Applied Mathematics and Optimization最新文献

{"title":"Coarse Correlated Equilibria in Linear Quadratic Mean Field Games and Application to an Emission Abatement Game","authors":"Luciano Campi,&nbsp;Federico Cannerozzi,&nbsp;Fanny Cartellier","doi":"10.1007/s00245-024-10198-3","DOIUrl":"10.1007/s00245-024-10198-3","url":null,"abstract":"<div><p>Coarse correlated equilibria (CCE) are a good alternative to Nash equilibria (NE), as they arise more naturally as outcomes of learning algorithms and as they may exhibit higher payoffs than NE. CCEs include a device which allows players’ strategies to be correlated without any cooperation, only through information sent by a mediator. We develop a methodology to concretely compute mean field CCEs in a linear-quadratic mean field game (MFG) framework. We compare their performance to mean field control solutions and mean field NE (usually named MFG solutions). Our approach is implemented in the mean field version of an emission abatement game between greenhouse gas emitters. In particular, we exhibit a simple and tractable class of mean field CCEs which allows to outperform very significantly the mean field NE payoff and abatement levels, bridging the gap between the mean field NE and the social optimum obtained by mean field control.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00245-024-10198-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142821384","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}

{"title":"Well-Posed Uniform Solvability of Convex Optimization Problems on a Uniform Differentiable Closed Convex Set","authors":"Shaoqiang Shang","doi":"10.1007/s00245-024-10206-6","DOIUrl":"10.1007/s00245-024-10206-6","url":null,"abstract":"<div><p>In this paper, we first give the definition of uniformly differentiable set and give the definitions of sets <span>(P(A,eta , r))</span> and <span>(P_{A,delta }(f))</span>. Secondly, we prove that if the set <i>A</i> is bounded closed convex set, then <i>A</i> is uniformly differentiable if and only if for any <span>(varepsilon , eta , r&gt;0)</span>, there exists <span>(delta =delta (varepsilon ,eta ,r )&gt;0)</span> such that <span>(Vert x-yVert &lt;varepsilon )</span> whenever <span>(fin P(A,eta , r))</span>, <span>(yin P_{A,delta }(f))</span> and <span>(xin P_{A}(f))</span>. Moreover, we also prove that if <i>A</i> is a bounded closed convex set in a finite-dimensional space <i>X</i>, then <i>A</i> is differentiable if and only if <i>A</i> is uniformly differentiable. Finally, we give some examples of uniformly differentiable set. Therefore, we extend some conclusions (SIAM J. Optim. Vol. 30, No. 1, pp. 490–512).</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142811195","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}

{"title":"Global Boundedness of Solutions to a Food Chain Model with Nonlinear Taxis Sensitivity","authors":"Enhui Pan,&nbsp;Changchun Liu","doi":"10.1007/s00245-024-10208-4","DOIUrl":"10.1007/s00245-024-10208-4","url":null,"abstract":"<div><p>In this paper, we investigate the initial boundary value problem of a three-species spatial food chain model with nonlinear taxis sensitivity in a bounded domain <span>(Omega subset {mathbb {R}}^2)</span> with a smooth boundary and homogeneous Neumann boundary conditions. By establishing a new energy functional, we demonstrate the global boundedness of classical solutions under appropriate initial data.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142798561","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}

{"title":"Optimal Consumption–Investment with Constraints in a Regime Switching Market with Random Coefficients","authors":"Ying Hu,&nbsp;Xiaomin Shi,&nbsp;Zuo Quan Xu","doi":"10.1007/s00245-024-10203-9","DOIUrl":"10.1007/s00245-024-10203-9","url":null,"abstract":"<div><p>This paper studies finite-time optimal consumption–investment problems with power, logarithmic and exponential utilities, in a regime switching market with random coefficients and possibly subject to non-convex constraints. Compared to the existing models, one distinguish feature of our model is that the trading constraints put on the consumption and investment strategies are coupled together in the cases of power and logarithmic utilities, leading to new technical challenges. We provide explicit optimal consumption–investment strategies and optimal values for these consumption–investment problems, which are expressed in terms of the solutions to some multi-dimensional diagonally quadratic backward stochastic differential equation (BSDE) and linear BSDE with unbound coefficients. These BSDEs are new in the literature and solving them is one of the main theoretical contributions of this paper. We accomplish the latter by applying the truncation, approximation technique to get some a priori uniformly lower and upper bounds for their solutions.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142798420","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}

