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Journal of Optimization Theory and Applications最新文献

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Fast Convex Optimization via Differential Equation with Hessian-Driven Damping and Tikhonov Regularization 通过带有黑森驱动阻尼和提霍诺夫正则化的微分方程实现快速凸优化
IF 1.9 3区 数学
Journal of Optimization Theory and Applications Pub Date : 2024-05-30 DOI: 10.1007/s10957-024-02462-x
Gangfan Zhong, Xiaozhe Hu, Ming Tang, Liuqiang Zhong
{"title":"Fast Convex Optimization via Differential Equation with Hessian-Driven Damping and Tikhonov Regularization","authors":"Gangfan Zhong, Xiaozhe Hu, Ming Tang, Liuqiang Zhong","doi":"10.1007/s10957-024-02462-x","DOIUrl":"https://doi.org/10.1007/s10957-024-02462-x","url":null,"abstract":"<p>In this paper, we consider a class of second-order ordinary differential equations with Hessian-driven damping and Tikhonov regularization, which arises from the minimization of a smooth convex function in Hilbert spaces. Inspired by Attouch et al. (J Differ Equ 261:5734–5783, 2016), we establish that the function value along the solution trajectory converges to the optimal value, and prove that the convergence rate can be as fast as <span>(o(1/t^2))</span>. By constructing proper energy function, we prove that the trajectory strongly converges to a minimizer of the objective function of minimum norm. Moreover, we propose a gradient-based optimization algorithm based on numerical discretization, and demonstrate its effectiveness in numerical experiments.</p>","PeriodicalId":50100,"journal":{"name":"Journal of Optimization Theory and Applications","volume":"33 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141196592","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
Modified Memoryless Spectral-Scaling Broyden Family on Riemannian Manifolds 黎曼曼曼体上的修正无记忆谱缩放布洛伊登家族
IF 1.9 3区 数学
Journal of Optimization Theory and Applications Pub Date : 2024-05-29 DOI: 10.1007/s10957-024-02449-8
Hiroyuki Sakai, Hideaki Iiduka
{"title":"Modified Memoryless Spectral-Scaling Broyden Family on Riemannian Manifolds","authors":"Hiroyuki Sakai, Hideaki Iiduka","doi":"10.1007/s10957-024-02449-8","DOIUrl":"https://doi.org/10.1007/s10957-024-02449-8","url":null,"abstract":"<p>This paper presents modified memoryless quasi-Newton methods based on the spectral-scaling Broyden family on Riemannian manifolds. The method involves adding one parameter to the search direction of the memoryless self-scaling Broyden family on the manifold. Moreover, it uses a general map instead of vector transport. This idea has already been proposed within a general framework of Riemannian conjugate gradient methods where one can use vector transport, scaled vector transport, or an inverse retraction. We show that the search direction satisfies the sufficient descent condition under some assumptions on the parameters. In addition, we show global convergence of the proposed method under the Wolfe conditions. We numerically compare it with existing methods, including Riemannian conjugate gradient methods and the memoryless spectral-scaling Broyden family. The numerical results indicate that the proposed method with the BFGS formula is suitable for solving an off-diagonal cost function minimization problem on an oblique manifold.</p>","PeriodicalId":50100,"journal":{"name":"Journal of Optimization Theory and Applications","volume":"70 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141171452","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
Stability of Minima in Constrained Optimization Problems and Implicit Function Theorem 约束优化问题中最小值的稳定性和隐函数定理
IF 1.9 3区 数学
Journal of Optimization Theory and Applications Pub Date : 2024-05-29 DOI: 10.1007/s10957-024-02459-6
Aram V. Arutyunov, Kirill A. Tsarkov, Sergey E. Zhukovskiy
{"title":"Stability of Minima in Constrained Optimization Problems and Implicit Function Theorem","authors":"Aram V. Arutyunov, Kirill A. Tsarkov, Sergey E. Zhukovskiy","doi":"10.1007/s10957-024-02459-6","DOIUrl":"https://doi.org/10.1007/s10957-024-02459-6","url":null,"abstract":"<p>In the paper, we consider both finite-dimensional and infinite-dimensional optimization problems with inclusion-type and equality-type constraints. We obtain sufficient conditions for the stability in the weak topology of a solution to this problem with respect to small perturbations of the problem parameters. In the finite-dimensional case, conditions for the stability in the strong topology of the solution are obtained for the problem with equality-type constraints. These conditions are based on a certain implicit function theorem.</p>","PeriodicalId":50100,"journal":{"name":"Journal of Optimization Theory and Applications","volume":"18 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141196666","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 Notion of Fenchel Conjugate for Set-Valued Mappings 定值映射的芬切尔共轭概念
IF 1.9 3区 数学
Journal of Optimization Theory and Applications Pub Date : 2024-05-28 DOI: 10.1007/s10957-024-02455-w
