Recent zbMATH articles in MSC 49Nhttps://zbmath.org/atom/cc/49N2024-09-13T18:40:28.020319ZWerkzeugExploring the behavior of malware propagation on mobile wireless sensor networks: stability and control analysishttps://zbmath.org/1540.340932024-09-13T18:40:28.020319Z"Kumari, Sangeeta"https://zbmath.org/authors/?q=ai:kumari.sangeeta"Upadhyay, Ranjit Kumar"https://zbmath.org/authors/?q=ai:kumar-upadhyay.ranjitSummary: This paper aims to explore the behavior of malware propagation on mobile wireless sensor networks (MWSNs). A new malware propagation model with nonlinear incidence rate and sigmoid type removal rate is established, and its global stability, spatiotemporal stability, and optimal control are analyzed. Specifically, the theoretical analysis shows that (i) a forward transcritical bifurcation occurs when the basic reproduction number \(R_0 > 1\); (ii) time and space affect the spreading behavior of malware due to spatial distribution; (iii) the optimization technology can effectively control the malware spreading on MWSNs. Finally, some numerical simulations are performed to verify the obtained theoretical results, and the experimental results confirm that the generated patterns are consistent with the field observations of actual MWSNs. Our study helps in controlling the propagation of malware and applicable to design and prediction of the security and robustness of a sensor network.A variational approach for price formation models in one dimensionhttps://zbmath.org/1540.354072024-09-13T18:40:28.020319Z"Ashrafyan, Yuri"https://zbmath.org/authors/?q=ai:ashrafyan.yuri-a"Bakaryan, Tigran"https://zbmath.org/authors/?q=ai:bakaryan.tigran-k"Gomes, Diogo"https://zbmath.org/authors/?q=ai:gomes.diogo-luis-aguiar"Gutierrez, Julian"https://zbmath.org/authors/?q=ai:gutierrez.julianSummary: In this paper, we study a class of first-order mean-field games (MFGs) that model price formation. Using Poincaré lemma, we eliminate one of the equations of the MFGs system and obtain a variational problem for a single function. We prove the uniqueness of the solutions to the variational problem and address the existence of solutions by applying relaxation arguments. Moreover, we establish a correspondence between solutions of the MFGs system and the variational problem. Based on this correspondence, we introduce an alternative numerical approach for the solution of the original MFGs problem. We end the paper with numerical results for a linear-quadratic model.Mean field games of controls with Dirichlet boundary conditionshttps://zbmath.org/1540.354082024-09-13T18:40:28.020319Z"Bongini, Mattia"https://zbmath.org/authors/?q=ai:bongini.mattia"Salvarani, Francesco"https://zbmath.org/authors/?q=ai:salvarani.francescoSummary: In this paper, we study a mean-field games system with Dirichlet boundary conditions in a closed domain and in a \textit{mean-field game of controls} setting, that is in which the dynamics of each agent is affected not only by the average position of the rest of the agents but also by their average optimal choice. This setting allows the modeling of more realistic real-life scenarios in which agents not only will leave the domain at a certain point in time (like during the evacuation of pedestrians or in debt refinancing dynamics) but also act competitively to anticipate the strategies of the other agents. We shall establish the existence of Nash Equilibria for such class of mean-field game of controls systems under certain regularity assumptions on the dynamics and the Lagrangian cost. Much of the paper is devoted to establishing several \textit{a priori} estimates which are needed to circumvent the fact that the mass is not conserved (as we are in a Dirichlet boundary condition setting). In the conclusive sections, we provide examples of systems falling into our framework as well as numerical implementations.Measure-valued optimal control for size-structured population models with diffusionhttps://zbmath.org/1540.354132024-09-13T18:40:28.020319Z"Kato, Nobuyuki"https://zbmath.org/authors/?q=ai:kato.nobuyukiSummary: We consider a control problem to maximize a profit from harvesting in agriculture or aquaculture, where the population is governed by size-structured population models with spatial diffusion. We show the existence of an optimal control of harvesting rate which is a measure with respect to size expressed by the distributional partial derivative of a function of bounded variation.Low-regret optimal control for an inverse electrocardiological problem with incomplete datahttps://zbmath.org/1540.354182024-09-13T18:40:28.020319Z"Ainseba, B."https://zbmath.org/authors/?q=ai:ainseba.bedreddine"Omrane, A."https://zbmath.org/authors/?q=ai:omrane.abdennebiSummary: This work deals with an inverse electrocardiological problem considering the reconstruction of where one has to reconstruct the heart transmembrane potential from thorax's high density measurements. The problem will be solved as an optimal control one for a partial differential system with incomplete data. The electrical activity on the heart is here modelled by a system of FitzHugh-Nagumo's type where the initial conditions corresponding to the transmembrane potential and to the gating variables are unknown. We use the low-regret optimal control method by \textit{J. L. Lions} [Some aspects of the optimal control of distributed parameter systems. