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Identification of Active Component Functions in Finite-Max Minimisation via a Smooth Reformulation 基于光滑重构的有限极大极小有源函数辨识
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 具有u相关和时间可测哈密顿量的路径相关哈密-雅可比方程
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 具有Robin边界条件的非自治退化抛物方程：Carleman估计和零可控性
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
Global Weak Solutions in a Haptotactic Cross-Diffusion System Modeling Oncolytic Virotherapy with Nonlinear Diffusion 模拟非线性扩散溶瘤病毒治疗的触致交叉扩散系统的全局弱解
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-02-14 DOI: 10.1007/s00245-025-10232-y
Yue Zhou, Changchun Liu
{"title":"Global Weak Solutions in a Haptotactic Cross-Diffusion System Modeling Oncolytic Virotherapy with Nonlinear Diffusion","authors":"Yue Zhou,&nbsp;Changchun Liu","doi":"10.1007/s00245-025-10232-y","DOIUrl":"10.1007/s00245-025-10232-y","url":null,"abstract":"<div><p>This paper discusses an initial-boundary value problem for a doubly haptotactic cross-diffusion system arising from the oncolytic virotherapy </p><div><div><span>$$begin{aligned} {left{ begin{array}{ll} u_t=Delta u^m-nabla cdot (unabla v) +mu u(1-u)-uz,;;&amp; ;xin Omega ,~t&gt;0, v_t=-(u+w)v,;;&amp; ;xin Omega ,~t&gt;0, w_t=Delta w-nabla cdot (wnabla v)-w+uz,;;&amp; ;xin Omega ,~t&gt;0, z_t=DDelta z-z-uz+beta w,;;&amp; ;xin Omega ,~t&gt;0, frac{partial u^m}{partial nu }-ufrac{partial v}{partial nu }=frac{partial w}{partial nu }-wfrac{partial v}{partial nu }=frac{partial z}{partial nu }=0,;;&amp; ;xin partial Omega ,~t&gt;0, u(x,0)=u_{0},~v(x,0)=v_{0},~w(x,0)=w_{0}, z(x,0)=z_{0},;;&amp; ;xin Omega , end{array}right. } end{aligned}$$</span></div></div><p>in a smooth bounded domain <span>( Omega subset {mathbb {R}}^{N}(N=1,2) )</span> with <span>( m&gt;1, beta&gt;0, mu &gt;0 )</span>, and <span>( D&gt;0)</span>. We prove that for any large initial datum, the problem admits a global ‘very’ weak solution for any <span>(m&gt;1)</span>.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 2","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143404145","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
Convergence of the Stochastic Navier–Stokes-(alpha ) Solutions Toward the Stochastic Navier–Stokes Solutions 随机纳维-斯托克斯（Navier-Stokes）-（alpha ）解向随机纳维-斯托克斯解的收敛性
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-02-13 DOI: 10.1007/s00245-025-10228-8
Jad Doghman, Ludovic Goudenège
{"title":"Convergence of the Stochastic Navier–Stokes-(alpha ) Solutions Toward the Stochastic Navier–Stokes Solutions","authors":"Jad Doghman,&nbsp;Ludovic Goudenège","doi":"10.1007/s00245-025-10228-8","DOIUrl":"10.1007/s00245-025-10228-8","url":null,"abstract":"<div><p>Loosely speaking, the Navier–Stokes-<span>(alpha )</span> model and the Navier–Stokes equations differ by a spatial filtration parametrized by a scale denoted <span>(alpha )</span>. Starting from a strong two-dimensional solution to the Navier–Stokes-<span>(alpha )</span> model driven by a multiplicative noise, we demonstrate that it generates a strong solution to the stochastic Navier–Stokes equations under the condition <span>(alpha rightarrow 0)</span>. The initially introduced probability space and the Wiener process are maintained throughout the investigation, thanks to a local monotonicity property that abolishes the use of Skorokhod’s theorem. High spatial regularity a priori estimates for the fluid velocity vector field are carried out within periodic boundary conditions.\u0000</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 2","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00245-025-10228-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143396661","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
Before and After Default: Information and Optimal Portfolio via Anticipating Calculus 违约前后：通过预期微积分获得信息和最佳投资组合
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-02-12 DOI: 10.1007/s00245-024-10210-w
Bernardo D’Auria, Giulia Di Nunno, Jose A. Salmeron
{"title":"Before and After Default: Information and Optimal Portfolio via Anticipating Calculus","authors":"Bernardo D’Auria,&nbsp;Giulia Di Nunno,&nbsp;Jose A. Salmeron","doi":"10.1007/s00245-024-10210-w","DOIUrl":"10.1007/s00245-024-10210-w","url":null,"abstract":"<div><p>Default risk calculus plays a crucial role in portfolio optimization when the risky asset is under threat of bankruptcy. However, traditional stochastic control techniques are not applicable in this scenario, and additional assumptions are required to obtain the optimal solution in a before-and-after default context. We propose an alternative approach using forward integration, which allows to avoid one of the restrictive assumptions, the <i>Jacod density hypothesis</i>. We demonstrate that, in the case of logarithmic utility, the weaker <i>intensity hypothesis</i> is the appropriate condition for optimality. Furthermore, we establish the semimartingale decomposition of the risky asset in the filtration that is progressively enlarged to accommodate the default process, under the assumption of the existence of the optimal portfolio. This work aims to provide valuable insights for developing effective risk management strategies when facing default risk.\u0000</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 2","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00245-024-10210-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143396678","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
Null Controllability for Stochastic Parabolic Equations Coupled by First and Zero Order Terms 一阶项和零阶项耦合随机抛物方程的零可控性
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-02-12 DOI: 10.1007/s00245-025-10231-z
Mahmoud Baroun, Said Boulite, Abdellatif Elgrou, Lahcen Maniar
