Marta Baldomero-Naranjo, Jörg Kalcsics, Alfredo Marín, Antonio M. Rodríguez-Chía
We study the upgrading version of the maximal covering location problem with edge length modifications on networks. This problem aims at locating p facilities on the vertices (of the network) so as to maximise coverage, considering that the length of the edges can be reduced at a cost, subject to a given budget. Hence, we have to decide on: the optimal location of p facilities and the optimal edge length reductions. This problem is NP-hard on general graphs. To solve it, we propose three different mixed-integer formulations and a preprocessing phase for fixing variables and removing some of the constraints. Moreover, we strengthen the proposed formulations including valid inequalities. Finally, we compare the three formulations and their corresponding improvements by testing their performance over different datasets.
我们研究的是网络上最大覆盖位置问题的升级版，该问题具有边长修正功能。该问题旨在确定（网络的）顶点上 p 个设施的位置，以便最大化覆盖范围，同时考虑到在给定预算的条件下，可以有代价地缩短边长。因此，我们必须决定：p 个设施的最优位置和最优边长缩减。在一般图上，这个问题很难解决。为了解决这个问题，我们提出了三种不同的混合整数公式和一个预处理阶段，用于固定变量和移除一些约束条件。此外，我们还加强了包含有效不等式的拟议公式。最后，我们通过对不同数据集的性能测试，比较了这三种公式及其相应的改进。
{"title":"Upgrading edges in the maximal covering location problem","authors":"Marta Baldomero-Naranjo, Jörg Kalcsics, Alfredo Marín, Antonio M. Rodríguez-Chía","doi":"arxiv-2409.11883","DOIUrl":"https://doi.org/arxiv-2409.11883","url":null,"abstract":"We study the upgrading version of the maximal covering location problem with\u0000edge length modifications on networks. This problem aims at locating p\u0000facilities on the vertices (of the network) so as to maximise coverage,\u0000considering that the length of the edges can be reduced at a cost, subject to a\u0000given budget. Hence, we have to decide on: the optimal location of p facilities\u0000and the optimal edge length reductions. This problem is NP-hard on general graphs. To solve it, we propose three\u0000different mixed-integer formulations and a preprocessing phase for fixing\u0000variables and removing some of the constraints. Moreover, we strengthen the\u0000proposed formulations including valid inequalities. Finally, we compare the\u0000three formulations and their corresponding improvements by testing their\u0000performance over different datasets.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142254597","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Motivated by optimal execution with stochastic signals, market impact and constraints in financial markets, and optimal storage management in commodity markets, we formulate and solve an optimal trading problem with a general propagator model under linear functional inequality constraints. The optimal control is given explicitly in terms of the corresponding Lagrange multipliers and their conditional expectations, as a solution to a linear stochastic Fredholm equation. We propose a stochastic version of the Uzawa algorithm on the dual problem to construct the stochastic Lagrange multipliers numerically via a stochastic projected gradient ascent, combined with a least-squares Monte Carlo regression step to approximate their conditional expectations. We illustrate our findings on two different practical applications with stochastic signals: (i) an optimal execution problem with an exponential or a power law decaying transient impact, with either a `no-shorting' constraint in the presence of a `sell' signal, a `no-buying' constraint in the presence of a `buy' signal or a stochastic `stop-trading' constraint whenever the exogenous price drops below a specified reference level; (ii) a battery storage problem with instantaneous operating costs, seasonal signals and fixed constraints on both the charging power and the load capacity of the battery.
