Journal of Global Optimization最新文献_第3页

Stochastic optimization problems with nonlinear dependence on a probability measure via the Wasserstein metric 通过瓦瑟斯坦度量非线性依赖概率度量的随机优化问题

IF 1.8 3区数学

Journal of Global Optimization Pub Date : 2024-06-20 DOI: 10.1007/s10898-024-01380-6

Vlasta Kaňková

{"title":"Stochastic optimization problems with nonlinear dependence on a probability measure via the Wasserstein metric","authors":"Vlasta Kaňková","doi":"10.1007/s10898-024-01380-6","DOIUrl":"https://doi.org/10.1007/s10898-024-01380-6","url":null,"abstract":"Nonlinear dependence on a probability measure has recently been encountered with increasing intensity in stochastic optimization. This type of dependence corresponds to many situations in applications; it can appear in problems static (one-stage), dynamic with finite (multi-stage) or infinite horizon, and single- and multi-objective ones. Moreover, the nonlinear dependence can appear not only in the objective functions but also in the constraint sets. In this paper, we will consider static one-objective problems in which the nonlinear dependence appears in the objective function and may also appear in the constraint sets. In detail, we consider “deterministic” constraint sets, whose dependence on the probability measure is nonlinear, constraint sets determined by second-order stochastic dominance, and sets given by mean-risk problems. The last mentioned instance means that the constraint set corresponds to solutions which guarantee acceptable values of both criteria. To obtain relevant assertions, we employ the stability results given by the Wasserstein metric, based on the ( {{mathcal {L}}}_{1} ) norm. We mainly focus on the case in which a solution has to be obtained on the basis of the data and of investigating a relationship between the original problem and its empirical version.","PeriodicalId":15961,"journal":{"name":"Journal of Global Optimization","volume":"31 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141501070","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

Curvature-constrained Steiner networks with three terminals 有三个终端的曲率受限斯坦纳网络

IF 1.8 3区数学

Journal of Global Optimization Pub Date : 2024-06-17 DOI: 10.1007/s10898-024-01414-z

Peter A. Grossman, David Kirszenblat, Marcus Brazil, J. Hyam Rubinstein, Doreen A. Thomas

引用次数: 0

Deep learning the efficient frontier of convex vector optimization problems 深度学习凸向量优化问题的有效前沿

IF 1.8 3区数学

Journal of Global Optimization Pub Date : 2024-05-30 DOI: 10.1007/s10898-024-01408-x

Zachary Feinstein, Birgit Rudloff

引用次数: 0

On exact and inexact RLT and SDP-RLT relaxations of quadratic programs with box constraints 论带盒式约束的二次方程程序的精确和非精确 RLT 和 SDP-RLT 放松

IF 1.8 3区数学

Journal of Global Optimization Pub Date : 2024-05-30 DOI: 10.1007/s10898-024-01407-y

Yuzhou Qiu, E. Alper Yıldırım

{"title":"On exact and inexact RLT and SDP-RLT relaxations of quadratic programs with box constraints","authors":"Yuzhou Qiu, E. Alper Yıldırım","doi":"10.1007/s10898-024-01407-y","DOIUrl":"https://doi.org/10.1007/s10898-024-01407-y","url":null,"abstract":"Quadratic programs with box constraints involve minimizing a possibly nonconvex quadratic function subject to lower and upper bounds on each variable. This is a well-known NP-hard problem that frequently arises in various applications. We focus on two convex relaxations, namely the reformulation–linearization technique (RLT) relaxation and the SDP-RLT relaxation obtained by combining the Shor relaxation with the RLT relaxation. Both relaxations yield lower bounds on the optimal value of a quadratic program with box constraints. We show that each component of each vertex of the RLT relaxation lies in the set ({0,frac{1}{2},1}). We present complete algebraic descriptions of the set of instances that admit exact RLT relaxations as well as those that admit exact SDP-RLT relaxations. We show that our descriptions can be converted into algorithms for efficiently constructing instances with (1) exact RLT relaxations, (2) inexact RLT relaxations, (3) exact SDP-RLT relaxations, and (4) exact SDP-RLT but inexact RLT relaxations. Our preliminary computational experiments illustrate that our algorithms are capable of generating computationally challenging instances for state-of-the-art solvers.","PeriodicalId":15961,"journal":{"name":"Journal of Global Optimization","volume":"13 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141194395","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

