Journal of Optimization, Differential Equations and their Applications (JODEA - Dnipro National Universuty) / Журнал з оптимізації, диференціальних рівнянь та їх застосувань
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On Anisotropic Variational Model for SAR Image Despeckling
Get PDFMostly motivated by practical applications especially in the field of satellite remote sensing of agricultural territories, we develop a novel approach to SAR image despeckling based on minimization of a special anisotropic energy functional. We propose a new statement of this problem in the weighted Sobolev spaces, provide a rigorous mathematical analysis of the proposed optimization problem, establish sufficient conditions of its solvability, show that the objective functional is Gateaux differentiable, and derive the corresponding optimality conditions. To illustrate the validity of the obtained results, we give some examples of numerical simulations with real satellite SAR image
Method of Feasible Directions with Hit-and-Run Sampling for Solving Linearly Constrained Multi-Objective Optimization Problems
Get PDFThis paper proposes an extension of Zoutendijk’s Method of Feasible Directions (MFD) for solving linearly constrained multi-objective optimization problems. The approach integrates a Hit-and-Run sampling technique to generate a diverse set of feasible points and uses an iterative two-step process. This process involves determining an improving feasible direction by solving a quadratic subproblem and adjusting the step size using the multi-objective Armijo rule. As a result, the method generates a sequence of feasible points that converge to a critical Pareto point, and under convexity assumptions, to a Pareto-optimal point. The process is applied to all points in the generated population, enabling an adequate approximation of the Pareto front. The convergence of the method is proven. A comparative study, conducted in MATLAB on 25 linearly constrained multi-objective optimization benchmark problems, evaluates our MFD against the NSGA-II algorithm and another variant of MFD that uses a different direction search subproblem and sampling procedure. The quality of the approximated Pareto front is assessed using four metrics: purity, spacing, hypervolume, and generalized spread. The results show that our MFD outperforms the other methods in terms of both convergence speed and the quality of the Pareto front for the tested problem
Variational Analysis of Non-Coercive Optimization Problems in Anisotropic Sobolev Spaces
Get PDFIn this paper we develop a novel approach to the analysis and study of one class optimization problems with non-coercive objective functionals. With this in mind we introduce a special class fo anisotropic functional spaces. We give a precise definition of such spaces and show that they can be considered as a natural generalization of the standard Sobolev spaces. Bases on this concept, we relax of a special class of non-coercive minimization problems in Sobolev spaces W1,2(Ω), provide a rigorous mathematical analysis of the proposed relaxed version, establish sufficient conditions of its solvability, show that the objective functional is coercive, and derive the corresponding optimality conditions. To demonstrate the validity of the obtained results, we apply the proposed approach to the relaxation of the well-know variational model for removing multiplicative noise in image processing
The Cauchy Problem for One Class of Parabolic Pseudodifferential Equation with Deviation of the Argument
Get PDFIn this paper, we study solvability of the Cauchy problem for a parabolic pseudodifferential equation with the deviation of the argument. Parabolic pseudodifferential operator with non-smooth symbols introduced by Eidel’man and Drin’ for the first time. For such equations, the initial condition is set on a certain interval. Technical and physical reasons for delays can be transport delays, delays in decision-making, delays in information transmission, etc. The most natural are delays when modeling objects in medicine, population dynamics, ecology, etc. Other physical and technical interpretations are also possible, for example, the molecular distribution of thermal energy in various media (liquids, solid bodies, etc.) is modeled by heat conduction equations. Features of the dynamics of vehicles in different environments (water, land, air) can also be taken into account by introducing a delay. The formula for the solution of the Cauchy problem is constructed for the nonlinear equation of heat conduction with a deviation of the argument, its properties are investigated
Accelerated Hybrid Subgradient Extragradient Methods for Solving Bilevel Split Quasimonotone Variational Inequality Problems
Get PDFIn this paper, we introduce and study a modified inertial subgradient extragradient iterative algorithm for solving bilevel split quasimonotone variational inequality problems with a fixed point constraint of demimetric mappings in the framework of real Hilbert spaces. The method involves a strongly monotone operator at the upper-level problem and quasimonotone mapping at the lower level. We obtain a strong convergence result of the proposed method under some mild conditions on the algorithm parameters without the prior knowledge of the operator norm or the coefficient of the underlying operator in the scope of infinite dimensional real Hilbert spaces. Finally, some numerical demonstrations are given to illustrate the gains of this method. Our results generalize and improve some well-known results in the literature
