Class Of Problems Research Articles

R-linear and strong convergence of Tseng methods for solving certain split and non-split problems

In the recent past, authors have fondly assumed the co-coercive condition for solving certain class of split inverse problems. Recently, some attempts have been made to relax this very strict condition, however, only few results exists in literature in such case. In this paper, we present some new Mann-type Tseng methods for solving split monotone variational inclusion and common fixed point problems for a finite collection of quasi-pseudocontractive operators. We prove strong convergence and R − linear convergence rate results of our methods, while the co-coerciveness property is dispensed with. Our methods incorporate the relaxation, inertial extrapolation and self-adaptive step size techniques to achieve better performance and faster convergence. With the aid of relevant numerical experiments, we showcase the performance profile of our methods in comparison with recent methods in literature.

Sufficiency of -cyclical monotonicity in a class of multi-marginal optimal transport problems

Sufficiency of -cyclical monotonicity in a class of multi-marginal optimal transport problems

A line search technique for a class of multi-objective optimization problems using subgradient

A line search technique for a class of multi-objective optimization problems using subgradient

Axisymmetric virtual elements for problems of elasticity and plasticity

AbstractThe virtual element method (VEM) allows discretization of elasticity and plasticity problems with polygons in 2D and polyhedrals in 3D. The polygons (and polyhedrals) can have an arbitrary number of sides and can be concave or convex. These features, among others, are attractive for meshing complex geometries. However, to the author's knowledge axisymmetric virtual elements have not appeared before in the literature. Hence, in this work a novel first order consistent axisymmetric VEM is applied to problems of elasticity and plasticity. The VEM specific implementation details and adjustments needed to solve axisymmetric simulations are presented. Representative benchmark problems including pressure vessels and circular plates are illustrated. Examples also show that problems of near incompressibility are solved successfully. Consequently, this research demonstrates that the axisymmetric VEM formulation successfully solves certain classes of solid mechanics problems. The work concludes with a discussion of results for the current formulation and future research directions.

Shape optimization for interface identification in nonlocal models

AbstractShape optimization methods have been proven useful for identifying interfaces in models governed by partial differential equations. Here we consider a class of shape optimization problems constrained by nonlocal equations which involve interface–dependent kernels. We derive a novel shape derivative associated to the nonlocal system model and solve the problem by established numerical techniques. The code for obtaining the results in this paper is published at (https://github.com/schustermatthias/nlshape).

Solving Euclidean Max-Sum problems exactly with cutting planes

This paper studies binary quadratic programs in which the objective is defined by the maximisation of a Euclidean distance matrix, subject to a general polyhedral constraint set. This class of nonconcave maximisation problems, which we refer to as the Euclidean Max-Sum problem, includes the capacitated, generalised and max-sum diversity problems as special cases. Due to the nonconcave objective, traditional cutting plane algorithms are not guaranteed to converge globally. In this paper, we introduce two exact cutting plane algorithms to address this limitation. The new algorithms remove the need for a concave reformulation, which is known to significantly slow down convergence. We establish exactness of the new algorithms by examining the concavity of the quadratic objective in a given direction, a concept we refer to as directional concavity. Numerical results show that the algorithms outperform other exact methods for benchmark diversity problems (capacitated, generalised and max-sum), and can easily solve problems of up to three thousand variables.

Logical Platforms for Mobile Application in Decision Support Systems Based on Color Information Processing

Logical Platforms for Mobile Application in Decision Support Systems Based on Color Information Processing

Existence, sign and asymptotic behaviour for a class of integro-differential elliptic type problems

Existence, sign and asymptotic behaviour for a class of integro-differential elliptic type problems

Existence results for boundary value problems of Hadamard fractional differential equations on unbounded domain

Abstract In this paper we investigate the existence and uniqueness of solutions for a class of boundary value problem for fractional differential equations involving the Hadamard’s fractional derivative, by applying a nonlinear alternative of Leray–Schauder due to Frigon and Granas for contraction maps in Fréchet spaces.

Various duality models associated with some constrained robust nonlinear optimal control problems

This paper deals with various duality results for a new class of constrained robust nonlinear control problems. Concretely, we introduce a minimisation problem associated with a vector of functionals of multiple integral type. In addition, the considered multi-objective controlled optimisation problem is governed by several mixed constraints generated by partial derivatives of second order and uncertain data. For this new class of control problems, we establish and characterise Wolfe, Mond-Weir and mixed type robust dual models. To this aim, by using the notion of convex multiple integral functional, generated by a controlled second-order Lagrangian with uncertain data, and the concept of robust weak efficient solution to the problem under study, we build a new mathematical context to state and prove the duality theorems.

