Variational Inclusions Research Articles

Variational inequality problem over the solution set of split monotone variational inclusion problem with application to bilevel programming problem

The purpose of this paper is to study variational inequality problem over the solution set of multiple-set split monotone variational inclusion problem. We propose an iterative algorithm with inertial method for finding an approximate solution of this problem in real Hilbert spaces. Strong convergence of the sequence of iterates generated from the proposed method is obtained under some mild assumptions. The iterative scheme does not require prior knowledge of operator norm. Also we present some applications of our main result to solve the bilevel programming problem, the bilevel monotone variational inequalities, the split minimization problem, the multiple-set split feasibility problem and the multiple set split variational inequality problem.

SEVERAL VARIATIONAL INCLUSIONS FOR A FRACTIONAL DIFFERENTIAL INCLUSION OF CAPUTO-FABRIZIO TYPE

We establish several fractional variational inclusions for solutions of a nonconvex fractional differential inclusion involving Caputo-Fabrizio fractional derivative.

Solving nonlinear implicit variational inclusion problems using S-iteration via relaxed resolvent operator

The goal of the draft is to launch a fresh iteration scheme for nonlinear implicit variational inclusion problems with the help of strongly ()I−-monotone operator. This scheme is known as relaxed S-iteration scheme. Here, we use relaxed resolvent operator into S-iteration and create a new operator and with the help of that operator we will establish the strong convergence result for the nonlinear implicit variational inclusion problems.

A generalized Halpern-type forward-backward splitting algorithm for solving variational inclusion problems

<abstract><p>In this paper, we investigate the problem of finding a zero of sum of two accretive operators in the setting of uniformly convex and $ q $-uniformly smooth real Banach spaces ($ q > 1 $). We incorporate the inertial and relaxation parameters in a Halpern-type forward-backward splitting algorithm to accelerate the convergence of its sequence to a zero of sum of two accretive operators. Furthermore, we prove strong convergence of the sequence generated by our proposed iterative algorithm. Finally, we provide a numerical example in the setting of the classical Banach space $ l_4(\mathbb{R}) $ to study the effect of the relaxation and inertial parameters in our proposed algorithm.</p></abstract>

System of Set-Valued Nonlinear Generalized Variational Inclusion Problems in Banach Spaces

System of Set-Valued Nonlinear Generalized Variational Inclusion Problems in Banach Spaces

Adaptive inertial Yosida approximation iterative algorithms for split variational inclusion and fixed point problems

<abstract><p>In this paper, we present self-adaptive inertial iterative algorithms involving Yosida approximation to investigate a split variational inclusion problem (SVIP) and common solutions of a fixed point problem (FPP) and SVIP in Hilbert spaces. We analyze the weak convergence of the proposed iterative algorithm to explore the approximate solution of the SVIP and strong convergence to estimate the common solution of the SVIP and FPP under some mild suppositions. A numerical example is demonstrated to validate the theoretical findings, and comparison of our iterative methods with some known schemes is outlined.</p></abstract>

On generalized extragradient implicit method for systems of variational inequalities with constraints of variational inclusion and fixed point problems

Abstract In a real Banach space, let the VI indicate a variational inclusion for two accretive operators and let the CFPP denote a common fixed point problem of countably many nonexpansive mappings. In this article, we introduce a generalized extragradient implicit method for solving a general system of variational inequalities (GSVI) with the VI and CFPP constraints. Strong convergence of the suggested method to a solution of the GSVI with the VI and CFPP constraints under some suitable assumptions is established.

AN ACCELERATED HALPERN-TYPE ALGORITHM FOR SOLVING VARIATIONAL INCLUSION PROBLEMS WITH APPLICATIONS

An inertial Halpern-type forward-backward iterative algorithm for approximating a zero of sum of two accretive operators is introduced and studied. Strong convergence theorem is established in a uniformly convex and q-uniformly smooth real Banach space. The convergence result obtained is applied to convex minimization and image restoration problems. Furthermore, numerical experiments are carried out on some classical test images and personal images degraded with motion blur and random noise. Finally, numerical illustrations in the Banach space, L5([−1, 1]) are presented to support the main theorem.

An iterative method involving a class of quasi-phi-nonexpansive mappings for solving split equality fixed point problems

"A new inertial iterative algorithm for approximating solution of split equality fixed point problem (SEFPP) for quasi-$\phi$- nonexpansive mappings is introduced and studied in $p$-uniformly convex and uniformly smooth real Banach spaces, $p>1$. A strong convergence theorem is proved without imposing any compactness-type condition on the mappings. Our theorems complement several important recent results that have been proved in 2-uniformly convex and uniformly smooth real Banach spaces. It is well known that these spaces do not include $L_p, l_p $ and the Sobolev spaces ${W^m}_p(\Omega)$, for $2< p < \infty$. Our theorems, in particular, are applicable in these spaces. Furthermore, application of our theorem to split equality variational inclusion problem is presented. Finally, numerical examples are presented to illustrate the convergence of our algorithms."

