Journal of Optimization Theory and Applications最新文献

A Positive Semidefinite Safe Approximation of Multivariate Distributionally Robust Constraints Determined by Simple Functions. 由简单函数确定的多元分布鲁棒约束的正半定安全逼近。

IF 1.5 3区数学

Journal of Optimization Theory and Applications Pub Date : 2026-01-01 Epub Date: 2025-09-02 DOI: 10.1007/s10957-025-02791-5

Jana Dienstbier, Frauke Liers, Jan Rolfes

{"title":"A Positive Semidefinite Safe Approximation of Multivariate Distributionally Robust Constraints Determined by Simple Functions.","authors":"Jana Dienstbier, Frauke Liers, Jan Rolfes","doi":"10.1007/s10957-025-02791-5","DOIUrl":"https://doi.org/10.1007/s10957-025-02791-5","url":null,"abstract":"Single-level reformulations of (nonconvex) distributionally robust optimization (DRO) problems are often intractable, as they contain semi-infinite dual constraints. Based on such a semi-infinite reformulation, we present a safe approximation that allows for the computation of feasible solutions for DROs that depend on nonconvex multivariate simple functions. Moreover, the approximation allows to address ambiguity sets that can incorporate information on moments as well as confidence sets. The typical strong assumptions on the structure of the underlying constraints, such as convexity in the decisions or concavity in the uncertainty found in the literature were, at least in part, recently overcome in [16]. We start from the duality-based reformulation approach in [16] that can be applied for DRO constraints based on simple functions that are univariate in the uncertainty parameters. We significantly extend their approach to multivariate simple functions, which leads to a considerably wider applicability of the proposed reformulation approach. In order to achieve algorithmic tractability, the presented safe approximation is then realized by a discretized counterpart for the semi-infinite dual constraints. The approximation leads to a computationally tractable mixed-integer positive semidefinite problem for which state-of-the-art software implementations are readily available. The tractable safe approximation provides sufficient conditions for distributional robustness of the original problem, i.e., obtained solutions are provably robust.","PeriodicalId":50100,"journal":{"name":"Journal of Optimization Theory and Applications","volume":"208 1","pages":"1"},"PeriodicalIF":1.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12405389/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145001823","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On Tractable Convex Relaxations of Standard Quadratic Optimization Problems under Sparsity Constraints. 稀疏约束下标准二次优化问题的可处理凸松弛。

IF 1.6 3区数学

Journal of Optimization Theory and Applications Pub Date : 2025-01-01 Epub Date: 2025-01-23 DOI: 10.1007/s10957-024-02593-1

Immanuel Bomze, Bo Peng, Yuzhou Qiu, E Alper Yıldırım

引用次数: 0

Generalized Robust Optimization using the Notion of Set-Valued Probability. 基于集值概率概念的广义鲁棒优化。

IF 1.5 3区数学

Journal of Optimization Theory and Applications Pub Date : 2025-01-01 Epub Date: 2025-08-29 DOI: 10.1007/s10957-025-02790-6

Davide La Torre, Franklin Mendivil, Matteo Rocca

引用次数: 0

General Perturbation Resilient Dynamic String-Averaging for Inconsistent Problems with Superiorization. 具有优越性的不一致问题的一般摄动弹性动态弦平均。

IF 1.5 3区数学

Journal of Optimization Theory and Applications Pub Date : 2025-01-01 Epub Date: 2025-07-08 DOI: 10.1007/s10957-025-02763-9

Kay Barshad, Yair Censor

{"title":"General Perturbation Resilient Dynamic String-Averaging for Inconsistent Problems with Superiorization.","authors":"Kay Barshad, Yair Censor","doi":"10.1007/s10957-025-02763-9","DOIUrl":"10.1007/s10957-025-02763-9","url":null,"abstract":"In this paper we introduce a General Dynamic String-Averaging (GDSA) iterative scheme and investigate its convergence properties in the inconsistent case, that is, when the input operators don't have a common fixed point. The Dynamic String-Averaging Projection (DSAP) algorithm itself was introduced in an 2013 paper, where its strong convergence and bounded perturbation resilience were studied in the consistent case (that is, when the sets under consideration had a nonempty intersection). Results involving combination of the DSAP method with superiorization, were presented in 2015. The proof of the weak convergence of our GDSA method is based on the notion of \"strong coherence\" of sequences of operators that was introduced in 2019. This is an improvement of the property of \"coherence\" of sequences of operators introduced in 2001 by Bauschke and Combettes. Strong coherence provides a more convenient sufficient convergence condition for methods that employ infinite sequences of operators and it turns out to be a useful general tool when applied to proving the convergence of many iterative methods. In this paper we combine the ideas of both dynamic string-averaging and strong coherence, in order to analyze our GDSA method for a general class of operators and its bounded perturbation resilience in the inconsistent case with weak and strong convergence. We then discuss an application of the GDSA method to the Superiorization Methodology, developing results on the behavior of its superiorized version.","PeriodicalId":50100,"journal":{"name":"Journal of Optimization Theory and Applications","volume":"207 1","pages":"9"},"PeriodicalIF":1.5,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12238131/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144610227","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Signed Tropicalization of Polar Cones. 极锥的签名热带化。