{"title":"Optimality Conditions for Parabolic Stochastic Optimal Control Problems with Boundary Controls","authors":"Piero Visconti","doi":"10.1007/s00245-024-10204-8","DOIUrl":"10.1007/s00245-024-10204-8","url":null,"abstract":"<div><p>In this paper, we study optimality conditions for a class of control problems driven by a cylindrical Wiener process, resulting in a stochastic maximum principle in differential form. The control acts on both the drift and volatility, potentially as unbounded operators, allowing for SPDEs with boundary control and/or noise. Through the factorization method, we establish a regularity property for the state equation, which, by duality, extends to the backward costate equation, understood in the transposition sense. Finally, we show that the cost functional is Gâteaux differentiable, with its derivative represented by the costate. The optimality condition is derived using results from set-valued analysis.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142798509","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}

{"title":"Stopper vs. Singular Controller Games With Degenerate Diffusions","authors":"Andrea Bovo,&nbsp;Tiziano De Angelis,&nbsp;Jan Palczewski","doi":"10.1007/s00245-024-10199-2","DOIUrl":"10.1007/s00245-024-10199-2","url":null,"abstract":"<div><p>We study zero-sum stochastic games between a singular controller and a stopper when the (state-dependent) diffusion matrix of the underlying controlled diffusion process is degenerate. In particular, we show the existence of a value for the game and determine an optimal strategy for the stopper. The degeneracy of the dynamics prevents the use of analytical methods based on solution in Sobolev spaces of suitable variational problems. Therefore we adopt a probabilistic approach based on a perturbation of the underlying diffusion modulated by a parameter <span>(gamma &gt;0)</span>. For each <span>(gamma &gt;0)</span> the approximating game is non-degenerate and admits a value <span>(u^gamma )</span> and an optimal strategy <span>(tau ^gamma _*)</span> for the stopper. Letting <span>(gamma rightarrow 0)</span> we prove convergence of <span>(u^gamma )</span> to a function <i>v</i>, which identifies the value of the original game. We also construct explicitly optimal stopping times <span>(theta ^gamma _*)</span> for <span>(u^gamma )</span>, related but not equal to <span>(tau ^gamma _*)</span>, which converge almost surely to an optimal stopping time <span>(theta _*)</span> for the game with degenerate dynamics.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00245-024-10199-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142778199","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}

{"title":"Almost Sectorial Operators in Fractional Superdiffusion Equations","authors":"Eduardo Cuesta,&nbsp;Rodrigo Ponce","doi":"10.1007/s00245-024-10201-x","DOIUrl":"10.1007/s00245-024-10201-x","url":null,"abstract":"<div><p>In this paper the resolvent family <span>({S_{alpha ,beta }(t)}_{tge 0}subset mathcal {L}(X,Y))</span> generated by an almost sectorial operator <i>A</i>,  where <span>(alpha ,beta &gt;0,)</span> <i>X</i>, <i>Y</i> are complex Banach spaces and its Laplace transform satisfies <span>(hat{S}_{alpha ,beta }(z)=z^{alpha -beta }(z^alpha -A)^{-1})</span> is studied. This family of operators allows to write the solution to an abstract initial value problem of time fractional type of order <span>(1&lt;alpha &lt;2)</span> as a variation of constants formula. Estimates of the norm <span>(Vert S_{alpha ,beta }(t)Vert ,)</span> as well as the continuity and compactness of <span>(S_{alpha ,beta }(t))</span>, for <span>(t&gt;0)</span>, are shown. Moreover, the Hölder regularity of its solutions is also studied.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142761958","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}