The Global existence and blow-up of solutions for a class of Steklov parabolic problems

In this paper, we study weak solutions to the following Steklov parabolic problem: We prove theorems of existence of weak solutions, via Galerkin approximation. Moreover, we show the existence of solutions which blow up in a finite time.

A solution to the only one object problem with dissolution rules

AbstractIn the framework of membrane computing, (non-)uniform families of recognizer membrane systems are usually defined to solve abstract decision problems. In this sense, the use of finite resources for each member of the family makes the difference with respect to Turing machines solving these problems. While keeping the finite nature of these systems, it is interesting to know which type of problems can be solved by means of a single membrane system. For this purpose, the complexity class $$\textbf{PMC}^{1p}_{\mathcal {R}}$$ PMC R 1 p was defined as the class of problems that can be solved by means of a single membrane system in polynomial time. Due to the polynomial-time encoding of the input, at least all the problems from P can be solved with a trivial system. To go below P, the class $$\textbf{PMC}^{1f}_{\mathcal {R}}$$ PMC R 1 f restricts the definition of this encoding. In this work, we study the capability of different types of membrane systems to solve the problem, while having the encoding restriction.

Informed Adaptive Sensing.

For many inverse problems, the data on which the solution is based is acquired sequentially. We present an approach to the solution of such inverse problems where a sensor can be directed (or otherwise reconfigured on the fly) to acquire a particular measurement. An example problem is magnetic resonance image reconstruction. We use an estimate of mutual information derived from an empirical conditional distribution provided by a generative model to guide our measurement acquisition given measurements acquired so far. The conditionally generated data is a set of samples which are representative of the plausible solutions that satisfy the acquired measurements. We present experiments on toy and real world data sets. We focus on image data but we demonstrate that the method is applicable to a broader class of problems. We also show how a learned model such as a deep neural network can be leveraged to allow generalisation to unseen data. Our informed adaptive sensing method outperforms random sampling, variance based sampling, sparsity based methods, and compressed sensing.

Resources of curriculum materials that induce teachers' professional knowledge of the additive conceptual field

Assuming that curriculum materials reverberate the knowledge of teachers, we sought to identify and discuss features of the materials, related to the additive field, which induce professional knowledge in Mathematics. Through a documentary analysis of three 2nd, 3rd and 4th grade Mathematics Teacher's Manuals, the addition and subtraction problems were mapped and analyzed; the texts presenting the material and the units corresponding to the mapped problems were analyzed, as well as the specific guidelines for working with these problems. Considering the Conceptual Fields Theory and the Knowledge of Knowledge of Curriculum Embedded Mathematics as references, we identified a variety of problem classes, as well as guidelines on the different meanings of operations. We observed weaknesses in the approach taken in the 2nd grade Manual corresponding to the addition and subtraction approach, to the detriment of the other Manuals. We noted the absence of explicitly stated information in the three manuals, which may have an impact on the way teachers read and interpret the guidelines, and evaluate the problems, implying the teaching knowledge mobilized or constructed.

Characterization of the solution set of nonsmooth semi-infinite programming problems on Hadamard manifolds

This article is concerned with a class of nonsmooth semi-infinite programming problems on Hadamard manifolds (abbreviated as, (NSIP)). We introduce the Guignard constraint qualification (abbreviated as, (GCQ)) for (NSIP). Subsequently, by employing (GCQ), we establish the Karush-Kuhn-Tucker (abbreviated as, KKT) type necessary optimality conditions for (NSIP). Further, we derive that the Lagrangian function associated with a fixed Lagrange multiplier, corresponding to a known solution, remains constant on the solution set of (NSIP) under geodesic pseudoconvexity assumptions. Moreover, we derive certain characterizations of the solution set of the considered problem (NSIP) in the framework of Hadamard manifolds. We provide illustrative examples that highlight the importance of our established results. To the best of our knowledge, characterizations of the solution set of (NSIP) using Clarke subdifferentials on Hadamard manifolds have not been investigated before.

