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On Global Error Bounds for Convex Inequalities Systems 论凸不等式系统的全局误差边界
IF 1.9 3区 数学
Journal of Optimization Theory and Applications Pub Date : 2024-05-30 DOI: 10.1007/s10957-024-02458-7
Vo Si Trong Long
{"title":"On Global Error Bounds for Convex Inequalities Systems","authors":"Vo Si Trong Long","doi":"10.1007/s10957-024-02458-7","DOIUrl":"https://doi.org/10.1007/s10957-024-02458-7","url":null,"abstract":"<p>In this paper, we first present necessary and sufficient conditions for the existence of global error bounds for a convex function without additional conditions on the function or the solution set. In particular, we obtain characterizations of such global error bounds in Euclidean spaces, which are often simple to check. Second, we prove that under a suitable assumption the subdifferential of the supremum function of an arbitrary family of convex continuous functions coincides with the convex hull of the subdifferentials of functions corresponding to the active indices at given points. As applications, we study the existence of global error bounds for infinite systems of linear and convex inequalities. Several examples are provided as well to explain the advantages of our results with existing ones in the literature.</p>","PeriodicalId":50100,"journal":{"name":"Journal of Optimization Theory and Applications","volume":"32 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141196682","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 Final Value Problem with a Non-local and a Source Term: Regularization by Truncation 带有非局部项和源项的终值问题：截断正则化
IF 1.9 3区 数学
Journal of Optimization Theory and Applications Pub Date : 2024-05-30 DOI: 10.1007/s10957-024-02460-z
Subhankar Mondal
{"title":"A Final Value Problem with a Non-local and a Source Term: Regularization by Truncation","authors":"Subhankar Mondal","doi":"10.1007/s10957-024-02460-z","DOIUrl":"https://doi.org/10.1007/s10957-024-02460-z","url":null,"abstract":"<p>This paper is concerned with recovering the solution of a final value problem associated with a parabolic equation involving a non linear source and a non-local term, which to the best of our knowledge has not been studied earlier. It is shown that the considered problem is ill-posed, and thus, some regularization method has to be employed in order to obtain stable approximations. In this regard, we obtain regularized approximations by solving some non linear integral equations which is derived by considering a truncated version of the Fourier expansion of the sought solution. Under different Gevrey smoothness assumptions on the exact solution, we provide parameter choice strategies and obtain the error estimates. A key tool in deriving such estimates is a version of Grönwalls’ inequality for iterated integrals, which perhaps, is proposed and analysed for the first time.</p>","PeriodicalId":50100,"journal":{"name":"Journal of Optimization Theory and Applications","volume":"91 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141196517","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
Constrained Markov Decision Processes with Non-constant Discount Factor 具有非恒定贴现因子的受约束马尔可夫决策过程
IF 1.9 3区 数学
Journal of Optimization Theory and Applications Pub Date : 2024-05-30 DOI: 10.1007/s10957-024-02453-y
Héctor Jasso-Fuentes, Tomás Prieto-Rumeau
{"title":"Constrained Markov Decision Processes with Non-constant Discount Factor","authors":"Héctor Jasso-Fuentes, Tomás Prieto-Rumeau","doi":"10.1007/s10957-024-02453-y","DOIUrl":"https://doi.org/10.1007/s10957-024-02453-y","url":null,"abstract":"<p>This paper studies constrained Markov decision processes under the total expected discounted cost optimality criterion, with a state-action dependent discount factor that may take any value between zero and one. Both the state and the action space are assumed to be Borel spaces. By using the linear programming approach, consisting in stating the control problem as a linear problem on a set of occupation measures, we show the existence of an optimal stationary Markov policy. Our results are based on the study of both weak-strong topologies in the space of occupation measures and Young measures in the space of Markov policies.</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":"141196665","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
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
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