Inclusion Problem Research Articles

New possibilities or problems for disability and inclusion? The case of AI and ADMs across work

In this paper, we examine new and emerging uses of artificial intelligence (AI) and automated decision making (ADM) across various aspects of work, namely hiring, job redesign, and team formation, and their impact on disabled people. Building on disability as both a generative form of embodiment and knowledge, we consider how AI and ADMs can enable and empower disabled people for work, but also their inherent problems and contradictions. We ask the following questions: What are the implications for disabled workers? And importantly, how can we make these systems fairer and more inclusive, especially for disability?

Non-degenerate necessary conditions for non-convex differential inclusions

This paper concerns dynamic optimization problems with pathwise state constraints, in which the dynamics are formulated as a differential inclusion. First order necessary conditions of optimality are available for these problems. Foremost among these conditions is the Euler Lagrange inclusion (combined with a transversality and Weierstrass conditions), which improves on earlier conditions such as Clarke's Hamiltonian inclusion. The most recent version of the Euler Lagrange inclusion (which we call the standard Euler Lagrange condition) has been validated under unrestrictive conditions, which allow the velocity sets of the differential inclusion to be non-convex. If the initial state is fixed and located in the boundary of the state constraint set then the Euler Lagrange inclusion conveys no information about minimizers. This is the degeneracy phenomenon for state constrained dynamic optimization. The non-degenerate necessary conditions literature provides additional conditions, to supplement the standard necessary conditions. These typically identify some properties of the boundary values of the maximized Hamiltonian which ensure non-triviality of the necessary conditions, under a simple controllability hypothesis. Non-degenerate conditions, incorporating the Euler Lagrange inclusion are currently available only under the hypothesis that the velocity sets are convex. Using new perturbation techniques, we derive a non-degenerate Euler Lagrange condition that is valid for non-convex velocity sets. These conditions bring into line non-degenerate optimality conditions for differential inclusion problems with those for problems involving controlled differential equations which have previously been validated for non-convex velocity sets.

ІNCLUSION IN HIGHER EDUCATION: PHILOSOPHICAL AND SOCIAL CONTEXT

The article analyses the problem of implementing inclusion in higher education in various developed countries. The author reviews the main international declarative and legal documents that form the basis for the implementation of the principles of inclusion in society in general and in the educational sector in particular. The author traces the connection between changes in public consciousness and activities of higher education institutions in the respective countries with regard to the adoption of the principles of equality and inclusion. It has been found that the implementation of the principles of inclusion in higher education is possible in societies with a high level of community well-being, as evidenced by the higher education systems of highly developed countries that are at the forefront of promoting inclusive university education. That is, inclusive practice in higher education, which is not a compulsory educational level, is developing thanks to social activism and support from government institutions. In fact, the task of the university is to provide a favourable inclusive educational space for a student with special needs. The author draws attention to the fact that promoting an inclusive form of education in a higher education institution should not impair the quality of educational services and limit the level of professional competencies acquired by a person with special needs. The author identifies the key problem of inclusion in higher education - achieving stability in its provision. The author believes that this stability can be achieved through the implementation of the following steps: equal admission of an applicant with special needs; effective training in an inclusive educational space with the acquisition of a full set of professional competencies and the ability to implement the acquired professional elements in professional activities. In the author's opinion, the current progress on the part of Ukrainian society has received a peculiar vector sequence: formation of an understanding of the demand for higher education for people with special needs; search for effective and efficient inclusive formats for organising the educational process in a higher education institution; creation of a unified and universal system of inclusive higher education, which will be integrated into the local educational strategies of a particular higher education institution. This algorithm harmonises the aspirations and wishes of a person with special needs and the capabilities and transformations of the university.

Fixed-Point Approaches for Multi-Valued Contraction Mappings in a Novel Space With an Application

The vital goals of this manuscript are to combine metric-like spaces with S-metric spaces under a control function to obtain a new space called the controlled S-metric-like spaces (CSMLSs, for short). Under this name, many fixed-point (FP) results have been obtained for multi-valued mappings (MVMs). In addition, we present several non-trivial examples to back up our statements. The results obtained generalize and unify many results in the same direction. Finally, to support and test the adequacy of the theoretical results, the existence of the solution to the differential inclusion problem (DIP) was studied as a type of application.

