Inclusion Problem Research Articles

A projective double inertial forward-backward splitting algorithm for variational inclusion problems application to data classification

A projective double inertial forward-backward splitting algorithm for variational inclusion problems application to data classification

Strong convergence for split variational inclusion problems under hybrid algorithms with applications

In this article, we present two inertial modifications of regularized algorithms for the split variational inclusion problem (SVIP, for short) in real Hilbert spaces (RHSs). When the circumstances are right, strong convergence theorems are demonstrated. The major findings are used to solve the split minimization, split common fixed point problem (SCFPP), split minimization problem (SMP), and split feasibility problems (SFP) in applications. The proposed algorithms are contrasted with a number of other existing algorithms in the literature in order to test their numerical performances. Finally, the computer tests demonstrate that the suggested algorithms outperform alternative strategies in terms of speed and efficiency.

Energy release rate for steady-state fiber debonding in structural battery composites

Structural battery composites are multifunctional materials intended to provide energy storage capacity while maintaining their strength and load bearing capacity under significant mechanical loads. In this study, we investigate the mechanics of carbon fiber debonding, a critical failure mechanism in structural battery composites. The carbon fibers are intended to serve both as an electrochemically active material and to bear mechanical load in the composite system. We derive an analytical solution to the energy release rate for steady-state fiber debonding for different electrochemical and mechanical loading cases with the aid of the classical solution for the Eshelby inclusion problem. The analytical solutions are validated with finite element simulations. We find a higher energy release rate and thus a greater driving force for fiber debonding is caused either by a lower lithium concentration in the fiber and/or by greater transverse mechanical loads such as biaxial tension or shear applied at the far field in the matrix. We find that the model is predictive even for transversely isotropic fibers despite the assumption that the fiber is elastically isotropic in the model. This work can provide guidance for the design of mechanically robust structural batteries.

CONVERGENCE ANALYSIS FOR APPROXIMATING SOLUTION OF VARIATIONAL INCLUSION PROBLEM

This article aims to define a new resolvent operator for variational inclusion problems in the framework of Banach spaces. We design a rapid algorithm using the resolvent operator to approximate the solution of the variational inclusion problem in Banach spaces. Additionally, we show that the algorithm articulated in this article converges faster than the well-known and notable algorithm due to Fang and Huang. To show the superiority and prevalence of the obtained results, we propound a numerical and computational example upholding our claim. Lastly, a minimization problem is solved with the help of the proposed algorithm, which is the first attempt in the current context of the study.

A new self-adaptive method for solving resolvent of sum of two monotone operators in Banach spaces

We introduce a Tseng extragradient method for solving monotone inclusion problem in Banach space. A strong convergence result of an Halpern inertial extrapolation method for solving the resolvent of sum of two monotone operators without the knowledge of the Lipschitz constant was established. Lastly, we illustrate some numerical behavior of our iterative scheme to showcase the performance of the proposed method compared to other related results in the literature.

Two regularized inertial Tseng methods for solving inclusion problems with applications to convex bilevel programming

Combining the inertial technique, regularization, and the Tseng method for approximating a zero of the sum of monotone operators in a real Hilbert space, we propose two regularized inertial Tseng methods for approximating a zero of the sum of two maximal monotone operators in the case where one of them is monotone and Lipschitz continuous. We establish strong convergence of the sequences generated by our algorithms and derive several interesting consequences of our results. We then apply our results to solving convex bilevel programming problems and illustrate the cost efficiency of our methods by numerically comparing them with other methods in the literature.

Dynamic stepsize iteration process for solving split common fixed point problems with applications

In this paper, we study the split common fixed point problem for two nonlinear mappings in p-uniformly convex and uniformly smooth Banach spaces. We propose an algorithm which uses dynamic stepsize, it allows to be easily implemented without prior information about operator norm. We further apply our result to solve the split variational inclusion problem, equilibrium problem and convexly constrained linear inverse problem. Moreover, we provide numerical examples to verify efficiency of our algorithm.