{"title":"Trading with propagators and constraints: applications to optimal execution and battery storage","authors":"Eduardo Abi Jaber, Nathan De Carvalho, Huyên Pham","doi":"arxiv-2409.12098","DOIUrl":"https://doi.org/arxiv-2409.12098","url":null,"abstract":"Motivated by optimal execution with stochastic signals, market impact and\u0000constraints in financial markets, and optimal storage management in commodity\u0000markets, we formulate and solve an optimal trading problem with a general\u0000propagator model under linear functional inequality constraints. The optimal\u0000control is given explicitly in terms of the corresponding Lagrange multipliers\u0000and their conditional expectations, as a solution to a linear stochastic\u0000Fredholm equation. We propose a stochastic version of the Uzawa algorithm on\u0000the dual problem to construct the stochastic Lagrange multipliers numerically\u0000via a stochastic projected gradient ascent, combined with a least-squares Monte\u0000Carlo regression step to approximate their conditional expectations. We\u0000illustrate our findings on two different practical applications with stochastic\u0000signals: (i) an optimal execution problem with an exponential or a power law\u0000decaying transient impact, with either a `no-shorting' constraint in the\u0000presence of a `sell' signal, a `no-buying' constraint in the presence of a\u0000`buy' signal or a stochastic `stop-trading' constraint whenever the exogenous\u0000price drops below a specified reference level; (ii) a battery storage problem\u0000with instantaneous operating costs, seasonal signals and fixed constraints on\u0000both the charging power and the load capacity of the battery.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142254595","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Yuichiro Aoyama, Oswin So, Augustinos D. Saravanos, Evangelos A. Theodorou
This paper provides an overview, analysis, and comparison of second-order dynamic optimization algorithms, i.e., constrained Differential Dynamic Programming (DDP) and Sequential Quadratic Programming (SQP). Although a variety of these algorithms has been proposed and used successfully, there exists a gap in understanding the key differences and advantages, which we aim to provide in this work. For constrained DDP, we choose methods that incorporate nolinear programming techniques to handle state and control constraints, including Augmented Lagrangian (AL), Interior Point, Primal Dual Augmented Lagrangian (PDAL), and Alternating Direction Method of Multipliers. Both DDP and SQP are provided in single- and multiple-shooting formulations, where constraints that arise from dynamics are encoded implicitly and explicitly, respectively. In addition to reviewing these methods, we propose a single-shooting PDAL DDP. As a byproduct of the review, we also propose a single-shooting PDAL DDP which is robust to the growth of penalty parameters and performs better than the normal AL variant. We perform extensive numerical experiments on a variety of systems with increasing complexity towards investigating the quality of the solutions, the levels of constraint violation, iterations for convergence, and the sensitivity of final solutions with respect to initialization. The results show that DDP often has the advantage of finding better local minima, while SQP tends to achieve better constraint satisfaction. For multiple-shooting formulation, both DDP and SQP can enjoy informed initial guesses, while the latter appears to be more advantageous in complex systems. It is also worth highlighting that DDP provides favorable computational complexity and feedback gains as a byproduct of optimization.
{"title":"Second-Order Constrained Dynamic Optimization","authors":"Yuichiro Aoyama, Oswin So, Augustinos D. Saravanos, Evangelos A. Theodorou","doi":"arxiv-2409.11649","DOIUrl":"https://doi.org/arxiv-2409.11649","url":null,"abstract":"This paper provides an overview, analysis, and comparison of second-order\u0000dynamic optimization algorithms, i.e., constrained Differential Dynamic\u0000Programming (DDP) and Sequential Quadratic Programming (SQP). Although a\u0000variety of these algorithms has been proposed and used successfully, there\u0000exists a gap in understanding the key differences and advantages, which we aim\u0000to provide in this work. For constrained DDP, we choose methods that\u0000incorporate nolinear programming techniques to handle state and control\u0000constraints, including Augmented Lagrangian (AL), Interior Point, Primal Dual\u0000Augmented Lagrangian (PDAL), and Alternating Direction Method of Multipliers.\u0000Both DDP and SQP are provided in single- and multiple-shooting formulations,\u0000where constraints that arise from dynamics are encoded implicitly and\u0000explicitly, respectively. In addition to reviewing these methods, we propose a\u0000single-shooting PDAL DDP. As a byproduct of the review, we also propose a\u0000single-shooting PDAL DDP which is robust to the growth of penalty parameters\u0000and performs better than the normal AL variant. We perform extensive numerical\u0000experiments on a variety of systems with increasing complexity towards\u0000investigating the quality of the solutions, the levels of constraint violation,\u0000iterations for convergence, and the sensitivity of final solutions with respect\u0000to initialization. The results show that DDP often has the advantage of finding\u0000better local minima, while SQP tends to achieve better constraint satisfaction.\u0000For multiple-shooting formulation, both DDP and SQP can enjoy informed initial\u0000guesses, while the latter appears to be more advantageous in complex systems.\u0000It is also worth highlighting that DDP provides favorable computational\u0000complexity and feedback gains as a byproduct of optimization.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142254601","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This study presents optimization problems to jointly determine long-term network design, mid-term fleet sizing strategy, and short-term routing and ridesharing matching in shared autonomous vehicle (SAV) systems with pre-booked and on-demand trip requests. Based on the dynamic traffic assignment framework, multi-stage stochastic linear programming is formulated for joint optimization of SAV system design and operations. Leveraging the linearity of the proposed problem, we can tackle the computational complexity due to multiple objectives and dynamic stochasticity through the weighted sum method and stochastic dual dynamic programming (SDDP). Our numerical examples verify that the solution to the proposed problem obtained through SDDP is close enough to the optimal solution. We also demonstrate the effect of introducing pre-booking options on optimized infrastructure planning and fleet sizing strategies. Furthermore, dedicated vehicles to pick-up and drop-off only pre-booked travelers can lead to incentives to reserve in advance instead of on-demand requests with little reduction in system performance.