A new projection and contraction method for solving split monotone variational inclusion, pseudomonotone variational inequality, and common fixed point problems

A new projection and contraction method for solving split monotone variational inclusion, pseudomonotone variational inequality, and common fixed point problems

Study on the effect of the addition of bulk and exfoliated graphitic carbon nitride on the dry sliding behavior of a commercial friction material formulation through pin on disc and subscale dynamometer analysis

A novel analysis was conducted on the friction and wear properties of a commercial friction material formulation with the addition of bulk (named: gCN) and exfoliated (named: TEX6) graphitic carbon nitride in varying quantities: 4.5, 9, 13.5, and 18 wt%. The analysis was two-fold. In the first part, the samples were tested in the form of pins on a pin on disc testing equipment. The typical trend was that the friction coefficient magnitude increased with the addition of gCN. On the other hand, the friction coefficient decreased with the TEX6 addition. The pin wear reduced with the addition of gCN until 9 wt%. Beyond this amount, an increase in pin wear was observed. The TEX6 samples generally noted a decrease in pin wear with the increase in its content. An improvement in the characteristics of the secondary plateaus was seen with the increase in both gCN and TEX6 content. Through this study, the 13.5 wt% addition of both gCN and TEX6 was considered to display permissible friction and wear magnitude, and desirable extension and compaction of secondary contact plateaus. In the second part of the study, the formulation with 13.5 wt% of gCN and TEX6 was tested on a subscale dynamometer to replicate a real-life braking scenario. The friction and wear magnitudes were similar to the pin on disc study and the extension of the secondary contact plateaus was better than the virgin formulation. This study provides a complete analysis of the feasibility of the inclusion of g-C3N4 variations in automotive braking applications.

A sufficient condition for local controllability of a Caputo type fractional differential inclusion

Abstract We consider a Cauchy problem for a fractional differential inclusion defined by a Caputo type fractional derivative and we obtain a sufficient condition for local controllability along a reference trajectory in terms of a certain fractional variational differential inclusion associated to the initial problem.

An iterative technique for solving split equality monotone variational inclusion and fixed point problems

Abstract The purpose of this paper is to introduce an iterative algorithm for approximating the solution of the split equality monotone variational inclusion problem (SEMVIP) for monotone operators, which is also a solution of the split equality fixed point problem (SEFPP) for strictly pseudocontractive maps in real Hilbert spaces. We establish the strong convergence of the sequence generated by our iterative algorithm. Our result complements and extends some related results in literature.

Patient variability in the blood-stage dynamics of Plasmodium falciparum captured by clustering historical data

BackgroundMathematical models provide an understanding of the dynamics of a Plasmodium falciparum blood-stage infection (within-host models), and can predict the impact of control strategies that affect the blood-stage of malaria. However, the dynamics of P. falciparum blood-stage infections are highly variable between individuals. Within-host models use different techniques to capture this inter-individual variation. This struggle may be unnecessary because patients can be clustered according to similar key within-host dynamics. This study aimed to identify clusters of patients with similar parasitaemia profiles so that future mathematical models can include an improved understanding of within-host variation.MethodsPatients’ parasitaemia data were analyzed to identify (i) clusters of patients (from 35 patients) that have a similar overall parasitaemia profile and (ii) clusters of patients (from 100 patients) that have a similar first wave of parasitaemia. For each cluster analysis, patients were clustered based on key features which previous models used to summarize parasitaemia dynamics. The clustering analyses were performed using a finite mixture model. The centroid values of the clusters were used to parameterize two established within-host models to generate parasitaemia profiles. These profiles (that used the novel centroid parameterization) were compared with profiles that used individual-specific parameterization (as in the original models), as well as profiles that ignored individual variation (using overall means for parameterization).ResultsTo capture the variation of within-host dynamics, when studying the overall parasitaemia profile, two clusters efficiently grouped patients based on their infection length and the height of the first parasitaemia peak. When studying the first wave of parasitaemia, five clusters efficiently grouped patients based on the height of the peak and the speed of the clearance following the peak of parasitaemia. The clusters were based on features that summarize the strength of patient innate and adaptive immune responses. Parameterizing previous within host-models based on cluster centroid values accurately predict individual patient parasitaemia profiles.ConclusionThis study confirms that patients have personalized immune responses, which explains the variation of parasitaemia dynamics. Clustering can guide the optimal inclusion of within-host variation in future studies, and inform the design and parameterization of population-based models.

Ionic Liquids Containing the Sulfonyl Fluoride Moiety: Integrating Chemical Biology with Materials Design

Research involving functionalized ionic liquids has become quite wide speared. They can serve as powerful tools to improve society, with a wide range of applications in medicine, science, and technology. As a SuFExable functionality, the sulfonyl fluoride has become widely adopted throughout the field of chemical biology due to its unique stability─reactivity pattern, highlighting the underappreciated potential of the S(VI)--F motif in ionic liquid design. For the first time, we have developed a new series of task-specific ionic liquids containing the sulfonyl fluoride motif -- a thermally stable and chemically robust functionality -- in gram-quantity scale. Significantly, inclusion of active pharmaceutical precursors and judicious variation of heterocyclic headgroups throughout the synthetic design process, resulted in structural diversity with a priori reduced ecological footprint. We employed a combination of molecular design, synthesis, computational modeling, and X-ray crystallographic studies for understanding of their structure-property relationships.