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (1972; Zbl 0275.49001); C. R. Acad. Sci., Paris, Sér. I 315, No. 12, 1253--1257 (1992; Zbl 0766.93033)] to tackle this problem. We prove the existence and uniqueness of a low-regret control that we characterise by a singular optimality system.Regularity results and optimal velocity control of the convective nonlocal Cahn-Hilliard equation in 3Dhttps://zbmath.org/1540.354232024-09-13T18:40:28.020319Z"Poiatti, Andrea"https://zbmath.org/authors/?q=ai:poiatti.andrea"Signori, Andrea"https://zbmath.org/authors/?q=ai:signori.andreaSummary: In this contribution, we study an optimal control problem for the celebrated nonlocal Cahn-Hilliard equation endowed with the singular Flory-Huggins potential in the three-dimensional setting. The control enters the governing \textit{state system} in a nonlinear fashion in the form of a prescribed solenoidal, that is a divergence-free, vector field, whereas the \textit{cost functional} to be minimized is of tracking-type. The novelties of the present paper are twofold: in addition to the control application, the intrinsic difficulties of the optimization problem forced us to first establish new regularity results on the nonlocal Cahn-Hilliard equation that were unknown even without the coupling with a velocity field and are therefore of independent interest. This happens to be shown using the recently proved separation property along with ad hoc Hölder regularities and a bootstrap method. For the control problem, the existence of an optimal strategy as well as first-order necessary conditions are then established.Regularity of almost minimizers for the parabolic thin obstacle problemhttps://zbmath.org/1540.354732024-09-13T18:40:28.020319Z"Jeon, Seongmin"https://zbmath.org/authors/?q=ai:jeon.seongmin"Petrosyan, Arshak"https://zbmath.org/authors/?q=ai:petrosyan.arshakLet \(\Omega\) be the domain in \(\mathbb{R}^n, \ n\ge2\), \(\mathcal{M}\) be a smooth \((n-1)\)-dimensional manifold dividing \(\Omega\) into two subdomains \(\Omega_1\) and \(\Omega_2\), \(\nu^\pm\) be the unit normal to \(\mathcal{M}\) directed into \(\Omega^\mp\). Let \(\Omega_T := \Omega\times (0,T]\), \((\partial \Omega)_T:= \partial \Omega \times (0,T]\). \({\mathcal{M}}_T := \mathcal{M}\times (0,\,T]\) is the thin obstacle space. There is assumed also that \(\psi\) is the thin obstacle function, \(\psi_0, g \) are the initial and boundary functions respectively and such that \(\psi_0 \geq \psi\) on \(\mathcal{M}\times \{0\}\), \(g\geq\psi\) on \((\mathcal{M}\cap \partial\Omega)\times(0,T]\), \(g = \psi_0\) on \(\partial\Omega\times\{0\}\),
The authors define the function \(u(x,t)\) as the solution of the parabolic thin obstacle (Signorini) problem in \(\Omega_T\) if it satisfies the variational inequality
\[
\int_{\Omega_T}\nabla u\nabla(v-u) + \partial_t (v - u) \geq 0 \text{ for any } v \in \mathcal{K},
\]
and \(u\in \mathcal{K}\), \(\partial_t u \in L_2(\Omega_T), u(\cdot,\,0) = \psi_0 \text{ on } \Omega\), where \(\mathcal{K} = \{v \in W^{1,0}_2(\Omega_T): v \geq \psi \text{ on } {\mathcal{M}}_T, \ v = g \text{ on } (\partial \Omega)_T\}\). The solution of the Signorini problem is the solution in the weak sense of the following problem:
\[
\Delta u - \partial_t u = 0 \ \text{ in } \Omega_T\setminus {\mathcal{M}_T},\tag{1}
\]
\[
u \geq\psi, \ \partial_{\nu^+}u + \partial_{\nu^-}u \geq 0, \ (u - \psi)(\partial_{\nu^+}u + \partial_{\nu^-}u) = 0 \ \text{ on } \mathcal{M}_T, \tag{2}
\]
\[
u = g \ \text{ on } (\partial \Omega)_T,\ u(\cdot,0) = \psi_0 \ \text{ on } \Omega\times\{0\}.\tag{3}
\]
There is determined the almost minimizer \(u \in W^{1,1}_2(\Omega_T)\) for the parabolic Signorini problem. Under the assumptions that \(\Omega_T\) is parabolic cylinder \(Q_1\), \({\mathcal{M}}_T\) is the flat thin obstacle space \(Q_1'\), \(\psi \equiv 0\), and \(u(x,t)\) is the almost minimizer of the parabolic Signorini problem the authors prove that 1)\, \(u\) belongs to the Hölder space \(H^{\sigma,\,\sigma/2}(Q_1)\) for any \(\sigma \in 0,\,1);\) \ 2) \,\(\nabla u\) belongs to \(H^{\beta,\beta/2}_{\mathrm{loc}}(Q_1^\pm\cup Q_1')\) for some definite \(\beta > 0\).