Generalized viscosity method for approximating solutions of countable families of certain nonlinear mappings in real Hilbert space

The purpose of this paper is to introduce a three step iterative algorithm which include a general viscosity explicit method for approximating a common solution of fixed point problem of an infinite family of k_i-demimetric mapping and a directed operator in the framework of real Hilbert space. Furthermore, we prove a strong convergence theorem for approximating a common solution of the aforementioned problems. We also show that our iterative algorithm holds for an infinite family of L-Lipschitzian and quasi-pseudocontractive mapping together with a directed operator. The iterative algorithm presented in this article is design in such a way that it solves some variational inequality problem and no compactness condition is impose on our scheme and mapping. Finally, we give applications of our main result to variational inclusion and equilibrium problems. Our result complements and extends some related result in literature.

Fixed point theorem for composition of multivalued and single-valued mappings in Banach spaces

n this paper, we present a new characterization for finding a solution of common fixed points problem involving multivalued and single-valued mappings in Banach spaces by applying the properties of composition without commuting assumption. We equally obtain a convergence result to a solution of system of inclusion problems in Banach spaces. Our results unify, generalize and complement various known comparable results from the current literatur

Errata of solution of differential inclusion problem in controlled S-metric spaces via new multivalued fixed point theorem

Errata of solution of differential inclusion problem in controlled S-metric spaces via new multivalued fixed point theorem

Strong convergence of a viscosity proximal point algorithm with new error sequences

In the paper, we consider a viscosity proximal point algorithm with over-relaxed factor for solving inclusion problem in the setting of Hilbert space. Moreover, we establish its strong convergences under two different error criteria, which generalize some existing conclusions.

New fast proximal point algorithms for monotone inclusion problems with applications to image recovery

The proximal point algorithm has many applications for convex optimization with several versions of the proximal point algorithm including generalized proximal point algorithms and accelerated proximal point algorithms that have been studied in the literature. In this paper, we propose accelerated versions of generalized proximal point algorithms to find a zero of a maximal monotone operator in Hilbert spaces. We give both weak and linear convergence results of our proposed algorithms under standard conditions. Numerical applications of our results to image recovery are given and numerical implementations show that our algorithms are effective and superior to other related accelerated proximal point algorithms in the literature.

On controllability for Sobolev-type fuzzy Hilfer fractional integro-differential inclusions with Clarke subdifferential

In this paper, our main purpose is to search and obtain the controllability for Sobolev-type fuzzy Hilfer fractional integro-differential inclusions with Clarke subdifferential. Some sufficient conditions for the controllability results of this inclusion problem are proposed by using related techniques of fuzzy set theory, Sobolev-type, fractional calculus and Clarke subdifferential. The theorem of the controllability results is proved by Bohnenblust–Karlin fixed point theorem. In addition, we show an example to explain the controllability results of this inclusion problem.

Modified proximal gradient methods involving double inertial extrapolations for monotone inclusion

In this work, we propose a novel class of forward‐backward‐forward algorithms for solving monotone inclusion problems. Our approach incorporates a self‐adaptive technique to eliminate the need for explicitly selecting Lipschitz assumptions and utilizes two‐step inertial extrapolations to enhance the convergence rate of the algorithm. We establish a weak convergence theorem under mild assumptions. Furthermore, we conduct numerical tests on image deblurring and data classification as practical applications. The experimental results demonstrate that our algorithm surpasses some existing methods in the literature which shows its superior performance and effectiveness.

Inertial iterative algorithms for common solution of variational inequality and system of variational inclusion problems

Inertial iterative algorithms for common solution of variational inequality and system of variational inclusion problems

Relaxed Inertial Projective Forward-backward Splitting Algorithms for Regularized Least Square Problems

This study presents flexible conditions of the inertial extrapolation parameter for easy implementation that is added to the algorithm in faster convergence. Modified inertial forward-backward splitting algorithms for solving variational inclusion problems are introduced to apply to solve the LASSO problem for image restoration and signal recovery, and the elastic net model for classification problem. Projection methods are used in the final step for narrowing down the search field, resulting in a better solution.