Mathematical micro–macro modeling of fully coupled nonlinear magneto-elastic reinforced composites

In this paper, integral equation formulations and field-dependent micromechanical modeling of global nonlinear magneto-mechanical behavior of magneto-elastic composites under high strain and magnetic field are elaborated. The modeling is obtained based on an extension of micro–macro transition inclusion problem to nonlinear behavior using field-dependent and highly nonlinear localization tensors. A methodological procedure is elaborated based on newly introduced strain and magnetic field-dependent Green tensors, strain and magnetic field-dependent integral equations linked to tensors of Eshelby and micromechanical approaches. The field-dependent global moduli are predicted based on the Mori–Tanaka approach and self-consistent method. Iterative incremental schemes based on the Newton–Raphson and fixed-point algorithms are examined and established precise semi-analytic equations of the effective magneto-elastic properties of composites that are dependent on the magnetic-strain field for different types of inclusions. A numerical code is elaborated for numerical predictions and the obtained field-dependent effective magneto-elastic coefficients are obtained and presented for various volume fractions of inclusion, types and shapes of the reinforced nonlinear composites.

Incorporating history and deviations in forward–backward splitting

We propose a variation of the forward–backward splitting method for solving structured monotone inclusions. Our method integrates past iterates and two deviation vectors into the update equations. These deviation vectors bring flexibility to the algorithm and can be chosen arbitrarily as long as they together satisfy a norm condition. We present special cases where the deviation vectors, selected as predetermined linear combinations of previous iterates, always meet the norm condition. Notably, we introduce an algorithm employing a scalar parameter to interpolate between the conventional forward–backward splitting scheme and an accelerated O1n2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {O}\\left( \\frac{1}{n^2}\\right) $$\\end{document}-convergent forward–backward method that encompasses both the accelerated proximal point method and the Halpern iteration as special cases. The existing methods correspond to the two extremes of the allowed scalar parameter range. By choosing the interpolation scalar near the midpoint of the permissible range, our algorithm significantly outperforms these previously known methods when addressing a basic monotone inclusion problem stemming from minimax optimization.

The Problems of Lexicography of Arabic, Persian Words with New Meanings

It is known that semantic changes occur in the lexical layer of any language over time. Some lexical units become obsolete and fall out of common use, while some lexical units acquire a new meaning and enrich the vocabulary. In connection with the transition to the new Latin alphabet, changes and additions are being made to the base of the Kazakh literary language, including the borrowed Arabic and Persian words due to the expansion and narrowing of its semantic field. Because nowadays, due to the development of various branches of science (economy, Information System, culture and art, religion, pedagogy and psychology, natural science, law, radio communication, chemistry, biology, etc.), some Arabic and Persian words have undergone semantic changes and are being revived. In these areas, they have acquired a new terminological meaning. It is easy to see that such words are used by native speakers in the mass media and social networks in a new meaning. In this regard, the mentioned article deals with the issue of lexicography of Arabic and Persian words, which have acquired a new meaning. The composition of Arabic and Persian words included in the vocabulary of the dictionary is analyzed (Arabic, Persian words of national, regional use; old book words; religious words), the problem of inclusion in the dictionary entry, the problem of narrowing, expanding the semantic field, lexical units created by affixation are discussed. At the same time, the experience of the Turkic peoples, who moved to the Latin alphabet earlier than us, is taken into account. When analyzing the meaning of a word, the semantic field of a word, we are guided by comparative, cumulative methods. The lexicographical criteria for inclusion of input Arabic and Persian words in the dictionary are proposed.

A new projection algorithm for variational inclusion problems and its application to cervical cancer disease prediction

This study proposes a new projection algorithm for solving variational inclusion problems that exhibit weak convergence under suitable conditions in Hilbert space. Furthermore, we apply our algorithm to solve data classification using the cervical cancer behavior risk dataset. The comparison is done in terms of accuracy, precision, recall, and F1-score with other literature. Our proposed algorithm has proved to be more performant than other benchmark techniques for solving regularized least squares problems with different norms.