The similar results are obtained for the problem (1)--(3) with \(\psi \equiv 0 \), and \(U\), \(\operatorname{div}(A \nabla U)\), \(\langle A \nabla U, \nu^{\pm} \rangle\) instead of \(u\), \(\Delta u\), \(\partial_{\nu^{\pm}} u\), where \(A = \{a_{ij}(z)\}_{i,j=1}^n\) is the symmetric, positive definite, \(n\times n\) matrix, \(z:=(x,t)\ \in \Omega_T\).
Reviewer: Galina Bizhanova (Almaty)Variational models for the interaction of surfactants with curvature -- existence and regularity of minimizers in the case of flexible curveshttps://zbmath.org/1540.490022024-09-13T18:40:28.020319Z"Brand, Christopher"https://zbmath.org/authors/?q=ai:brand.christopher"Dolzmann, Georg"https://zbmath.org/authors/?q=ai:dolzmann.georg"Pluda, Alessandra"https://zbmath.org/authors/?q=ai:pluda.alessandraAuthors' abstract: Existence and regularity of minimizers for a geometric variational problem is shown. The variational integral models an energy contribution of the interface between two immiscible fluids in the presence of surfactants and includes a Helfrich type contribution, a Frank type contribution and a coupling term between the orientation of the surfactants and the curvature of the interface. Analytical results are proven in a one-dimensional situation for curves.
Reviewer: Giorgio Saracco (Firenze)The duality theory of fractional calculus and a new fractional calculus of variations involving left operators onlyhttps://zbmath.org/1540.490192024-09-13T18:40:28.020319Z"Torres, Delfim F. M."https://zbmath.org/authors/?q=ai:torres.delfim-f-mSummary: Through duality, it is possible to transform left fractional operators into right fractional operators and vice versa. In contrast to existing literature, we establish integration by parts formulas that exclusively involve either left or right operators. The emergence of these novel fractional integration by parts formulas inspires the introduction of a new calculus of variations, where only one type of fractional derivative (left or right) is present. This applies to both the problem formulation and the corresponding necessary optimality conditions. As a practical application, we present a new Lagrangian that relies solely on left-hand side fractional derivatives. The fractional variational principle derived from this Lagrangian leads us to the equation of motion for a dissipative/damped system.Optimal control of differential inclusions with endpoint constraints and dualityhttps://zbmath.org/1540.490252024-09-13T18:40:28.020319Z"Mahmudov, Elimhan N."https://zbmath.org/authors/?q=ai:mahmudov.elimhan-nadirSummary: The article considers a high-order optimal control problem and its dual problems described by high-order differential inclusions. In this regard, the established Euler-Lagrange type inclusion, containing the Euler-Poisson equation of the calculus of variations, is a sufficient optimality condition for a differential inclusion of a higher order. It is shown that the adjoint inclusion for the first-order differential inclusions, defined in terms of a locally adjoint mapping, coincides with the classical Euler-Lagrange inclusion. Then the duality theorems are proved.A new computational approach for optimal control of switched systemshttps://zbmath.org/1540.490362024-09-13T18:40:28.020319Z"Zhu, Xi"https://zbmath.org/authors/?q=ai:zhu.xi"Bai, Yanqin"https://zbmath.org/authors/?q=ai:bai.yanqin"Yu, Changjun"https://zbmath.org/authors/?q=ai:yu.changjun"Teo, Kok Lay"https://zbmath.org/authors/?q=ai:teo.kok-lay(no abstract)Second Chebyshev wavelets (SCWs) method for solving finite-time fractional linear quadratic optimal control problemshttps://zbmath.org/1540.490372024-09-13T18:40:28.020319Z"Baghani, Omid"https://zbmath.org/authors/?q=ai:baghani.omidSummary: In this paper, we present an indirect computational procedure based on the truncated second kind Chebyshev wavelets for finding the solutions of Caputo fractional time-invariant linear optimal control systems which the functional cost consists of the finite-time quadratic cost function. Utilizing the operational matrices of second Chebyshev wavelets (SCWs) of the Riemann-Liouville fractional integral, the corresponding linear two-point boundary value problem (TPBVP), obtained from the fractional Euler-Lagrange equations, is reduced to a coupled Sylvester-type matrix equation. An equivalent linear matrix form using the Kronecker product is constructed. The upper bound of the error of the SCWs approximation and the convergence of the proposed method are investigated. Low computational complexity and flexible accuracy are two important superiorities of this approach. Numerical experiments provide satisfactory results compared to the exiting techniques.Extremal controls searching methods based on fixed point problemshttps://zbmath.org/1540.490382024-09-13T18:40:28.020319Z"Buldaev, Alexander"https://zbmath.org/authors/?q=ai:buldaev.aleksandr-sergeevich"Kazmin, Ivan"https://zbmath.org/authors/?q=ai:kazmin.ivanSummary: New methods of searching for extremal controls are considered in the class of linear-quadratic optimal control problems that arise in control models of quantum systems. The proposed approach is based on special forms of the maximum principle, which have the form of operator problems on a fixed point in the space of controls, which are equivalent to the well-known condition of the maximum principle in the considered class of optimal control problems. The considered operator forms of the conditions of the maximum principle make it possible to construct new algorithms for searching for extremal controls in problems of the class under consideration. A comparative analysis of the effectiveness of new algorithms for finding extremal controls is carried out on a well-known model example of optimizing a quantum system, which is characterized by the degeneracy of the maximum principle condition.