本研究提出了优化问题，以共同确定具有预预订和按需出行请求的共享自动驾驶汽车（SAV）系统中的长期网络设计、中期车队规模策略以及短期路由和乘车匹配。基于动态交通分配框架，制定了多阶段随机线性规划，用于联合优化 SAV 系统的设计和运营。利用所提问题的线性，我们可以通过加权和方法和随机双动态编程（SDDP）来解决多目标和动态随机性带来的计算复杂性问题。我们的数值实例验证了通过 SDDP 获得的拟议问题解与最优解足够接近。我们还演示了引入预预订选项对优化基础设施规划和车队规模策略的影响。此外，专用车辆只接送预先订票的旅客，可以激励人们提前订票，而不是按需订票，同时对系统性能的影响很小。
{"title":"Multi-stage stochastic linear programming for shared autonomous vehicle system operation and design with on-demand and pre-booked requests","authors":"Riki Kawase","doi":"arxiv-2409.11611","DOIUrl":"https://doi.org/arxiv-2409.11611","url":null,"abstract":"This study presents optimization problems to jointly determine long-term\u0000network design, mid-term fleet sizing strategy, and short-term routing and\u0000ridesharing matching in shared autonomous vehicle (SAV) systems with pre-booked\u0000and on-demand trip requests. Based on the dynamic traffic assignment framework,\u0000multi-stage stochastic linear programming is formulated for joint optimization\u0000of SAV system design and operations. Leveraging the linearity of the proposed\u0000problem, we can tackle the computational complexity due to multiple objectives\u0000and dynamic stochasticity through the weighted sum method and stochastic dual\u0000dynamic programming (SDDP). Our numerical examples verify that the solution to\u0000the proposed problem obtained through SDDP is close enough to the optimal\u0000solution. We also demonstrate the effect of introducing pre-booking options on\u0000optimized infrastructure planning and fleet sizing strategies. Furthermore,\u0000dedicated vehicles to pick-up and drop-off only pre-booked travelers can lead\u0000to incentives to reserve in advance instead of on-demand requests with little\u0000reduction in system performance.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142254603","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Vo Si Trong Long, Nguyen Mau Nam, Jacob Sharkansky, Nguyen Dong Yen
In this paper, we study generalized versions of the k-center problem, which involves finding k circles of the smallest possible equal radius that cover a finite set of points in the plane. By utilizing the Minkowski gauge function, we extend this problem to generalized balls induced by various convex sets in finite dimensions, rather than limiting it to circles in the plane. First, we establish several fundamental properties of the global optimal solutions to this problem. We then introduce the notion of local optimal solutions and provide a sufficient condition for their existence. We also provide several illustrative examples to clarify the proposed problems.