Some well-posedness equivalent results for a generalized split variational-hemivariational inequality

In this paper, we introduce a generalized split variational-hemivariational inequality in Banach space and are devoted to discussing the equivalence of this inequality with its derived inclusion problem and associated problem. Under very mild assumptions, we prove that the three problems contain the same solution. Moreover, we also show the equivalence of the strong and weak well-posedness of these problems. Finally, we give some equivalent conditions for the strong and weak well-posedness.

Социальное самочувствие и социально-психологическая безопасность студентов с инвалидностью в мегаполисе

Currently the study of the problems of people with special needs is seen in an interdisciplinary field, where medicine and physiology come into contact with urban, socio-cultural aspects of life, allowing to expand the range of problems of social inclusion and disability and consider them from a new research perspective. The purpose of the research is to study the social well-being of persons with special needs in the context of the inclusiveness into urban space. The article presents the results of the research, conducted in 2022 at inclusive higher education institution in Moscow. The research was based on the focus group method using the sample group of students with special needs (N = 40) of the musculoskeletal system who came from Russian medium and small size towns to Moscow. The research methodology was built on the interdisciplinary approach to disability in the context of urban studies. The study made it possible to identify the levels of social well-being of students with special needs (high, medium and low) and correlate them with the degree of their socio-psychological security (maximum, moderate and minimum). It has been empirically proven that Russian towns, depending on the number of inhabitants (megacities, large, medium and small) have a significant impact on the social well-being and socio-psychological safety of students with special needs, which is due, firstly, to varying degrees of space inclusiveness; secondly, the different attitudes of citizens towards young people with special needs (positive, neutral, negative). According to the subjective assessments of the majority of focus group participants, after moving to the capital in order to receive vocational education, their level of social well-being and the degree of socio-psychological safety increased due to a more comfortable and adapted urban environment for the needs of people with special needs, as well as a more friendly attitude of residents to young disabled people with ODA compared with small and medium-sized towns.

A new kind of double phase elliptic inclusions with logarithmic perturbation terms I: Existence and extremality results

This paper is devoted to introduce a new double phase elliptic inclusion problem (DPEI) involving nonlinear and nonhomogeneous partial differential operator which has unbalanced growth and logarithmic perturbation terms, and two multivalued functions which are defined in the domain and its boundary. The main goal of this paper is to establish the existence and extremality results to the elliptic inclusion problem under consideration. More exactly, we give the definitions of weak solutions, subsolutions and supersolutions to (DPEI). Then, under the coercive setting, an existence theorem of weak solutions to (DPEI) is obtained by employing a surjectivity theorem for pseudomonotone operators. Moreover, in the noncoercive framework, we apply the method of sub-supersolution combined with the nonsmooth calculus analysis and truncation techniques to prove that (DPEI) has at least a weak solution within an ordered interval of sub-supersolution. Finally, when the constraint set K satisfies a lattice condition, the existence of smallest and greatest elements of solution set to (DPEI) is established.

On Bilevel Monotone Inclusion and Variational Inequality Problems

In this article, the problem of solving a strongly monotone variational inequality problem over the solution set of a monotone inclusion problem in the setting of real Hilbert spaces is considered. To solve this problem, two methods, which are improvements and modifications of the Tseng splitting method, and projection and contraction methods, are presented. These methods are equipped with inertial terms to improve their speed of convergence. The strong convergence results of the suggested methods are proved under some standard assumptions on the control parameters. Also, strong convergence results are achieved without prior knowledge of the operator norm. Finally, the main results of this research are applied to solve bilevel variational inequality problems, convex minimization problems, and image recovery problems. Some numerical experiments to show the efficiency of our methods are conducted.