For the entire collection see [Zbl 1531.90013].Synthesis of an optimal stable affine systemhttps://zbmath.org/1540.490392024-09-13T18:40:28.020319Z"Ashchepkov, L. T."https://zbmath.org/authors/?q=ai:ashchepkov.leonid-timofeevichIn this paper, the author investigates on synthesis of an optimal stable affine system. More precisely, the author proposes a method for constructing a feedback that ensures the attraction of trajectories of an affine system to an equilibrium state and to a given manifold.
Reviewer: Savin Treanţă (Bucureşti)An analysis on the optimal feedback control for Caputo fractional neutral evolution systems in Banach spaceshttps://zbmath.org/1540.490402024-09-13T18:40:28.020319Z"Vivek, S."https://zbmath.org/authors/?q=ai:vivek.srinivas|vivek.s-sree"Vijayakumar, V."https://zbmath.org/authors/?q=ai:vijayakumar.velusamy|vijayakumar.vaidehiIn this paper, the authors investigate on the optimal feedback control for Caputo fractional neutral evolution systems in Banach spaces. Concretely, feasible pairs are established by using the Filippov theorem and the Cesari property.
Reviewer: Savin Treanţă (Bucureşti)Differential equation-constrained optimization with stochasticityhttps://zbmath.org/1540.490412024-09-13T18:40:28.020319Z"Li, Qin"https://zbmath.org/authors/?q=ai:li.qin"Wang, Li"https://zbmath.org/authors/?q=ai:wang.li.6"Yang, Yunan"https://zbmath.org/authors/?q=ai:yang.yunanSummary: Most inverse problems from physical sciences are formulated as PDE-constrained optimization problems. This involves identifying unknown parameters in equations by optimizing the model to generate PDE solutions that closely match measured data. The formulation is powerful and widely used in many science and engineering fields. However, one crucial assumption is that the unknown parameter must be deterministic. In reality, however, many problems are stochastic in nature, and the unknown parameter is random. The challenge then becomes recovering the full distribution of this unknown random parameter. It is a much more complex task. In this paper, we examine this problem in a general setting. In particular, we conceptualize the PDE solver as a push-forward map that pushes the parameter distribution to the generated data distribution. In this way, the SDE-constrained optimization translates to minimizing the distance between the generated distribution and the measurement distribution. We then formulate a gradient flow equation to seek the ground-truth parameter probability distribution. This opens up a new paradigm for extending many techniques in PDE-constrained optimization to optimization for systems with stochasticity.Optimization method for determining the source term in fractional diffusion equationhttps://zbmath.org/1540.490422024-09-13T18:40:28.020319Z"Ma, Yong-Ki"https://zbmath.org/authors/?q=ai:ma.yong-ki"Prakash, P."https://zbmath.org/authors/?q=ai:prakash.periasamy"Deiveegan, A."https://zbmath.org/authors/?q=ai:deiveegan.arumugamSummary: In this paper, we determine a spacewise dependent source in one-dimensional fractional diffusion equation. On the basis of the optimal control method, the existence, uniqueness and stability of the minimizer for the cost functional are established. The Landweber iteration method is applied to the inverse problem.An optimal control problem for the continuity equation arising in smart charginghttps://zbmath.org/1540.490432024-09-13T18:40:28.020319Z"Séguret, Adrien"https://zbmath.org/authors/?q=ai:seguret.adrienSummary: This paper is focused on the mathematical modeling and solution of the optimal charging of a large population of identical plug-in electric vehicles (PEVs) with mixed state variables (continuous and discrete). A mean field assumption is formulated to describe the evolution interaction of the PEVs population. The optimal control of the resulting continuity equation of the mixed system under state constraints is investigated. We prove the existence of a minimizer. We then characterize the solution as the weak solution of a system of two coupled PDEs: a continuity equation and of a Hamilton-Jacobi equation. We provide regularity results of the optimal feedback control.Optimal control study on Michaelis-Menten kinetics -- a fractional versionhttps://zbmath.org/1540.490442024-09-13T18:40:28.020319Z"Kokila, J."https://zbmath.org/authors/?q=ai:kokila.jayakumar"Vellappandi, M."https://zbmath.org/authors/?q=ai:vellappandi.madasamy"Meghana, D."https://zbmath.org/authors/?q=ai:meghana.d"Govindaraj, V."https://zbmath.org/authors/?q=ai:govindaraj.venkatesanSummary: Systems biology adopts a holistic approach and brings a whole new way of understanding complex biological systems where it becomes important to study the interactions within its components. This article is concerned with the analysis of Michaelis Menten kinetics in the sense of fractional derivatives which fills the gap in the existing literature. Further, the study extends with the optimal control. Thus aiming for better accuracy and understanding, the comparison of classical