IF 1.6 3区数学

Journal of Optimization Theory and Applications Pub Date : 2025-01-01 Epub Date: 2025-07-10 DOI: 10.1007/s10957-025-02732-2

Marianne Akian, Xavier Allamigeon, Stéphane Gaubert, Sergeĭ Sergeev

{"title":"Signed Tropicalization of Polar Cones.","authors":"Marianne Akian, Xavier Allamigeon, Stéphane Gaubert, Sergeĭ Sergeev","doi":"10.1007/s10957-025-02732-2","DOIUrl":"https://doi.org/10.1007/s10957-025-02732-2","url":null,"abstract":"We study the tropical analogue of the notion of polar of a cone, working over the semiring of tropical numbers with signs. We characterize the cones which arise as polars of sets of tropically nonnegative vectors by an invariance property with respect to a tropical analogue of Fourier-Motzkin elimination. We also relate tropical polars with images by the nonarchimedean valuation of classical polars over real closed nonarchimedean fields and show, in particular, that for semi-algebraic sets over such fields, the operation of taking the polar commutes with the operation of signed valuation (keeping track both of the nonarchimedean valuation and sign). We apply these results to characterize images by the signed valuation of classical cones of matrices, including the cones of positive semidefinite matrices, completely positive matrices, completely positive semidefinite matrices, and their polars, including the cone of co-positive matrices, showing that hierarchies of classical cones collapse under tropicalization. We finally discuss an application of these ideas to optimization with signed tropical numbers.","PeriodicalId":50100,"journal":{"name":"Journal of Optimization Theory and Applications","volume":"207 1","pages":"10"},"PeriodicalIF":1.6,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12246033/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144627625","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Effects of patient education on the oral behavior of patients with temporomandibular degenerative joint disease: a prospective case series study. 患者教育对颞下颌关节退行性疾病患者口腔行为的影响：前瞻性病例系列研究。

IF 1.6 3区数学

Journal of Optimization Theory and Applications Pub Date : 2025-01-01 Epub Date: 2022-06-09 DOI: 10.1080/08869634.2022.2085410

Shasha Liu, Bin Cai, Shuai Fan, Yuxin Zhang, Shenji Lu, Lili Xu

{"title":"Effects of patient education on the oral behavior of patients with temporomandibular degenerative joint disease: a prospective case series study.","authors":"Shasha Liu, Bin Cai, Shuai Fan, Yuxin Zhang, Shenji Lu, Lili Xu","doi":"10.1080/08869634.2022.2085410","DOIUrl":"10.1080/08869634.2022.2085410","url":null,"abstract":"Objective: To evaluate the effects of patient education and related factors on oral behaviors (OBs) in patients with temporomandibular joint degenerative diseases.Methods: Sixty-three patients were included. Temporomandibular joint specialists conducted clinical examinations, provided patient education, and administered the Oral Behavior Checklist (OBC) questionnaire at baseline. Patients were followed up at 6 months.Results: Eight OBs showed a high incidence among patients. At the 6-month follow-up, the incidence of 6 of the OBs decreased, all of which were high incidence OBs. The frequency of 9 OBs decreased, of which 8 were high incidence OBs. The average OBC score decreased from 22.97 ± 9.30 to 17.90 ± 9.28. Age, education level, and original OBC score had a significant effect on OB improvement.Conclusion: Patient education and the corresponding treatment are conducive to OB improvement. The related factors affecting the improvement in patients' OBs were age, education level, and OB severity.","PeriodicalId":50100,"journal":{"name":"Journal of Optimization Theory and Applications","volume":"158 1","pages":"100-109"},"PeriodicalIF":1.6,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74072873","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

