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Stochastic Linear-Quadratic Optimal Control Problems with Multi-dimensional State, Random Coefficients and Regime Switching
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-03-05 DOI: 10.1007/s00245-025-10235-9
Yuyang Chen, Peng Luo
{"title":"Stochastic Linear-Quadratic Optimal Control Problems with Multi-dimensional State, Random Coefficients and Regime Switching","authors":"Yuyang Chen,&nbsp;Peng Luo","doi":"10.1007/s00245-025-10235-9","DOIUrl":"10.1007/s00245-025-10235-9","url":null,"abstract":"<div><p>This paper investigates the stochastic linear-quadratic (LQ, for short) optimal control problems with random coefficients and regime switching in a finite time horizon where the state equation is multi-dimensional. Similar to the classical stochastic LQ problems, we establish the relationship between the stochastic LQ optimal control problems with regime switching and the related extended stochastic Riccati equations. To solve the extended stochastic Riccati equations, we construct a monotone Piccard iterative sequence and present the link between this sequence and solutions of a family of forward-backward stochastic differential equations. Relying on <span>(L^p)</span> estimates for FBSDEs, we show that the extended stochastic Riccati equation has a solution. This partially addresses one question left in Hu et al. (Ann. Appl. Probab. 32(1): 426-460, 2022). Finally, the stochastic LQ optimal control problems with regime switching is solved.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 2","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143553939","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Boundary Controllability for Degenerate/Singular Hyperbolic Equations in Nondivergence Form with Drift
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-03-05 DOI: 10.1007/s00245-025-10236-8
Genni Fragnelli, Dimitri Mugnai, Amine Sbai
{"title":"Boundary Controllability for Degenerate/Singular Hyperbolic Equations in Nondivergence Form with Drift","authors":"Genni Fragnelli,&nbsp;Dimitri Mugnai,&nbsp;Amine Sbai","doi":"10.1007/s00245-025-10236-8","DOIUrl":"10.1007/s00245-025-10236-8","url":null,"abstract":"<div><p>We study the null controllability for a degenerate/singular wave equation with drift in non divergence form. In particular, considering a control localized on the non degenerate boundary point, we provide some conditions for the boundary controllability via energy methods and boundary observability.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 2","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00245-025-10236-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143553938","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
A Generalization of Hoffman’s Lemma in Banach Spaces and Applications
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-02-24 DOI: 10.1007/s00245-025-10238-6
Nguyen Quang Huy, Hoang Ngoc Tuan, Nguyen Dong Yen
{"title":"A Generalization of Hoffman’s Lemma in Banach Spaces and Applications","authors":"Nguyen Quang Huy,&nbsp;Hoang Ngoc Tuan,&nbsp;Nguyen Dong Yen","doi":"10.1007/s00245-025-10238-6","DOIUrl":"10.1007/s00245-025-10238-6","url":null,"abstract":"<div><p>A generalized version of an important theorem called Hoffman’s lemma in the book by Bonnans and Shapiro (Perturbation analysis of optimization problems, Springer, Berlin, 2000), which deals with generalized polyhedral convex multifunctions, is obtained in this paper. Under a mild assumption, the result allows us to demonstrate that the domain of a generalized polyhedral convex multifunction is closed and the multifunction is Lipschitz continuous on its effective domain. As concrete applications of the results, we prove some local error bounds for generalized affine variational inequalities and a theorem on the (strong) convergence of feasible descent methods for solving generalized quadratic programming problems.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 2","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143475282","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Systematic Design of Compliant Morphing Structures: A Phase-Field Approach
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-02-24 DOI: 10.1007/s00245-025-10237-7
Jamal Shabani, Kaushik Bhattacharya, Blaise Bourdin
{"title":"Systematic Design of Compliant Morphing Structures: A Phase-Field Approach","authors":"Jamal Shabani,&nbsp;Kaushik Bhattacharya,&nbsp;Blaise Bourdin","doi":"10.1007/s00245-025-10237-7","DOIUrl":"10.1007/s00245-025-10237-7","url":null,"abstract":"<div><p>We investigate the systematic design of compliant morphing structures composed of materials reacting to an external stimulus. We add a perimeter penalty term to ensure existence of solutions. We propose a phase-field approximation of this sharp interface problem, prove its convergence as the regularization length approaches 0 and present an efficient numerical implementation. We illustrate the strengths of our approach through a series of numerical examples.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 2","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143475283","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 Nonlocal Cahn–Hilliard–Darcy System with Singular Potential, Degenerate Mobility, and Sources