Nguyen Mau Nam, Gary Sandine, Nguyen Nang Thieu, Nguyen Dong Yen
{"title":"A Notion of Fenchel Conjugate for Set-Valued Mappings","authors":"Nguyen Mau Nam, Gary Sandine, Nguyen Nang Thieu, Nguyen Dong Yen","doi":"10.1007/s10957-024-02455-w","DOIUrl":"https://doi.org/10.1007/s10957-024-02455-w","url":null,"abstract":"<p>In this paper, we present a novel concept of the Fenchel conjugate for set-valued mappings and investigate its properties in finite and infinite dimensions. After establishing some fundamental properties of the Fenchel conjugate for set-valued mappings, we derive its main calculus rules in various settings. Our approach is geometric and draws inspiration from the successful application of this method by B.S. Mordukhovich and coauthors in variational and convex analysis. Subsequently, we demonstrate that our new findings for the Fenchel conjugate of set-valued mappings can be utilized to obtain many old and new calculus rules of convex generalized differentiation in both finite and infinite dimensions.</p>","PeriodicalId":50100,"journal":{"name":"Journal of Optimization Theory and Applications","volume":"5 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141173522","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
Optimality and Duality for Robust Optimization Problems Involving Intersection of Closed Sets 涉及封闭集交集的稳健优化问题的最优性和对偶性
IF 1.9 3区 数学
Journal of Optimization Theory and Applications Pub Date : 2024-05-28 DOI: 10.1007/s10957-024-02447-w
Nguyen Canh Hung, Thai Doan Chuong, Nguyen Le Hoang Anh
{"title":"Optimality and Duality for Robust Optimization Problems Involving Intersection of Closed Sets","authors":"Nguyen Canh Hung, Thai Doan Chuong, Nguyen Le Hoang Anh","doi":"10.1007/s10957-024-02447-w","DOIUrl":"https://doi.org/10.1007/s10957-024-02447-w","url":null,"abstract":"<p>In this paper, we study a robust optimization problem whose constraints include nonsmooth and nonconvex functions and the intersection of closed sets. Using advanced variational analysis tools, we first provide necessary conditions for the optimality of the robust optimization problem. We then establish sufficient conditions for the optimality of the considered problem under the assumption of generalized convexity. In addition, we present a dual problem to the primal robust optimization problem and examine duality relations.\u0000</p>","PeriodicalId":50100,"journal":{"name":"Journal of Optimization Theory and Applications","volume":"28 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141171526","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
Optimal R &D Investment Problem with Regime-Switching 具有制度转换功能的最佳研发投资问题
IF 1.9 3区 数学
Journal of Optimization Theory and Applications Pub Date : 2024-05-27 DOI: 10.1007/s10957-024-02451-0
Ming-hui Wang, Jia Yue, Nan-jing Huang
{"title":"Optimal R &D Investment Problem with Regime-Switching","authors":"Ming-hui Wang, Jia Yue, Nan-jing Huang","doi":"10.1007/s10957-024-02451-0","DOIUrl":"https://doi.org/10.1007/s10957-024-02451-0","url":null,"abstract":"<p>In this paper, we study the optimal research and development (R &amp;D) investment problem under the framework of real options in a regime-switching environment. We assume that the firm has an R &amp;D project whose input process with technical uncertainty is affected by different regimes. By the method of dynamic programming, we have obtained the related Hamilton–Jacobi–Bellman (HJB) equation and solved it in three different cases. Then, the optimal solution for our model is constructed and the related verification theorem is also provided. Finally, some numerical examples are given to investigate the properties of our model.</p>","PeriodicalId":50100,"journal":{"name":"Journal of Optimization Theory and Applications","volume":"54 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141171225","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
An Iterative Method for Horizontal Tensor Complementarity Problems 水平张量互补问题的迭代法
IF 1.9 3区 数学
Journal of Optimization Theory and Applications Pub Date : 2024-05-26 DOI: 10.1007/s10957-024-02450-1
Chen Sun, Yong Wang, Zheng-Hai Huang
{"title":"An Iterative Method for Horizontal Tensor Complementarity Problems","authors":"Chen Sun, Yong Wang, Zheng-Hai Huang","doi":"10.1007/s10957-024-02450-1","DOIUrl":"https://doi.org/10.1007/s10957-024-02450-1","url":null,"abstract":"<p>In this paper, we focus on a class of horizontal tensor complementarity problems (HTCPs). By introducing the block representative tensor, we show that finding a solution of HTCP is equivalent to finding a nonnegative solution of a related tensor equation. We establish the theory of the existence and uniqueness of solution of HTCPs under the proper assumptions. In particular, in the case of the concerned block representative tensor possessing the strong <i>M</i>-property, we propose an algorithm to solve HTCPs by efficiently exploiting the beneficial properties of block representative tensor, and show that the iterative sequence generated by the algorithm is monotone decreasing and converges to a solution of HTCPs. The final numerical experiments verify the correctness of the theory in this paper and show the effectiveness of the proposed algorithm.</p>","PeriodicalId":50100,"journal":{"name":"Journal of Optimization Theory and Applications","volume":"56 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141171383","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