and fractional systems shall be examined through numerical illustrations. The basic study of chemical reaction networks with fractional derivative is discussed at the end with numerical results.The cost optimal control system based on the Kermack-McKendrick worm propagation modelhttps://zbmath.org/1540.490452024-09-13T18:40:28.020319Z"Tong, Xiao-Jun"https://zbmath.org/authors/?q=ai:tong.xiaojun"Zhang, Miao"https://zbmath.org/authors/?q=ai:zhang.miao"Wang, Zhu"https://zbmath.org/authors/?q=ai:wang.zhu.2(no abstract)Wasserstein steepest descent flows of discrepancies with Riesz kernelshttps://zbmath.org/1540.490492024-09-13T18:40:28.020319Z"Hertrich, Johannes"https://zbmath.org/authors/?q=ai:hertrich.johannes"Gräf, Manuel"https://zbmath.org/authors/?q=ai:graf.manuel"Beinert, Robert"https://zbmath.org/authors/?q=ai:beinert.robert"Steidl, Gabriele"https://zbmath.org/authors/?q=ai:steidl.gabrieleIn this paper, the interest in Wasserstein flows arises from the approximation of probability measures by empirical measures when halftoning images, i.e., the gray values of an image are considered as values of a probability density function of a measure.
The Wasserstein space \({\mathcal P}_2({\mathbb R}^d)\) is defined as metric space of all Borel measures with finite second moments equipped with the Wasserstein distance. First the authors introduce Wasserstein steepest descent flows which are locally absolutely continuous curves in \({\mathcal P}_2({\mathbb R}^d)\) whose tangent vectors point into a steepest descent direction of a given functional. This allows the use of Euler forward schemes instead of Jordan-Kinderlehrer-Otto schemes. For a \(\lambda\)-convex functional, the Wasserstein steepest descent flow coincides with the Wasserstein gradient flow.
Further, the authors study Wasserstein flows of the maximum mean discrepancy with respect to certain Riesz kernels. They present analytic expressions for Wasserstein steepest descent flows of the interaction energy starting at Dirac measures. Finally, for halftoning images they provide several numerical simulations of Wasserstein steepest descent flows of discrepancies.
Reviewer: Manfred Tasche (Rostock)Exact controllability for mean-field type linear game-based control systemshttps://zbmath.org/1540.601072024-09-13T18:40:28.020319Z"Chen, Cui"https://zbmath.org/authors/?q=ai:chen.cui.1|chen.cui"Yu, Zhiyong"https://zbmath.org/authors/?q=ai:yu.zhiyongSummary: Motivated by the self-pursuit of controlled objects, we consider the exact controllability of a linear mean-field type game-based control system (MF-GBCS, for short) generated by a linear-quadratic (LQ, for short) Nash game. A Gram-type criterion for the general time-varying coefficients case and a Kalman-type criterion for the special time-invariant coefficients case are obtained. At the same time, the equivalence between the exact controllability of this MF-GBCS and the exact observability of a dual system is established. Moreover, an admissible control that can steer the state from any initial vector to any terminal random variable is constructed in closed form.A posteriori error estimation for the optimal control of time-periodic eddy current problemshttps://zbmath.org/1540.654672024-09-13T18:40:28.020319Z"Wolfmayr, Monika"https://zbmath.org/authors/?q=ai:wolfmayr.monikaSummary: This work presents the multiharmonic analysis and derivation of functional type a posteriori estimates of a distributed eddy current optimal control problem and its state equation in a time-periodic setting. The existence and uniqueness of the solution of a weak space-time variational formulation for the optimality system and the forward problem are proved by deriving inf-sup and sup-sup conditions. Using the inf-sup and sup-sup conditions, we derive guaranteed, sharp and fully computable bounds of the approximation error for the optimal control problem and the forward problem in the functional type a posteriori estimation framework. We present here the first computational results on the derived estimates.Sediment minimization in canals: an optimal control approachhttps://zbmath.org/1540.860142024-09-13T18:40:28.020319Z"Alvarez-Vázquez, L. J."https://zbmath.org/authors/?q=ai:alvarez-vazquez.lino-jose"Martínez, A."https://zbmath.org/authors/?q=ai:martinez.aurea"Rodríguez, C."https://zbmath.org/authors/?q=ai:rodriguez.carmen-e"Vázquez-Méndez, M. E."https://zbmath.org/authors/?q=ai:vazquez-mendez.miguel-ernestoSummary: This work deals with the computational modelling and control of the processes related to the sedimentation of suspended particles in large streams. To analyse this ecological problem, we propose two alternative mathematical models (1D and 2D, respectively) coupling the system for shallow water hydrodynamics with the sediment transport equations. Our main goal is related to establishing the optimal management of a canal (for instance, from a wastewater treatment plant) to avoid the settling of suspended particles and their unwanted effects: channel malfunction, undesired growth of