在本文中，我们研究了 k 中心问题的广义版本，该问题涉及寻找覆盖平面内无限点集的最小等半径的 k 个圆。通过利用闵科夫斯基规函数，我们将这个问题扩展到由各种无限维凸集引起的广义球，而不是局限于平面中的圆。首先，我们建立了该问题全局最优解的几个基本性质。然后，我们引入了局部最优解的概念，并提供了它们存在的充分条件。我们还提供了几个示例来阐明所提出的问题。
{"title":"Qualitative Properties of $k-$Center Problems","authors":"Vo Si Trong Long, Nguyen Mau Nam, Jacob Sharkansky, Nguyen Dong Yen","doi":"arxiv-2409.12091","DOIUrl":"https://doi.org/arxiv-2409.12091","url":null,"abstract":"In this paper, we study generalized versions of the k-center problem, which\u0000involves finding k circles of the smallest possible equal radius that cover a\u0000finite set of points in the plane. By utilizing the Minkowski gauge function,\u0000we extend this problem to generalized balls induced by various convex sets in\u0000finite dimensions, rather than limiting it to circles in the plane. First, we\u0000establish several fundamental properties of the global optimal solutions to\u0000this problem. We then introduce the notion of local optimal solutions and\u0000provide a sufficient condition for their existence. We also provide several\u0000illustrative examples to clarify the proposed problems.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142254604","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Marta Baldomero-Naranjo, Jörg Kalcsics, Antonio M. Rodríguez-Chía
In this article, we study the complexity of the upgrading version of the maximal covering location problem with edge length modifications on networks. This problem is NP-hard on general networks. However, in some particular cases, we prove that this problem is solvable in polynomial time. The cases of star and path networks combined with different assumptions for the model parameters are analysed. In particular, we obtain that the problem on star networks is solvable in O(nlogn) time for uniform weights and NP-hard for non-uniform weights. On paths, the single facility problem is solvable in O(n^3) time, while the p-facility problem is NP-hard even with uniform costs and upper bounds (maximal upgrading per edge), as well as, integer parameter values. Furthermore, a pseudo-polynomial algorithm is developed for the single facility problem on trees with integer parameters.
在本文中，我们研究了网络上边长修正的最大覆盖位置问题升级版的复杂性。然而，在某些特殊情况下，我们证明这个问题可以在多项式时间内求解。我们分析了星形网络和路径网络的情况，并结合了对模型参数的不同假设。特别是，我们得出星形网络上的问题，在权重均匀的情况下，可以在 O(nlogn) 时间内求解，而在权重不均匀的情况下，则很难求解。在路径上，单设施问题可在 O(n^3) 时间内求解，而 p 设施问题即使在成本和上限（每条边的最大升级）均匀以及参数值为整数的情况下也是 NP-hard。
{"title":"On the complexity of the upgrading version of the maximal covering location problem","authors":"Marta Baldomero-Naranjo, Jörg Kalcsics, Antonio M. Rodríguez-Chía","doi":"arxiv-2409.11900","DOIUrl":"https://doi.org/arxiv-2409.11900","url":null,"abstract":"In this article, we study the complexity of the upgrading version of the\u0000maximal covering location problem with edge length modifications on networks.\u0000This problem is NP-hard on general networks. However, in some particular cases,\u0000we prove that this problem is solvable in polynomial time. The cases of star\u0000and path networks combined with different assumptions for the model parameters\u0000are analysed. In particular, we obtain that the problem on star networks is\u0000solvable in O(nlogn) time for uniform weights and NP-hard for non-uniform\u0000weights. On paths, the single facility problem is solvable in O(n^3) time,\u0000while the p-facility problem is NP-hard even with uniform costs and upper\u0000bounds (maximal upgrading per edge), as well as, integer parameter values.\u0000Furthermore, a pseudo-polynomial algorithm is developed for the single facility\u0000problem on trees with integer parameters.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142254606","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We construct a static feedback control in a trajectory sense and a dynamic feedback control to obtain the local rapid boundary stabilization of a KdV system using Gramian operators. We also construct a time-varying feedback control in the trajectory sense and a time varying dynamic feedback control to reach the local finite-time boundary stabilization for the same system.
{"title":"Rapid and finite-time boundary stabilization of a KdV system","authors":"Hoai-Minh Nguyen","doi":"arxiv-2409.11768","DOIUrl":"https://doi.org/arxiv-2409.11768","url":null,"abstract":"We construct a static feedback control in a trajectory sense and a dynamic\u0000feedback control to obtain the local rapid boundary stabilization of a KdV\u0000system using Gramian operators. We also construct a time-varying feedback\u0000control in the trajectory sense and a time varying dynamic feedback control to\u0000reach the local finite-time boundary stabilization for the same system.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142254600","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Marta Baldomero-Naranjo, Jörg Kalcsics, Antonio M. Rodríguez-Chía
This paper addresses a version of the single-facility Maximal Covering Location Problem on a network where the demand is: (i) distributed along the edges and (ii) uncertain with only a known interval estimation. To deal with this problem, we propose a minmax regret model where the service facility can be located anywhere along the network. This problem is called Minmax Regret Maximal Covering Location Problem with demand distributed along the edges (MMR-EMCLP). Furthermore, we present two polynomial algorithms for finding the location that minimises the maximal regret assuming that the demand realisation is an unknown constant or linear function on each edge. We also include two illustrative examples as well as a computational study for the unknown constant demand case to illustrate the potential and limits of the proposed methodology.