ABB Theorems: Results and Limitations in Infinite Dimensions. ABB定理：无限维的结果和限制。

IF 1.5 3区数学

Journal of Optimization Theory and Applications Pub Date : 2025-01-01 Epub Date: 2025-08-01 DOI: 10.1007/s10957-025-02797-z

Aris Daniilidis, Carlo Alberto De Bernardi, Enrico Miglierina

引用次数: 0

Simultaneous Diagonalization Under Weak Regularity and a Characterization 弱规则性下的同时对角线化及其特征

IF 1.9 3区数学

Journal of Optimization Theory and Applications Pub Date : 2024-09-17 DOI: 10.1007/s10957-024-02526-y

Fabián Flores-Bazán, Felipe Opazo

引用次数: 0

Seeking Consensus on Subspaces in Federated Principal Component Analysis 在联合主成分分析中寻求子空间共识

IF 1.9 3区数学

Journal of Optimization Theory and Applications Pub Date : 2024-09-14 DOI: 10.1007/s10957-024-02523-1

Lei Wang, Xin Liu, Yin Zhang

{"title":"Seeking Consensus on Subspaces in Federated Principal Component Analysis","authors":"Lei Wang, Xin Liu, Yin Zhang","doi":"10.1007/s10957-024-02523-1","DOIUrl":"https://doi.org/10.1007/s10957-024-02523-1","url":null,"abstract":"In this paper, we develop an algorithm for federated principal component analysis (PCA) with emphases on both communication efficiency and data privacy. Generally speaking, federated PCA algorithms based on direct adaptations of classic iterative methods, such as simultaneous subspace iterations, are unable to preserve data privacy, while algorithms based on variable-splitting and consensus-seeking, such as alternating direction methods of multipliers (ADMM), lack in communication-efficiency. In this work, we propose a novel consensus-seeking formulation by equalizing subspaces spanned by splitting variables instead of equalizing variables themselves, thus greatly relaxing feasibility restrictions and allowing much faster convergence. Then we develop an ADMM-like algorithm with several special features to make it practically efficient, including a low-rank multiplier formula and techniques for treating subproblems. We establish that the proposed algorithm can better protect data privacy than classic methods adapted to the federated PCA setting. We derive convergence results, including a worst-case complexity estimate, for the proposed ADMM-like algorithm in the presence of the nonlinear equality constraints. Extensive empirical results are presented to show that the new algorithm, while enhancing data privacy, requires far fewer rounds of communication than existing peer algorithms for federated PCA.","PeriodicalId":50100,"journal":{"name":"Journal of Optimization Theory and Applications","volume":"18 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260878","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 Multilevel Method for Self-Concordant Minimization 自洽最小化的多层次方法

IF 1.9 3区数学

Journal of Optimization Theory and Applications Pub Date : 2024-09-14 DOI: 10.1007/s10957-024-02509-z

Nick Tsipinakis, Panos Parpas

{"title":"A Multilevel Method for Self-Concordant Minimization","authors":"Nick Tsipinakis, Panos Parpas","doi":"10.1007/s10957-024-02509-z","DOIUrl":"https://doi.org/10.1007/s10957-024-02509-z","url":null,"abstract":"The analysis of second-order optimization methods based either on sub-sampling, randomization or sketching has two serious shortcomings compared to the conventional Newton method. The first shortcoming is that the analysis of the iterates has only been shown to be scale-invariant only under specific assumptions on the problem structure. The second shortfall is that the fast convergence rates of second-order methods have only been established by making assumptions regarding the input data. In this paper, we propose a randomized Newton method for self-concordant functions to address both shortfalls. We propose a Self-concordant Iterative-minimization-Galerkin-based Multilevel Algorithm (SIGMA) and establish its super-linear convergence rate using the theory of self-concordant functions. Our analysis is based on the connections between multigrid optimization methods, and the role of coarse-grained or reduced-order models in the computation of search directions. We take advantage of the insights from the analysis to significantly improve the performance of second-order methods in machine learning applications. We report encouraging initial experiments that suggest SIGMA outperforms other state-of-the-art sub-sampled/sketched Newton methods for both medium and large-scale problems.","PeriodicalId":50100,"journal":{"name":"Journal of Optimization Theory and Applications","volume":"87 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142261102","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