vegetation, etc. So, we formulate the problem as an optimal control problem of partial differential equations, where we consider a set of design variables (the shape of the channel section and the water inflow entering the canal) in order to control the velocity of water and, therefore, the settling of suspended particles. In this first approach to the problem from an environmental/mathematical control viewpoint, in addition to a well-posed mathematical formulation of the problem, we present theoretical and numerical results for a realistic case (interfacing MIKE21 package with our own MATLAB code for Nelder-Mead optimization algorithm).Designing an ecologically optimized road corridor surrounding restricted urban areas: a mathematical methodologyhttps://zbmath.org/1540.900642024-09-13T18:40:28.020319Z"García-Chan, N."https://zbmath.org/authors/?q=ai:garcia-chan.nestor"Alvarez-Vázquez, L. J."https://zbmath.org/authors/?q=ai:alvarez-vazquez.lino-jose"Martínez, A."https://zbmath.org/authors/?q=ai:martinez.aurea"Vázquez-Méndez, M. E."https://zbmath.org/authors/?q=ai:vazquez-mendez.miguel-ernestoSummary: The use of optimization techniques for the optimal design of roads and railways has increased in recent years. The environmental impact of a layout is usually given in terms of the land use where it runs (avoiding some ecologically protected areas), without taking into account air pollution (in these or other sensitive areas) due to vehicular traffic on the road. This work addresses this issue and proposes an automatic method for obtaining a specific corridor (optimal in terms of air pollution), where the economically optimized road must be designed in a later stage. Combining a 1D traffic simulation model with a 2D air pollution model, and using classical techniques for optimal control of partial differential equations, the problem is formulated and solved in the framework of Mixed Integer Nonlinear Programming. The usefulness of this approach is shown in a real case study posed in a region that suffers from serious episodes of environmental pollution, the Guadalajara Metropolitan Area (México).Strong and total duality for constrained composed optimization via a coupling conjugation schemehttps://zbmath.org/1540.902042024-09-13T18:40:28.020319Z"You, Manxue"https://zbmath.org/authors/?q=ai:you.manxue"Li, Genghua"https://zbmath.org/authors/?q=ai:li.genghuaSummary: Based on a coupling conjugation scheme and the perturbational approach, we build Fenchel-Lagrange dual problem of a composed optimization model with infinite constraints in separated locally convex spaces. This paper has mainly two targets. One is to establish strong duality under a new regularity condition \((\mathrm{RC}_A\)) and an extension closed-type condition \((\mathrm{ECRC}_A\)). The e-convex counterpart of Fenchel-Moreau theorem plays a key role in analysing the relation between them. The other aim is to achieve the sufficient and necessary characterizations for total duality in terms of \(c\)-subdifferentials. For this purpose, a formula for \(\varepsilon\)-\(c\)-subdifferentials of a proper function composed with a linear continuous operator is proved and applied.A high-order scheme for mean field gameshttps://zbmath.org/1540.910042024-09-13T18:40:28.020319Z"Calzola, Elisa"https://zbmath.org/authors/?q=ai:calzola.elisa"Carlini, Elisabetta"https://zbmath.org/authors/?q=ai:carlini.elisabetta"Silva, Francisco J."https://zbmath.org/authors/?q=ai:silva.francisco-jSummary: In this paper we propose a high-order numerical scheme for time-dependent mean field games systems. The scheme, which is built by combining Lagrange-Galerkin and semi-Lagrangian techniques, is consistent and stable for large time steps compared with the space steps. We provide a convergence analysis for the exactly integrated Lagrange-Galerkin scheme applied to the Fokker-Planck equation, and we propose an implementable version with inexact integration. Finally, we validate the convergence rate of the proposed scheme through the numerical approximation of two mean field games systems.A numerical iterative method for solving two-point BVPs in infinite-horizon nonzero-sum differential games: economic applicationshttps://zbmath.org/1540.910062024-09-13T18:40:28.020319Z"Nikooeinejad, Z."https://zbmath.org/authors/?q=ai:nikooeinejad.z"Heydari, M."https://zbmath.org/authors/?q=ai:heydari.mohammad-hossein.3|heydari.majeed|heydari.maysam|heydari.mohammad-mehdi|heydari.mehdi|heydari.mojgan|heydari.m-reza|heydari.maryam.1|heydari.mohammadhossein|heydari.mahdi|heydari.mohammad-bagher|heydari.mohammad-taghi|heydari.masoud"Loghmani, G. B."https://zbmath.org/authors/?q=ai:loghmani.g-barid|loghmani.ghasem-baridSummary: In this work, the Nash equilibrium solution of nonlinear infinite-horizon nonzero-sum differential games with open-loop information is investigated numerically. For this class of games, some difficulties are involved in finding an open-loop Nash equilibrium. For instance, we must solve a nonlinear differential equations system with split boundary