{"title":"Null Controllability for Stochastic Parabolic Equations Coupled by First and Zero Order Terms","authors":"Mahmoud Baroun,&nbsp;Said Boulite,&nbsp;Abdellatif Elgrou,&nbsp;Lahcen Maniar","doi":"10.1007/s00245-025-10231-z","DOIUrl":"10.1007/s00245-025-10231-z","url":null,"abstract":"<div><p>We prove the null controllability of forward and backward linear stochastic parabolic equations with first and zero order coupling terms, and with bounded coefficients. The null controllability results rely on novel Carleman estimates for the backward and forward adjoint equations, established through the application of the duality technique. In doing so, we resolve an open question (see Remark 2.2 in [Tang and Zhang in SIAM J Control Optim 48:2191–2216, 2009]). Moreover, we provide more accurate estimates for the null-control costs.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 2","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143396679","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
Global Well-posedness of the Nonhomogeneous Initial Boundary Value Problem for the Hirota Equation Posed in a Finite Domain 在有限域内求解广田方程的非均质初始边界值问题的全局良好求解性
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-02-12 DOI: 10.1007/s00245-025-10226-w
Mengtao Xu, Chunxiao Guo, Boling Guo, Xin-guang Yang
{"title":"Global Well-posedness of the Nonhomogeneous Initial Boundary Value Problem for the Hirota Equation Posed in a Finite Domain","authors":"Mengtao Xu,&nbsp;Chunxiao Guo,&nbsp;Boling Guo,&nbsp;Xin-guang Yang","doi":"10.1007/s00245-025-10226-w","DOIUrl":"10.1007/s00245-025-10226-w","url":null,"abstract":"<div><p>We study a system described by a type of initial and boundary value problem of the Hirota equation with nonhomogeneous boundary conditions posed on a bounded interval. Firstly, we prove the local well-posedness of the system in the space <span>(H^s(0,1))</span> by using an explicit solution formula and contraction mapping principle for any <span>(sge 1)</span>. Secondly, we obtain the global well-posedness in <span>(H^1(0,1))</span> and <span>(H^2(0,1))</span> by the norm estimation. Especially, the main difficulty is that the characteristic equation corresponding to Hirota equation needs to be solved by construction and that nonlinear terms are taken into consideration. In addition, the norm estimate for global well-posedness of solution in <span>(H^1(0,1))</span> and <span>(H^2(0,1))</span> are complicated.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 2","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143396680","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
Linear-Quadratic Mean-Field Backward Stackelberg Game with Mixed Terminal Perturbation 具有混合终端摄动的线性二次平均场后向Stackelberg对策
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-02-08 DOI: 10.1007/s00245-025-10225-x
Tian Chen, Xinwei Feng, Yunxiao Jia
{"title":"Linear-Quadratic Mean-Field Backward Stackelberg Game with Mixed Terminal Perturbation","authors":"Tian Chen,&nbsp;Xinwei Feng,&nbsp;Yunxiao Jia","doi":"10.1007/s00245-025-10225-x","DOIUrl":"10.1007/s00245-025-10225-x","url":null,"abstract":"<div><p>This paper investigates a linear-quadratic (LQ) Stackelberg game for mean-field type backward stochastic system, in which the cost functional is also mean-field type. In our model, the leader first announces the terminal goal satisfying pointwise and affine constraints and open-loop dynamic decisions at the initial time which takes into account the best response of the follower. Then two interrelated optimization problems are sequentially solved by the follower (a backward LQ problem) and the leader (a backward-forward LQ problem). The open-loop Stackelberg equilibrium is obtained by virtue of duality theory and represented by some fully coupled mean-field backward-forward stochastic differential equations with mixed initial-terminal conditions, whose global solvability is discussed in some nontrivial cases by Riccati decoupling method and discounting method. As an application, we address a product pricing problem.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 2","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143361670","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
The Sticky Particle Dynamics of the 1D Pressureless Euler-Alignment System as a Gradient Flow 梯度流动下一维无压力欧拉对准系统的粘性粒子动力学
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-02-08 DOI: 10.1007/s00245-025-10223-z
Sondre Tesdal Galtung
{"title":"The Sticky Particle Dynamics of the 1D Pressureless Euler-Alignment System as a Gradient Flow","authors":"Sondre Tesdal Galtung","doi":"10.1007/s00245-025-10223-z","DOIUrl":"10.1007/s00245-025-10223-z","url":null,"abstract":"<div><p>We show how the sticky dynamics for the one-dimensional pressureless Euler-alignment system can be obtained as an <span>(L^2)</span>-gradient flow of a convex functional. This is analogous to the Lagrangian evolution introduced by Natile and Savaré for the pressureless Euler system, and by Brenier et al. for the corresponding system with a self-interacting force field. Our Lagrangian evolution can be seen as the limit of sticky particle Cucker–Smale dynamics, similar to the solutions obtained by Leslie and Tan from a corresponding scalar balance law, and provides us with a uniquely determined distributional solution of the original system in the space of probability measures with quadratic moments and corresponding square-integrable velocities. Moreover, we show that the gradient flow also provides an entropy solution to the balance law of Leslie and Tan, and how their results on cluster formation follow naturally from (non-)monotonicity properties of the so-called natural velocity of the flow.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 2","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00245-025-10223-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143361671","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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