{"title":"Null Controllability of Coupled Parabolic Systems with Switching Control","authors":"Yuanhang Liu,&nbsp;Weijia Wu,&nbsp;Donghui Yang","doi":"10.1007/s00245-024-10197-4","DOIUrl":"10.1007/s00245-024-10197-4","url":null,"abstract":"<div><p>The focus of this paper is on the null controllability of two kinds of coupled systems including both degenerate and non-degenerate equations with switching control. We first establish the observability inequality for measurable subsets in time for such coupled system, and then by the HUM method to obtain the null controllability. Next, we investigate the null controllability of such coupled system for segmented time intervals. Notably, these results are obtained through spectral inequalities rather than using the method of Carleman estimates. Such coupled systems with switching control, to the best of our knowledge, are among the first to discuss.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142645729","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}

{"title":"Pullback Measure Attractors for Non-autonomous Fractional Stochastic Reaction-Diffusion Equations on Unbounded Domains","authors":"Shaoyue Mi,&nbsp;Ran Li,&nbsp;Dingshi Li","doi":"10.1007/s00245-024-10196-5","DOIUrl":"10.1007/s00245-024-10196-5","url":null,"abstract":"<div><p>This paper is concerned with the pullback measure attractors of the non-autonomous fractional reaction-diffusion equations defined on <span>(mathbb {R}^{n})</span>. We first prove the existence and uniqueness of pullback measure attractors for such equations. Then we establish the upper semi-continuity of these attractors as the noise intensity <span>(varepsilon )</span> tends to zero. Specifically, we apply the uniform estimates on the tails of solutions to prove the asymptotic compactness of a family of probability distributions of solutions to overcome the non-compactness of usual Sobolev embeddings on unbounded domains.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"90 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142598978","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}

{"title":"Longtime Dynamics for a Class of Strongly Damped Wave Equations with Variable Exponent Nonlinearities","authors":"Yanan Li,&nbsp;Yamei Li,&nbsp;Zhijian Yang","doi":"10.1007/s00245-024-10193-8","DOIUrl":"10.1007/s00245-024-10193-8","url":null,"abstract":"<div><p>The paper investigates the global well-posedness and the longtime dynamics for a class of strongly damped wave equations with evolutional <i>p</i>(<i>x</i>, <i>t</i>)-Laplacian and <i>q</i>(<i>x</i>, <i>t</i>)-growth source term on a bounded domain <span>( Omega subset {mathbb {R}}^3: u_{tt}-nabla cdot (|nabla u|^{p(x, t)-2} nabla u)-lambda Delta u- Delta u_t+ |u|^{q(x, t)-2}u=g)</span>, together with the perturbed parameter <span>(lambda in [0,1])</span> and the Dirichlet boundary condition. We show that under rather relaxed conditions, (i) the model is global well-posed; (ii) for each <span>(lambda _0in (0,1])</span>, the related nonautonomous dynamical systems acting on the time-dependent phase spaces have a family of pullback <span>({mathscr {D}})</span>-exponential attractor <span>({mathcal {E}}_lambda ={E_lambda (t)}_{tin {mathbb {R}}}in {mathscr {D}})</span> which is Hölder continuous w.r.t. <span>(lambda )</span> at <span>(lambda _0)</span>; (iii) they have also a family of finite dimensional pullback <span>({mathscr {D}})</span>-attractors <span>({mathcal {A}}_lambda ={A_lambda (t)}_{tin {mathbb {R}}})</span> which are upper semicontinuous and residual continuous w.r.t. <span>(lambda in (0,1])</span>. In particular, when <span>(lambda in (0,1])</span> and without the <i>p</i>(<i>x</i>, <i>t</i>)-Laplacian, the above mentioned results can be greatly improved, in the concrete; (iv) the weak solutions of the corresponding model possess additionally partial regularity and the Hölder stability in stronger <span>(H^1times H^1)</span>-norm, the pullback <span>({mathscr {D}})</span>-attractor and pullback <span>({mathscr {D}})</span>-exponential attractor in weaker <span>({mathcal {Y}}_1)</span>-norm can be regularized to be those in stronger <span>(H^1times H^1)</span>-norm, which are also the standard ones in <span>({mathcal {H}}_t)</span>-norm. The method provided here allows overcoming the difficulties arising from variable exponent nonlinearities and extending the analysis and the results for these type of models with constant exponent nonlinearities.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"90 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142595257","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}