Exterior-Point Optimization for Sparse and Low-Rank Optimization 稀疏和低域优化的外点优化
IF 1.9 3区 数学
Journal of Optimization Theory and Applications Pub Date : 2024-05-26 DOI: 10.1007/s10957-024-02448-9
Shuvomoy Das Gupta, Bartolomeo Stellato, Bart P. G. Van Parys
{"title":"Exterior-Point Optimization for Sparse and Low-Rank Optimization","authors":"Shuvomoy Das Gupta, Bartolomeo Stellato, Bart P. G. Van Parys","doi":"10.1007/s10957-024-02448-9","DOIUrl":"https://doi.org/10.1007/s10957-024-02448-9","url":null,"abstract":"<p>Many problems of substantial current interest in machine learning, statistics, and data science can be formulated as sparse and low-rank optimization problems. In this paper, we present the nonconvex exterior-point optimization solver <span>(NExOS)</span>—a first-order algorithm tailored to sparse and low-rank optimization problems. We consider the problem of minimizing a convex function over a nonconvex constraint set, where the set can be decomposed as the intersection of a compact convex set and a nonconvex set involving sparse or low-rank constraints. Unlike the convex relaxation approaches, <span>NExOS</span> finds a locally optimal point of the original problem by solving a sequence of penalized problems with strictly decreasing penalty parameters by exploiting the nonconvex geometry. <span>NExOS</span> solves each penalized problem by applying a first-order algorithm, which converges linearly to a local minimum of the corresponding penalized formulation under regularity conditions. Furthermore, the local minima of the penalized problems converge to a local minimum of the original problem as the penalty parameter goes to zero. We then implement and test <span>NExOS</span> on many instances from a wide variety of sparse and low-rank optimization problems, empirically demonstrating that our algorithm outperforms specialized methods.</p>","PeriodicalId":50100,"journal":{"name":"Journal of Optimization Theory and Applications","volume":"84 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141171300","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
Stabilizability for Quasilinear Klein–Gordon–Schrödinger System with Variable Coefficients 具有可变系数的准线性克莱因-戈登-薛定谔系统的稳定性
IF 1.9 3区 数学
Journal of Optimization Theory and Applications Pub Date : 2024-05-25 DOI: 10.1007/s10957-024-02445-y
Weijia Li, Yuqi Shangguan, Weiping Yan
{"title":"Stabilizability for Quasilinear Klein–Gordon–Schrödinger System with Variable Coefficients","authors":"Weijia Li, Yuqi Shangguan, Weiping Yan","doi":"10.1007/s10957-024-02445-y","DOIUrl":"https://doi.org/10.1007/s10957-024-02445-y","url":null,"abstract":"<p>This paper concerns with the stabilizability for a quasilinear Klein–Gordon–Schrödinger system with variable coefficients in dimensionless form. The stabilizability of quaslinear Klein–Gordon-Wave system with the Kelvin–Voigt damping has been considered by Liu–Yan–Zhang (SIAM J Control Optim 61:1651–1678, 2023). Our main contribution is to find a suitable linear feedback control law such that the quasilinear Klein–Gordon–Schrödinger system is exponentially stable under certain smallness conditions.</p>","PeriodicalId":50100,"journal":{"name":"Journal of Optimization Theory and Applications","volume":"54 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141146990","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
Rigidity Results for the p-Laplacian Poisson Problem with Robin Boundary Conditions 带罗宾边界条件的 p 拉普拉斯泊松问题的刚性结果
IF 1.9 3区 数学
Journal of Optimization Theory and Applications Pub Date : 2024-05-14 DOI: 10.1007/s10957-024-02442-1
Alba Lia Masiello, Gloria Paoli
{"title":"Rigidity Results for the p-Laplacian Poisson Problem with Robin Boundary Conditions","authors":"Alba Lia Masiello, Gloria Paoli","doi":"10.1007/s10957-024-02442-1","DOIUrl":"https://doi.org/10.1007/s10957-024-02442-1","url":null,"abstract":"<p>Let <span>(Omega subset mathbb {R}^n)</span> be an open, bounded and Lipschitz set. We consider the Poisson problem for the <i>p</i>-Laplace operator associated to <span>(Omega )</span> with Robin boundary conditions. In this setting, we study the equality case in the Talenti-type comparison: we prove that the equality is achieved only if <span>(Omega )</span> is a ball and both the solution <i>u</i> and the right-hand side <i>f</i> of the Poisson equation are radial and decreasing.</p>","PeriodicalId":50100,"journal":{"name":"Journal of Optimization Theory and Applications","volume":"71 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140925257","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
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