conditions, namely the two-point boundary value problem (TPBVP), in which some of the boundary conditions are specified at the initial time and some at the infinite final time. In the current study, we provide a combined numerical algorithm based on a new set of basis functions on the half-line, called the exponential Chelyshkov functions (ECFs), and quasilinearization (QL) method to solve TPBVPs. In the first step, we reduce the nonlinear TPBVP to a sequence of linear differential equations by using the QL method. Although we have now a linearized system, another difficulty is finding the approximate solution of this linear system such that the transversality conditions at the infinite final time are satisfied. So, in the second step, we apply a collocation method based on the ECFs to solve the obtained linear system in the semi-infinite domain. The convergence of the proposed method is discussed in detail. To confirm the validity and efficiency of the proposed scheme, we compute the approximate solution of TPBVP as well as the open-loop Nash equilibrium for four applications of differential games in economics and management science.Multiscale control of Stackelberg gameshttps://zbmath.org/1540.910112024-09-13T18:40:28.020319Z"Herty, Michael"https://zbmath.org/authors/?q=ai:herty.michael-matthias"Steffensen, Sonja"https://zbmath.org/authors/?q=ai:steffensen.sonja"Thünen, Anna"https://zbmath.org/authors/?q=ai:thunen.annaSummary: We introduce a bilevel problem of the optimal control of an interacting agent system that can be interpreted as Stackelberg game with a large number of followers. It is shown that the model is well posed by providing conditions that allow to formally reduce the problem to a single level unconstrained problem. The mean-field limit is derived formally for infinitely many followers at three different stages of the optimization and the commutativity of these operations (the mean-field limit and first-order optimality on leader and on follower level) is studied. Further, we establish conditions for consistency for the relation between bilevel optimization and mean-field limit. Finally, we propose a numerical method based on the derived models and present numerical examples.Takeoff vs. stagnation in endogenous recombinant growth modelshttps://zbmath.org/1540.910492024-09-13T18:40:28.020319Z"Privileggi, Fabio"https://zbmath.org/authors/?q=ai:privileggi.fabioSummary: This paper concludes the study of transition paths in the continuous-time recombinant endogenous growth model by providing numerical methods to estimate the threshold initial value of capital (a Skiba-type point) above which the economy takes off toward sustained growth in the long run, while it is doomed to stagnation otherwise. The model is based on the setting first introduced by Tsur and Zemel and then further specified by Privileggi, in which knowledge evolves according to the Weitzman recombinant process. We pursue a direct approach based on the comparison of welfare estimations along optimal consumption trajectories either diverging to sustained growth or converging to a steady state. To this purpose, we develop and test three algorithms capable of numerically simulating the initial Skiba-value of capital, each corresponding to initial stock of knowledge values belonging to three different ranges, thus covering all possible scenarios.Hopf bifurcation analysis and optimal control of treatment in a delayed oncolytic virus dynamicshttps://zbmath.org/1540.920682024-09-13T18:40:28.020319Z"Kim, Kwang Su"https://zbmath.org/authors/?q=ai:kim.kwangsu"Kim, Sangil"https://zbmath.org/authors/?q=ai:kim.sangil"Jung, Il Hyo"https://zbmath.org/authors/?q=ai:jung.il-hyoSummary: During cancer viral therapy, there is a time delay from the initial virus infection of the tumor cells up to the time those infected cells reach the stage of being able to infect other cells. Because the duration of this ``time delay'' varies with each virus, it is important to understand how the delay affects the cancer viral therapy. Herein, we have introduced a mathematical model to explain this time delay. The existence of equilibrium (i.e., whether the treatment was unsuccessful or partially successful) was determined in this model by using a basic reproduction ratio of viral infection \((R_0)\) to immune response \((R_1)\). By using the bifurcation parameter as a delay \(\tau \), we proved a sufficient condition for the local asymptotic stability of two equilibrium points and the existence of Hopf bifurcation. In addition, we observed that the time delay caused the partial success equilibrium to be unstable and worked together with Hopf bifurcation to create a stable periodic oscillation. Therefore, we investigated the effects of viral cytotoxicity or infection rate, which are characteristics of viruses, on the Hopf bifurcation point. In order to support the analytical findings and to further analyze the effects of delay during cancer viral therapy, we reconstructed the model to include two controls: cancer viral therapy