":"This article proposes new practical methods for furnishing generalized derivative information of optimal-value functions with embedded parameterized convex programs, with potential applications in nonsmooth equation-solving and optimization. We consider three cases of parameterized convex programs: (1) partial convexity—functions in the convex programs are convex with respect to decision variables for fixed values of parameters, (2) joint convexity—the functions are convex with respect to both decision variables and parameters, and (3) linear programs where the parameters appear in the objective function. These new methods calculate an LD-derivative, which is a recently established useful generalized derivative concept, by constructing and solving a sequence of auxiliary linear programs. In the general partial convexity case, our new method requires that the strong Slater conditions are satisfied for the embedded convex program’s decision space, and requires that the convex program has a unique optimal solution. It is shown that these conditions are essentially less stringent than the regularity conditions required by certain established methods, and our new method is at the same time computationally preferable over these methods. In the joint convexity case, the uniqueness requirement of an optimal solution is further relaxed, and to our knowledge, there is no established method for computing generalized derivatives prior to this work. In the linear program case, both the Slater conditions and the uniqueness of an optimal solution are not required by our new method.","PeriodicalId":15961,"journal":{"name":"Journal of Global Optimization","volume":"9 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139560266","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

A strong P-formulation for global optimization of industrial water-using and treatment networks 工业用水和水处理网络全局优化的强 P 公式

IF 1.8 3区数学

Journal of Global Optimization Pub Date : 2024-01-25 DOI: 10.1007/s10898-023-01363-z

Xin Cheng, Xiang Li

{"title":"A strong P-formulation for global optimization of industrial water-using and treatment networks","authors":"Xin Cheng, Xiang Li","doi":"10.1007/s10898-023-01363-z","DOIUrl":"https://doi.org/10.1007/s10898-023-01363-z","url":null,"abstract":"The problem of finding the optimal flow allocation within an industrial water-using and treatment network can be formulated into nonconvex nonlinear program or nonconvex mixed-integer nonlinear program. The efficiency of global optimization of the nonconvex program relies heavily on the strength of the problem formulation. In this paper, we propose a variant of the commonly used P-formulation, called the P(^*)-formulation, for the water treatment network (WTN) and the total water network (TWN) that includes water-using and water treatment units. For either type of networks, we prove that the P(^*)-formulation is at least as strong as the P-formulation under mild bound consistency conditions. We also prove for either type of networks that the P(^*)-formulation is at least as strong as the split-fraction based formulation (called SF-formulation) under certain bound consistency conditions. The computational study shows that the P(^*)-formulation significantly outperforms the P- and the SF-formulations. For some problem instances, the P(^*)-formulation is faster than the other two formulations by several orders of magnitudes.","PeriodicalId":15961,"journal":{"name":"Journal of Global Optimization","volume":"9 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139560375","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

First- and second-order optimality conditions of nonsmooth sparsity multiobjective optimization via variational analysis 通过变分分析实现非光滑稀疏性多目标优化的一阶和二阶最优条件

IF 1.8 3区数学

Journal of Global Optimization Pub Date : 2024-01-22 DOI: 10.1007/s10898-023-01357-x

Jiawei Chen, Huasheng Su, Xiaoqing Ou, Yibing Lv

引用次数: 0

Interval constraint programming for globally solving catalog-based categorical optimization 基于目录的分类优化全局求解的区间约束编程

IF 1.8 3区数学

Journal of Global Optimization Pub Date : 2024-01-22 DOI: 10.1007/s10898-023-01362-0

引用次数: 0

Gaining or losing perspective for convex multivariate functions on a simplex 单纯形上凸多元函数的视角增减

IF 1.8 3区数学

Journal of Global Optimization Pub Date : 2024-01-22 DOI: 10.1007/s10898-023-01356-y

Luze Xu, Jon Lee

{"title":"Gaining or losing perspective for convex multivariate functions on a simplex","authors":"Luze Xu, Jon Lee","doi":"10.1007/s10898-023-01356-y","DOIUrl":"https://doi.org/10.1007/s10898-023-01356-y","url":null,"abstract":"MINLO (mixed-integer nonlinear optimization) formulations of the disjunction between the origin and a polytope via a binary indicator variable have broad applicability in nonlinear combinatorial optimization, for modeling a fixed cost c associated with carrying out a set of d activities and a convex variable cost function f associated with the levels of the activities. The perspective relaxation is often used to solve such models to optimality in a branch-and-bound context, especially in the context in which f is univariate (e.g., in Markowitz-style portfolio optimization). But such a relaxation typically requires conic solvers and are typically not compatible with general-purpose NLP software which can accommodate additional classes of constraints. This motivates the study of weaker relaxations to investigate when simpler relaxations may be adequate. Comparing the volume (i.e., Lebesgue measure) of the relaxations as means of comparing them, we lift some of the results related to univariate functions f to the multivariate case. Along the way, we survey, connect and extend relevant results on integration over a simplex, some of which we concretely employ, and others of which can be used for further exploration on our main subject.","PeriodicalId":15961,"journal":{"name":"Journal of Global Optimization","volume":"121 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139514938","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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