A micromechanical view of enhanced reversibility in shape memory alloys

Transformation-induced plasticity (TIP) is the source of poor reversibility and functional fatigue in shape memory alloys (SMA)s undergoing martensitic phase transformation. The TIP is believed to originate from the defect generation at the highly-stressed austenite/martensite transition layer. It is suggested that under satisfaction of compatibility criteria (also known as cofactor conditions) the highly-stressed transition layer is removed and the phase transformation reversibility is highly enhanced. In this study, we employ the inclusion problem of micromechanics along with crystallographic theory of martensite to quantify the generated internal stresses associated with the nucleation of martensite in a wide range of SMAs. The micromechanical calculations show that the nucleation of martensite in SMAs with high degree of compatibility and enhanced reversibility generates much reduced internal stresses. For example, the maximum shear stress generated by nucleation of twinned martensite in Ni50.3Ti29.7Zr20 is ∼ 5 GPa, which is reduced to ∼ 400 MPa (about an order of magnitude reduction) in single-variant martensite of Ni39Ti50Pd11 with excellent reversibility and low functional fatigue. It is also shown that the internal stresses are much lower in a supercompatible twinned martensite microstructure (Cu25Au30Zn45) compared with a conventional twinned microstructure such as those formed in NiTi-based alloys. Analysis of the deformation state of the matrix shows that the underlying mechanism behind the reduced internal stresses is the reduction in the maximum shear strain ((λ3 - λ1)/2) imposed by the nucleation of martensite. The results present a quantified picture of internal (interfacial) stresses in different SMAs to better understand the origin of reversibility and functional fatigue.

On the Bregman-proximal iterative algorithm for the monotone inclusion problem in Banach spaces

In this paper, we focus on the solution of a class of monotone inclusion problems in reflexive Banach spaces. To reflect the geometry of the space and the operator, a more general proximal point iterative algorithm with Bregman divergence is proposed and some strong convergence results for the proposed scheme under standard assumptions are obtained. Meanwhile, the convex optimization problems and the critical point problems are studied in the applications, and the recovery of the sparse signal is simulated in the numerical experiments.

Splitting algorithms for solving state-dependent maximal monotone inclusion problems

We consider the state-dependent maximal monotone inclusion problem and propose forward-backward splitting algorithms for solving it. Strong convergence of the proposed algorithms is established under suitable conditions. For the special separable case, we present an improved Douglas–Rachford variant that can be easily implemented. Moreover, some accelerated forward-backward splitting algorithms are also presented. Preliminary numerical experiments with comparisons to existing results are presented, illustrating the advantages of our methods.

Solvability of a Class of Generalized System of Variational Inclusion Problems Involving \(\oplus\) Operation

Solvability of a Class of Generalized System of Variational Inclusion Problems Involving \(\oplus\) Operation

Relaxed Inertial Method for Solving Split Monotone Variational Inclusion Problem with Multiple Output Sets Without Co-coerciveness and Lipschitz Continuity

Relaxed Inertial Method for Solving Split Monotone Variational Inclusion Problem with Multiple Output Sets Without Co-coerciveness and Lipschitz Continuity

A second order dynamical system method for solving a maximally comonotone inclusion problem

In this paper a second order dynamical system model is proposed for computing a zero of a maximally comonotone operator in a Hilbert space. Under mild conditions, we prove existence and uniqueness of a strong global solution of the proposed dynamical system. A proper tuning of the parameters can allow us to establish fast convergence properties of the trajectories generated by the dynamical system. The weak convergence of the trajectory to a zero of the maximally comonotone operator is also proved. Furthermore, a discrete version of the dynamical system is considered and convergence properties matching to that of the dynamical system are established under a same framework. Finally, the validity of the proposed dynamical system and its discrete version is demonstrated by two numerical examples.

A Relaxed Inertial Method for Solving Monotone Inclusion Problems with Applications

We study a relaxed inertial forward–backward–half-forward splitting approach with variable step size to solve a monotone inclusion problem involving a maximal monotone operator, a cocoercive operator, and a monotone Lipschitz operator. The convergence of the sequence of iterations generated by the discretisations of a continuous-time dynamical system is established under suitable conditions. Given the challenges associated with computing the resolvent of the composite operator, the proposed method is employed to tackle the composite monotone inclusion problem. Additionally, a convergence analysis is conducted under certain conditions. To demonstrate the effectiveness of the algorithm, numerical experiments are performed on the image deblurring problem.