and immunotherapy. In addition, using numerical simulation, we suggested an optimal control problem to examine the effects of delay on oncolytic immunotherapy.The impact of invasive species on some ecological services in a harvested predator-prey systemhttps://zbmath.org/1540.921062024-09-13T18:40:28.020319Z"Das, Debabrata"https://zbmath.org/authors/?q=ai:das.debabrata"Kar, T. K."https://zbmath.org/authors/?q=ai:kar.tapan-kumar"Pal, Debprasad"https://zbmath.org/authors/?q=ai:pal.debprasadSummary: Biological invasion is a critical and emerging problem in the ecosystem as it has been the reason for the extinction and endangeredness of several species. Besides, harvesting on the different trophic levels also substantially impacts the dynamics of several interacting species. For this, we have considered a mathematical model consisting of prey, a predator, and an invasive species with Holling type II functional response and nonlinear harvesting to study the dual impact of harvesting and the presence of invasive species. Our results show that in the case of prey harvesting only, increasing effort on prey promotes the yield but reduces resilience. Whereas for the predator harvesting only, the intermediate effort level on the predator supports both the services simultaneously. In the case of joint harvesting of both species, predator-oriented harvesting gives more yield and resilience at the MSY level. Therefore, we conclude that the optimal yield and resilience in invasive species induced predator-prey systems can be found for the case predator or predator-oriented harvesting system with low predator catchability only. We also note no significant variation in the biomass, yield, and resilience between the linear and nonlinear models concerning the above cases except the number of equilibria and the specific ecosystem services. Invasions always harm the biological conservation of the ecosystem.Optimal vaccine for human papillomavirus and age-difference between partnershttps://zbmath.org/1540.922112024-09-13T18:40:28.020319Z"Madhu, Kalyanasundaram"https://zbmath.org/authors/?q=ai:madhu.kalyanasundaram"Al-arydah, Mo'tassem"https://zbmath.org/authors/?q=ai:al-arydah.motassemSummary: We introduce a two sex age-structured mathematical model to describe the dynamics of HPV disease with childhood and catch up vaccines. We find the basic reproduction number \(( R_0)\) for the model and show that the disease free equilibrium is locally asymptotically stable when \(R_0 \leq 1\). We introduce an optimal control problem and prove that optimal vaccine solution exists and is unique. Using numerical simulation, we show that 77\% childhood vaccination controls HPV disease in a 20 years period, but 77\% catch up vaccine does not. In fact, catch up vaccine has a slight effect on HPV disease when applied alone or with childhood vaccine. We estimate the optimal vaccine needed to control HPV in a 25 year period. We show that reducing the partners between youths and adults is an effective way in reducing the number of HPV cases, the vaccine needed and the cost of HPV. In sum, we show that choosing partners within the same age group is more effective in controlling HPV disease than providing adult catch up vaccination.Optimal control of harvesting effort in a phytoplankton-zooplankton model with infected zooplankton under the influence of toxicityhttps://zbmath.org/1540.922682024-09-13T18:40:28.020319Z"Agnihotri, Kulbhushan"https://zbmath.org/authors/?q=ai:agnihotri.kulbhushan"Kaur, Harpreet"https://zbmath.org/authors/?q=ai:kaur.harpreetSummary: In the present investigation, a prey-predator model consisting of phytoplankton, susceptible zooplankton, and infected zooplankton, incorporating the response function of Holling type II, has been explored. Logistic growth is assumed to be followed by the phytoplankton species. A combined effort \((E)\) is applied to harvest all of the three populations. Environmental toxicity is considered to affect the phytoplankton species directly and the predating zooplankton indirectly. The dynamical behaviour of the model is examined for each of the possible steady states. Hopf-bifurcation analysis has been carried out with the combined harvesting effort \(E\) as the bifurcation parameter. The optimal control is characterized by using Pontryagin's maximum principle. In the end, the analytical discoveries found so far have been established employing numerical simulations.Lyapunov matrices approach to the parametric optimization of a neutral system with two delayshttps://zbmath.org/1540.930312024-09-13T18:40:28.020319Z"Duda, Jozef"https://zbmath.org/authors/?q=ai:duda.jozefSummary: In the paper a Lyapunov matrices approach to the parametric optimization problem of a neutral system with two delays and with a P-controller is presented. The value of integral quadratic performance index of quality is equal to the value of Lyapunov functional for the initial function of the neutral system with two delays. The Lyapunov functional is determined by means of the Lyapunov matrix.