{"title":"Minmax regret maximal covering location problems with edge demands","authors":"Marta Baldomero-Naranjo, Jörg Kalcsics, Antonio M. Rodríguez-Chía","doi":"arxiv-2409.11872","DOIUrl":"https://doi.org/arxiv-2409.11872","url":null,"abstract":"This paper addresses a version of the single-facility Maximal Covering\u0000Location Problem on a network where the demand is: (i) distributed along the\u0000edges and (ii) uncertain with only a known interval estimation. To deal with\u0000this problem, we propose a minmax regret model where the service facility can\u0000be located anywhere along the network. This problem is called Minmax Regret\u0000Maximal Covering Location Problem with demand distributed along the edges\u0000(MMR-EMCLP). Furthermore, we present two polynomial algorithms for finding the\u0000location that minimises the maximal regret assuming that the demand realisation\u0000is an unknown constant or linear function on each edge. We also include two\u0000illustrative examples as well as a computational study for the unknown constant\u0000demand case to illustrate the potential and limits of the proposed methodology.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142254598","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Lucas PalazzoloCRISAM, Laëtitia GiraldiCRISAM, Mickael BinoisACUMES, CRISAM, LJAD, Luca BertiIRMA
Understanding and optimizing the design of helical micro-swimmers is crucial for advancing their application in various fields. This study presents an innovative approach combining Free-Form Deformation with Bayesian Optimization to enhance the shape of these swimmers. Our method facilitates the computation of generic swimmer shapes that achieve optimal average speed and efficiency. Applied to both monoflagellated and biflagellated swimmers, our optimization framework has led to the identification of new optimal shapes. These shapes are compared with biological counterparts, highlighting a diverse range of swimmers, including both pushers and pullers.
{"title":"Parametric Shape Optimization of Flagellated Micro-Swimmers Using Bayesian Techniques","authors":"Lucas PalazzoloCRISAM, Laëtitia GiraldiCRISAM, Mickael BinoisACUMES, CRISAM, LJAD, Luca BertiIRMA","doi":"arxiv-2409.11776","DOIUrl":"https://doi.org/arxiv-2409.11776","url":null,"abstract":"Understanding and optimizing the design of helical micro-swimmers is crucial\u0000for advancing their application in various fields. This study presents an\u0000innovative approach combining Free-Form Deformation with Bayesian Optimization\u0000to enhance the shape of these swimmers. Our method facilitates the computation\u0000of generic swimmer shapes that achieve optimal average speed and efficiency.\u0000Applied to both monoflagellated and biflagellated swimmers, our optimization\u0000framework has led to the identification of new optimal shapes. These shapes are\u0000compared with biological counterparts, highlighting a diverse range of\u0000swimmers, including both pushers and pullers.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142254599","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper investigates the asymptotic behavior of the solution to a linear-quadratic stochastic optimal control problems. The so-called probability cell problem is introduced the first time. It serves as the probability interpretation of the well-known cell problem in the homogenization of Hamilton-Jacobi equations. By establishing a connection between this problem and the ergodic cost problem, we reveal the turnpike properties of the linear-quadratic stochastic optimal control problems from various perspectives.
{"title":"Long-Time Behaviors of Stochastic Linear-Quadratic Optimal Control Problems","authors":"Jiamin Jian, Sixian Jin, Qingshuo Song, Jiongmin Yong","doi":"arxiv-2409.11633","DOIUrl":"https://doi.org/arxiv-2409.11633","url":null,"abstract":"This paper investigates the asymptotic behavior of the solution to a\u0000linear-quadratic stochastic optimal control problems. The so-called probability\u0000cell problem is introduced the first time. It serves as the probability\u0000interpretation of the well-known cell problem in the homogenization of\u0000Hamilton-Jacobi equations. By establishing a connection between this problem\u0000and the ergodic cost problem, we reveal the turnpike properties of the\u0000linear-quadratic stochastic optimal control problems from various perspectives.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142254602","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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