An Extension of the Reflected Waves Method to the IBVP for the 1D Non-Homogeneous Wave Equation
Get PDFThe method of reflected waves was extended to the finite vibrating string, subject to concentrated (at both its ends) and distributed (along its length) forces. To this end, the periodic odd continuation along the infinite space-time strip was implemented to all functions, influencing the above vibrations: 1) the initial, 2) the boundary (converted into the double layers) and 3) the right-hand side of the 1D non-homogeneous wave equation, resulting to a weak formulation of the IBVP, instead of the original strong one. The weak solution to the IBVP as the sum of regular and singular distributions was obtained by convolving the fundamental solution of the 1D wave operator and the above continued functions, similarly to obtaining the weak solution to the Cauchy problem for the 1D non-homogeneous wave equation. The weak solution to the IBVP was shown can be transformed (through some intermediate representations) into the well known strong one, obtained by the method of separation of variables. The opposite is also true, that is the strong solution to the IBVP can be transformed into a representation of the weak one by two successive integrations by parts, provided that the convergence of some Fourier series is interpreted in the weak sense (as distributions)
Zero-Hopf Bifurcation in Two Classes of Autonomous and Non-Autonomous Third-Order Gerk Differential Equations
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
Identification of the Coordinates of Impulse Pollution Sources in Anisotropic Environments using Numerical Quasiconformal Mapping Methods
Get PDFA combined approach to identifying the coordinates of point impulse sources, using observation data at certain time intervals at characteristic points, has been transferred to the case of anisotropy. The corresponding mathematical model is constructed based on the assumption that the movement of particles in the domain is quasiideal and satisfies the generalization of Darcy’s law; at the same time, the diffusion component of the movement of pollutants is neglected. The initial problem is divided into two smaller ones: it is assumed to construct a hydrodynamic mesh and, based on this, to identify the coordinates of pollution sources. In the first case, numerical methods of quasiconformal mappings are applied. In the second case, based on the use of the method of characteristics with respect to the convection equation, an integral equation is constructed. Numerical experiments were conducted, confirming the effectiveness of the previously developed approach in the case of anisotropy. The most significant residuals between the a priori known and calculated coordinates of pollution sources occur on those streamlines that pass near stagnant zones and intersect areas in the vicinity of so-called “key” points (critical points of quasiconformal mapping violation) at the boundary of the domain. In certain cases of filtration tensor distribution, this can have a significant negative impact on the accuracy of the solution
A New and Efficient Interior Point Method Based on a Weight Vector for Solving LCCO Problems
Get PDFIn this paper, we propose a new full-Newton step weighted interior point method for solving linearly constrained convex optimization problems (LCCO). This method is based on relaxing the complementarity condition using a non-negative variable weight vector to overcome the difficulty of finding an initial point in the neighborhood of central path required to start the classical interior point algorithms. With a zero of variable weight vector, the limit of the weighted path exists and satisfies the complementarity condition, this limit yields an optimal solution of LCCO problem. The advantage of this method is the use of a full-Newton step, which eliminates the step-size calculations with a quadratic rate of convergence. We study the complexity analysis of our method and derive a new iteration bound for small-update methods. Finally, some comparative numerical tests are stated to validate the effectiveness of our new method
Long-Term Dynamics of a Stochastic SIRV Model for TB with Random Disturbances
Get PDFWe investigate the long-term behavior of an epidemic using a stochastic SIRV (Susceptible-Infectious-Recovered-Vaccinated) model that incorporates time dependent parameters and random perturbations. The model is motivated by tuberculosis (TB) transmission dynamics and includes vaccination of newborns as a key intervention strategy. Random environmental fluctuations are modeled via Wiener processes, and the systems stochastic stability is analyzed. We derive conditions for the existence of a unique global solution and examine the extinction and persistence of the disease under stochastic influences. Numerical simulations are provided to illustrate the theoretical results and to explore the impact of parameter variability and noise intensity on the epidemic’s evolution. This work contributes to the understanding of how random disturbances affect long-term epidemic dynamics and can inform public health strategies under uncertainty. This project has received funding through the MSCA4Ukraine project (AvH ID:1233636), which is funded by the European Union