Optimal control problem of fractional evolution inclusions with Clarke subdifferential driven by quasi-hemivariational inequalities

In this paper, we introduce and study an optimal control problem for a new class of fractional differential quasi-hemivariational inequalities with nonlocal initial conditions and Clarke subdifferentials. The main tools in our study are the theory of fractional calculus, the fixed point argument for condensing multimaps and Balder’s theorem. We prove the solvability of abstract nonlocal fractional differential quasi-hemivariational inequalities and then show the existence of solutions to the associated optimal control problems.

A Regularized Tseng Method for Solving Various Variational Inclusion Problems and Its Application to a Statistical Learning Model

We study three classes of variational inclusion problems in the framework of a real Hilbert space and propose a simple modification of Tseng’s forward-backward-forward splitting method for solving such problems. Our algorithm is obtained via a certain regularization procedure and uses self-adaptive step sizes. We show that the approximating sequences generated by our algorithm converge strongly to a solution of the problems under suitable assumptions on the regularization parameters. Furthermore, we apply our results to an elastic net penalty problem in statistical learning theory and to split feasibility problems. Moreover, we illustrate the usefulness and effectiveness of our algorithm by using numerical examples in comparison with some existing relevant algorithms that can be found in the literature.

Two-step inertial forward–reflected–anchored–backward splitting algorithm for solving monotone inclusion problems

The main purpose of this paper is to propose and study a two-step inertial anchored version of the forward–reflected–backward splitting algorithm of Malitsky and Tam in a real Hilbert space. Our proposed algorithm converges strongly to a zero of the sum of a set-valued maximal monotone operator and a single-valued monotone Lipschitz continuous operator. It involves only one forward evaluation of the single-valued operator and one backward evaluation of the set-valued operator at each iteration; a feature that is absent in many other available strongly convergent splitting methods in the literature. Finally, we perform numerical experiments involving image restoration problem and compare our algorithm with known related strongly convergent splitting algorithms in the literature.

State Complexity of Permutation and the Language Inclusion Problem up to Parikh Equivalence on Alphabetical Pattern Constraints and Partially Ordered NFAs

We investigate the state complexity of the permutation operation, or the commutative closure, on Alphabetical Pattern Constraints (APCs). This class corresponds to level [Formula: see text] of the Straubing-Thérien hierarchy and includes the finite, the piecewise testable, or [Formula: see text]-trivial, and the [Formula: see text]-trivial and [Formula: see text]-trivial languages. We give a sharp state complexity bound expressed in terms of the longest strings in the unary projection languages of an associated finite language. Additionally, for a subclass, we give sharp bounds expressed in terms of the size of a recognizing input automaton and the size of the alphabet. We also state a related state complexity bound for the commutative closure on finite languages. Lastly, we investigate the language inclusion, equivalence and universality problems on APCs up to permutational, or Parikh, equivalence. These problems are known to be [Formula: see text]-complete on APCs in general, even for fixed alphabets. We show them to be decidable in polynomial time for fixed alphabets if we only want to solve them up to Parikh equivalence. We also correct a mistake from the conference version in a bound on the size of recognizing automata for the commutative closure.

The problem of inclusion and invisibility: working with disabled students in HE

For many, the word ‘inclusion’ has not only become emptied of meaning but also sets up a problematic contradiction. To be included depends on the willingness of those who hold this power to allow entry. Being allowed entry doesn’t change the power relationships but merely allows access to already ‘existing cultures, structures and practices’ (Biesta, Wainwright and Aldridge, 2022, p.1). For disabled people and minoritised groups, the problem of equity and participation in education is one that runs deep and, for many, extends right the way through their educational trajectories. What’s overlooked and not recognised is the invisible work of being disabled. Similarly, and to paraphrase Donna Williams (1996), from the start, disabled people have been judged from the outside, by their appearances, rather than from the inside and according to how their disability is experienced. This mini keynote opens up a space to discuss the problems inherent in inclusion and what this means for disabled people and other minoritised groups. Questions: Inclusion has been co-opted into HE’s performativity agenda; does this create more problems than it pretends to solve? How do we acknowledge and understand the invisible work of being disabled? As practitioners, how can we create a more authentically democratic environment for disabled people and other minoritised groups in HE?