Optimization in complex spaces with the mixed Newton method 用混合牛顿法优化复杂空间

IF 1.8 3区数学

Journal of Global Optimization Pub Date : 2024-05-30 DOI: 10.1007/s10898-023-01355-z

Sergei Bakhurin, Roland Hildebrand, Mohammad Alkousa, Alexander Titov, Nikita Yudin

{"title":"Optimization in complex spaces with the mixed Newton method","authors":"Sergei Bakhurin, Roland Hildebrand, Mohammad Alkousa, Alexander Titov, Nikita Yudin","doi":"10.1007/s10898-023-01355-z","DOIUrl":"https://doi.org/10.1007/s10898-023-01355-z","url":null,"abstract":"We propose a second-order method for unconditional minimization of functions f(z) of complex arguments. We call it the mixed Newton method due to the use of the mixed Wirtinger derivative (frac{partial ^2f}{partial {bar{z}}partial z}) for computation of the search direction, as opposed to the full Hessian (frac{partial ^2f}{partial (z,{bar{z}})^2}) in the classical Newton method. The method has been developed for specific applications in wireless network communications, but its global convergence properties are shown to be superior on a more general class of functions f, namely sums of squares of absolute values of holomorphic functions. In particular, for such objective functions minima are surrounded by attraction basins, while the iterates are repelled from other types of critical points. We provide formulas for the asymptotic convergence rate and show that in the scalar case the method reduces to the well-known complex Newton method for the search of zeros of holomorphic functions. In this case, it exhibits generically fractal global convergence patterns.","PeriodicalId":15961,"journal":{"name":"Journal of Global Optimization","volume":"44 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141194259","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 surrogate-assisted a priori multiobjective evolutionary algorithm for constrained multiobjective optimization problems 用于受约束多目标优化问题的代理辅助先验多目标进化算法

IF 1.8 3区数学

Journal of Global Optimization Pub Date : 2024-05-29 DOI: 10.1007/s10898-024-01387-z

Pouya Aghaei pour, Jussi Hakanen, Kaisa Miettinen

{"title":"A surrogate-assisted a priori multiobjective evolutionary algorithm for constrained multiobjective optimization problems","authors":"Pouya Aghaei pour, Jussi Hakanen, Kaisa Miettinen","doi":"10.1007/s10898-024-01387-z","DOIUrl":"https://doi.org/10.1007/s10898-024-01387-z","url":null,"abstract":"We consider multiobjective optimization problems with at least one computationally expensive constraint function and propose a novel surrogate-assisted evolutionary algorithm that can incorporate preference information given a priori. We employ Kriging models to approximate expensive objective and constraint functions, enabling us to introduce a new selection strategy that emphasizes the generation of feasible solutions throughout the optimization process. In our innovative model management, we perform expensive function evaluations to identify feasible solutions that best reflect the decision maker’s preferences provided before the process. To assess the performance of our proposed algorithm, we utilize two distinct parameterless performance indicators and compare them against existing algorithms from the literature using various real-world engineering and benchmark problems. Furthermore, we assemble new algorithms to analyze the effects of the selection strategy and the model management on the performance of the proposed algorithm. The results show that in most cases, our algorithm has a better performance than the assembled algorithms, especially when there is a restricted budget for expensive function evaluations.","PeriodicalId":15961,"journal":{"name":"Journal of Global Optimization","volume":"239 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141172451","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

Node selection through upper bounding local search methods in branch & bound solvers for NCOPs 在 NCOP 的分支与边界求解器中通过上界局部搜索方法选择节点

IF 1.8 3区数学

Journal of Global Optimization Pub Date : 2024-05-25 DOI: 10.1007/s10898-024-01403-2