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-02-21 DOI: 10.1007/s00245-025-10239-5
Cecilia Cavaterra, Sergio Frigeri, Maurizio Grasselli
{"title":"A Nonlocal Cahn–Hilliard–Darcy System with Singular Potential, Degenerate Mobility, and Sources","authors":"Cecilia Cavaterra,&nbsp;Sergio Frigeri,&nbsp;Maurizio Grasselli","doi":"10.1007/s00245-025-10239-5","DOIUrl":"10.1007/s00245-025-10239-5","url":null,"abstract":"<div><p>We consider a Cahn–Hilliard–Darcy system for an incompressible mixture of two fluids we already analyzed in [9]. In this system, the relative concentration difference <span>(varphi )</span> obeys a convective nonlocal Cahn–Hilliard equation with degenerate mobility and singular (e.g., logarithmic) potential, while the volume averaged fluid velocity <span>(varvec{u})</span> is given by a Darcy’s law subject to the Korteweg force <span>(mu nabla varphi )</span>, where the chemical potential <span>(mu )</span> is defined by means of a nonlocal Helmholtz free energy. The kinematic viscosity <span>(eta )</span> depends on <span>(varphi )</span>. With respect to the quoted contribution, here we assume that the Darcy’s law is subject to gravity and to a given additional source. Moreover, we suppose that the Cahn–Hilliard equation and the chemical potential contain source terms. Our main goal is to establish the existence of two notions of weak solutions. The first, called “generalized” weak solution, is based a convenient splitting of <span>(mu )</span> so that the entropy derivative does not need to be integrable. The second is slightly stronger and allows to reconstruct <span>(mu )</span> and to prove the validity of a canonical energy identity. For this reason, the latter is called “natural” weak solution. The rigorous relation between the two notions of weak solution is also analyzed. The existence of a global attractor for generalized weak solutions and time independent sources is then demonstrated via the theory of generalized semiflows introduced by J.M. Ball.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 2","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00245-025-10239-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143455656","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Mean-Field Partial Information Non-zero Sum Stochastic Differential Games
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-02-19 DOI: 10.1007/s00245-025-10233-x
Tianyang Nie, Ke Yan
{"title":"Mean-Field Partial Information Non-zero Sum Stochastic Differential Games","authors":"Tianyang Nie,&nbsp;Ke Yan","doi":"10.1007/s00245-025-10233-x","DOIUrl":"10.1007/s00245-025-10233-x","url":null,"abstract":"<div><p>In this paper, we study a general mean-field partial information non-zero sum stochastic differential game, in which the dynamic of state is described by a stochastic differential equation (SDE) depending on the distribution of the state and the control domain of each player can be non-convex. Moreover, the control variables of both players can enter the diffusion coefficients of the state equation. We establish a necessary condition in the form of Pontryagin’s maximum principle for optimality. Then a verification theorem is obtained for optimal control when the control domain is convex. As an application, our results are applied to studying linear–quadratic (LQ) mean-field game in the type of scalar interaction.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 2","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143438720","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Correction: Optimality Conditions for Sparse Optimal Control of Viscous Cahn–Hilliard Systems with Logarithmic Potential
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-02-19 DOI: 10.1007/s00245-025-10234-w
Pierluigi Colli, Jürgen Sprekels, Fredi Tröltzsch
{"title":"Correction: Optimality Conditions for Sparse Optimal Control of Viscous Cahn–Hilliard Systems with Logarithmic Potential","authors":"Pierluigi Colli,&nbsp;Jürgen Sprekels,&nbsp;Fredi Tröltzsch","doi":"10.1007/s00245-025-10234-w","DOIUrl":"10.1007/s00245-025-10234-w","url":null,"abstract":"","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 2","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00245-025-10234-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143446516","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Identification of Active Component Functions in Finite-Max Minimisation via a Smooth Reformulation
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-02-18 DOI: 10.1007/s00245-025-10229-7
Charl J. Ras, Matthew K. Tam, Daniel J. Uteda