Input Regularization for Integer Optimal Control in BV with Applications to Control of Poroelastic and Poroviscoelastic Systems

We revisit a class of integer optimal control problems for which a trust-region method has been proposed and analyzed in arXiv:2106.13453v3 [math.OC]. While the algorithm proposed in arXiv:2106.13453v3 [math.OC] successfully solves the class of optimization problems under consideration, its convergence analysis requires restrictive regularity assumptions. There are many examples of integer optimal control problems involving partial differential equations where these regularity assumptions are not satisfied. In this article we provide a way to bypass the restrictive regularity assumptions by introducing an additional partial regularization of the control inputs by means of mollification and proving a $\Gamma$-convergence-type result when the support parameter of the mollification is driven to zero. We highlight the applicability of this theory in the case of fluid flows through deformable porous media equations that arise in biomechanics. We show that the regularity assumptions are violated in the case of poro-visco-elastic systems, and thus one needs to use the regularization of the control input introduced in this article. Associated numerical results show that while the homotopy can help to find better objective values and points of lower instationarity, the practical performance of the algorithm without the input regularization may be on par with the homotopy.

Existence and regularity results for a class of singular parabolic problems with L1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^1$$\\end{document} data

In this paper we prove existence and regularity results for a class of parabolic problems with irregular initial data and lower order terms singular with respect to the solution. We prove that, even if the initial datum is not bounded but only in L1(Ω)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^1(\\Omega )$$\\end{document}, there exists a solution that “instantly” becomes bounded. Moreover we study the behavior in time of these solutions showing that this class of problems admits global solutions which all have the same behavior in time independently of the size of the initial data.

Existence and multiplicity of nontrivial solutions to a class of elliptic Kirchhoff-Boussinesq type problems

Existence and multiplicity of nontrivial solutions to a class of elliptic Kirchhoff-Boussinesq type problems

Uniqueness of solutions to some classes of anisotropic and isotropic curvature problems

In this paper, we apply various methods to establish the uniqueness of solutions to some classes of anisotropic and isotropic curvature problems. Firstly, by employing integral formulas derived by S. S. Chern [20], we obtain the uniqueness of smooth admissible solutions to a class of Orlicz-(Christoffel)-Minkowski problems. Secondly, inspired by Simon's uniqueness result [61], we then prove that the only smooth strictly convex solution to the following isotropic curvature problem(0.1)(Pk(W)Pl(W))1k−l=ψ(u,r)onSn must be an origin-centred sphere, where W=(∇2u+ug0), ∂1ψ≥0,∂2ψ≥0 and at least one of these inequalities is strict. As an application, we establish the uniqueness of solutions to the isotropic Gaussian-Minkowski problem. Finally, we derive the uniqueness result for the following isotropic Lp dual Minkowski problem(0.2)u1−prq−n−1det⁡(W)=1onSn, where −n−1<p≤−1 and n+1≤q≤n+12+14−(1+p)(n+1+p)n(n+2). This result utilizes the method developed by Ivaki and Milman [42] and generalizes a result due to Brendle, Choi and Daskalopoulos [10].

STUDY OF MULTI-STAGE SOFTWARE DEPLOYMENT STRATEGYWITH THE EXCLUSION OF SIDE EFFECTS

The article addresses a problem and its solution that arose during onboarding of new subscribers to the existing data import and distribution service. The analysis of all available solutions demonstrates that none fully meet the requirements. The process of searching for the values of the required indicators and the process of creating reports necessarily uses indexes. Messages of different types are placed in their respective MongoDB collections. Over the long period of operation of the repository, up to 64 indexes per collection have accumulated. According to the policies of connecting to the storage (Connect timeout) and waiting for a response (Socket timeout), the need to set such long-time expectations for consumers is unacceptable and usually, by default, is equal to 30 seconds. A multi-step strategy for delivering the solution that allows the service to meet availability requirements was proposed. The novelty of the article is in the description and investigation of a new method of delivering solutions to the software deployment environment—production. The implementation of the described strategy opens a new approach for solving similar classes of problems related to the type of interaction with users, when custom settings are a mandatory part of the service and are guaranteed to carry the threat of service unavailability. This approach opens up new opportunities for achieving high availability of systems, reducing risks and increasing user satisfaction. Based on the analysis of the proposed approaches, the latest strategy of multi-step delivery of the service to users was developed, the result of which was the acceptable response waiting time of up to 5 seconds. The implementation of this strategy contributed to the achievement of the availability of software products - 99.999%, ensuring the reliability and stability of services for end users.