Victor Reyes, Ignacio Araya

{"title":"Node selection through upper bounding local search methods in branch & bound solvers for NCOPs","authors":"Victor Reyes, Ignacio Araya","doi":"10.1007/s10898-024-01403-2","DOIUrl":"https://doi.org/10.1007/s10898-024-01403-2","url":null,"abstract":"Interval-based branch & bound solvers are commonly used for solving Nonlinear Continuous global Optimization Problems (NCOPs). In each iteration, the solver strategically chooses and processes a node within the search tree. The node is bisected and the two generated offspring nodes are processed by filtering methods. For each of these nodes, the solver also searches for new feasible solutions in order to update the best candidate solution. The cost of this solution is used for pruning non-optimal branches of the search tree. Thus, node selection and finding new solutions, stands as pivotal aspects in the functionality of these kind of solvers. The ability to find close-to-optimal solutions early in the search process may discard extensive non-optimal search space regions, thereby effectively reducing the overall size of the search tree. In this work, we propose three novel node selection algorithms that use the feasible solutions obtained through a cost-effective iterative method. Upon updating the best candidate solution, these algorithms strategically choose the node containing this solution for subsequent processing. The newly introduced strategies have been incorporated as node selection methods in a state-of-the-art branch & bound solver, showing promising results in a set of 57 benchmark instances.\u0000","PeriodicalId":15961,"journal":{"name":"Journal of Global Optimization","volume":"47 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141150599","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

The edge labeling of higher order Voronoi diagrams 高阶 Voronoi 图的边标注

IF 1.8 3区数学

Journal of Global Optimization Pub Date : 2024-05-21 DOI: 10.1007/s10898-024-01386-0

Mercè Claverol, Andrea de las Heras Parrilla, Clemens Huemer, Alejandra Martínez-Moraian

引用次数: 0

Dual optimality conditions for the difference of extended real valued increasing co-radiant functions 扩展实值递增共辐射函数差分的双重最优条件

IF 1.8 3区数学

Journal of Global Optimization Pub Date : 2024-05-11 DOI: 10.1007/s10898-024-01404-1

Mohammad Hossein Daryaei, Hossein Mohebi

引用次数: 0

On polling directions for randomized direct-search approaches: application to beam angle optimization in intensity-modulated proton therapy 随机直接搜索方法的投票方向：应用于强度调制质子疗法中的射束角优化

IF 1.8 3区数学

Journal of Global Optimization Pub Date : 2024-05-10 DOI: 10.1007/s10898-024-01400-5

H. Rocha, J. Dias

{"title":"On polling directions for randomized direct-search approaches: application to beam angle optimization in intensity-modulated proton therapy","authors":"H. Rocha, J. Dias","doi":"10.1007/s10898-024-01400-5","DOIUrl":"https://doi.org/10.1007/s10898-024-01400-5","url":null,"abstract":"Deterministic direct-search methods have been successfully used to address real-world challenging optimization problems, including the beam angle optimization (BAO) problem in radiation therapy treatment planning. BAO is a highly non-convex optimization problem typically treated as the optimization of an expensive multi-modal black-box function which results in a computationally time consuming procedure. For the recently available modalities of radiation therapy with protons (instead of photons) further efficiency in terms of computational time is required despite the success of the different strategies developed to accelerate BAO approaches. Introducing randomization into otherwise deterministic direct-search approaches has been shown to lead to excellent computational performance, particularly when considering a reduced number (as low as two) of random poll directions at each iteration. In this study several randomized direct-search strategies are tested considering different sets of polling directions. Results obtained using a prostate and a head-and-neck cancer cases confirmed the high-quality results obtained by deterministic direct-search methods. Randomized strategies using a reduced number of polling directions showed difficulties for the higher dimensional search space (head-and-neck) and, despite the excellent mean results for the prostate cancer case, outliers were observed, a result that is often ignored in the literature. While, for general global optimization problems, mean results (or obtaining the global optimum once) might be enough for assessing the performance of the randomized method, in real-world problems one should not disregard the worst-case scenario and beware of the possibility of poor results since, many times, it is only possible to run the optimization problem once. This is even more important in healthcare applications where the mean patient does not exist and the best treatment possible must be assured for every patient.","PeriodicalId":15961,"journal":{"name":"Journal of Global Optimization","volume":"20 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140937382","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