{"title":"Identification of Active Component Functions in Finite-Max Minimisation via a Smooth Reformulation","authors":"Charl J. Ras,&nbsp;Matthew K. Tam,&nbsp;Daniel J. Uteda","doi":"10.1007/s00245-025-10229-7","DOIUrl":"10.1007/s00245-025-10229-7","url":null,"abstract":"<div><p>In this work, we consider a nonsmooth minimisation problem in which the objective function can be represented as the maximum of finitely many smooth “component functions”. First, we study a smooth min–max reformulation of the problem. Due to this smoothness, the model provides enhanced capability of exploiting the structure of the problem, when compared to methods that attempt to tackle the nonsmooth problem directly. Then, we present several approaches to identify the set of active component functions at a minimiser, all within finitely many iterations of a first order method for solving the smooth model. As is well known, the problem can be equivalently rewritten in terms of these component functions, but a key challenge is to identify this set a priori. Such an identification is clearly beneficial in an algorithmic sense, since we can discard those component functions which are not necessary to describe the solution, which in turn can facilitate faster convergence. Finally, numerical results comparing the accuracy of each of these approaches are presented, along with the effect they have on reducing the complexity of the original problem.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 2","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00245-025-10229-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143430941","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Path-Dependent Hamilton–Jacobi Equations with u-Dependence and Time-Measurable Hamiltonians
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-02-15 DOI: 10.1007/s00245-025-10230-0
Elena Bandini, Christian Keller
{"title":"Path-Dependent Hamilton–Jacobi Equations with u-Dependence and Time-Measurable Hamiltonians","authors":"Elena Bandini,&nbsp;Christian Keller","doi":"10.1007/s00245-025-10230-0","DOIUrl":"10.1007/s00245-025-10230-0","url":null,"abstract":"<div><p>We establish existence and uniqueness of minimax solutions for a fairly general class of path-dependent Hamilton–Jacobi equations. In particular, the relevant Hamiltonians can contain the solution and they only need to be measurable with respect to time. We apply our results to optimal control problems of (delay) functional differential equations with cost functionals that have discount factors and with time-measurable data. Our main results are also crucial for our companion paper Bandini and Keller (Non-local Hamilton–Jacobi–Bellman equations for the stochastic optimal control of path-dependent piecewise deterministic processes, 2024, http://arxiv.org/abs/2408.02147), where non-local path-dependent Hamilton–Jacobi–Bellman equations associated to the stochastic optimal control of non-Markovian piecewise deterministic processes are studied.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 2","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143423370","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Non-Autonomous Degenerate Parabolic Equations with Robin Boundary Conditions: Carleman Estimates and Null-Controllability
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-02-15 DOI: 10.1007/s00245-025-10227-9
Mohammad Akil, Genni Fragnelli, Sarah Ismail
{"title":"Non-Autonomous Degenerate Parabolic Equations with Robin Boundary Conditions: Carleman Estimates and Null-Controllability","authors":"Mohammad Akil,&nbsp;Genni Fragnelli,&nbsp;Sarah Ismail","doi":"10.1007/s00245-025-10227-9","DOIUrl":"10.1007/s00245-025-10227-9","url":null,"abstract":"<div><p>The Earth’s climate system naturally adjusts to maintain a balance between the energy received from the Sun and the energy reflected back into space, a concept known as the “Earth’s radiation budget”. However, this balance has been disrupted by human activities, leading to global warming. Starting from the energy balance model proposed by Budyko and Sellers, and considering a time-dependent diffusion coefficient, we prove the null-controllability of non-autonomous degenerate parabolic problems, in the sense that the Earth achieves a desired temperature, by finding new Carleman estimates for the non-homogeneous adjoint problems. At the degeneracy point, we impose Robin boundary condition which is appropriate for modeling heat transfer at the Earth’s surface. Moreover, we provide the equivalence between null-controllability and observability inequality for the non-autonomous case. At the end, we present some extensions and open problems.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 2","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00245-025-10227-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143423369","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
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