Set-Valued Variational Inclusion Governed by Generalized αiβj-Hp(., ., ...)-Accretive Mapping

This work is concerned with the new notion called generalized αiβj-Hp(., ., ...)-accretive mapping that is the sum of two symmetric accretive mappings. It is an extension of the generalized αβ-H(., .)-accretive mapping. The proximal point mapping linked to the generalized αiβj-Hp(., ., ...)-accretive mappings is defined, and some of its characteristics are discussed. As an application of the new proximal point mapping, we consider a set-valued variational inclusion problem in q-uniformly smooth Banach spaces. Further, we propose an iterative scheme connected with αiβj-Hp(., ., ...)-proximal point mapping to find the solution of a variational inclusion problem and discuss its convergence criteria under appropriate assumptions. Some examples are constructed in support of generalized αiβj-Hp(., ., ...)-accretive mappings.

Artificial intelligence and clinical anatomical education: Promises and perils.

Anatomy educators are often at the forefront of adopting innovative and advanced technologies for teaching, such as artificial intelligence (AI). While AI offers potential new opportunities for anatomical education, hard lessons learned from the deployment of AI tools in other domains (e.g., criminal justice, healthcare, and finance) suggest that these opportunities are likely to be tempered by disadvantages for at least some learners and within certain educational contexts. From the perspectives of an anatomy educator, public health researcher, medical ethicist, and an educational technology expert, this article examines five tensions between the promises and the perils of integrating AI into anatomy education. These tensions highlight the ways in which AI is currently ill-suited for incorporating the uncertainties intrinsic to anatomy education in the areas of (1) human variations, (2) healthcare practice, (3) diversity and social justice, (4) student support, and (5) student learning. Practical recommendations for a considered approach to working alongside AI in the contemporary (and future) anatomy education learning environment are provided, including enhanced transparency about how AI is integrated, AI developer diversity, inclusion of uncertainty and anatomical variations within deployed AI, provisions made for educator awareness of AI benefits and limitations, building in curricular "AI-free" time, and engaging AI to extend human capacities. These recommendations serve as a guiding framework for how the clinical anatomy discipline, and anatomy educators, can work alongside AI, and develop a more nuanced and considered approach to the role of AI in healthcare education.

New Approach to Split Variational Inclusion Issues through a Three-Step Iterative Process

Split variational inclusions are revealed as a large class of problems that includes several other pre-existing split-type issues: split feasibility, split zeroes problems, split variational inequalities and so on. This makes them not only a rich direction of theoretical study but also one with important and varied practical applications: large dimensional linear systems, optimization, signal reconstruction, boundary value problems and others. In this paper, the existing algorithmic tools are complemented by a new procedure based on a three-step iterative process. The resulting approximating sequence is proved to be weakly convergent toward a solution. The operation mode of the new algorithm is tracked in connection with mixed optimization–feasibility and mixed linear–feasibility systems. Standard polynomiographic techniques are applied for a comparative visual analysis of the convergence behavior.

The galaxy-wide stellar initial mass function in the presence of cluster-to-cluster IMF variations

We calculate the stellar integrated galactic initial mass function (IGIMF) in the presence of cluster-to-cluster variations of the IMF. Variations of the IMF for a population of coeval clusters that populate the initial cluster mass function (ICLMF) are taken into account in the form of Gaussian distribution functions of the IMF parameters. For the tapered power-law function used in this work, these are the slope at the high-mass end, Γ, the slope at the low-mass end, γ, and the characteristic mass Mch. The level of variations is modeled by varying the width of the Gaussian distributions. The reference values are the standard deviations of the parameters observed for the population of young clusters in the present-day Milky Way, which are σΓ = 0.6, σγ = 0.25, and σMch = 0.27 M⊙. We find that increasing the levels of dispersion for γ and Γ tends to moderately flatten the IGIMF at the low and high-mass end, respectively. The characteristic mass of the IGIMF is, however, strongly impacted by variations in Mch. Increasing the value of σMch shifts the peak of the IGIMF to lower masses, rendering the IGIMF more bottom heavy. This can provide a simple explanation for the bottom-heavy stellar mass function that is inferred for early-type galaxies since these are likely the result of a merger of disk galaxies where the physical conditions of the star-forming gas may vary significantly both in time and space in the merging system. The effect of IMF variations on the IGIMF is compared to the effects of other processes and sources of systematic variations such as those due to variations in the shape of ICLMF, the gas-phase metallicity, and the galactic star formation rate (SFR) which can potentially affect the maximum mass of stellar clusters in a galaxy and set the mean value of the characteristic mass in clusters. For the various dependencies we have explored, we found that the effect of IMF variations is a dominant factor that always affects the characteristic mass of the IGIMF. For the regimes at low metallicity where the IGIMF resembles a single power law, an increased level of IMF variations renders the IGIMF steeper and more bottom heavy, especially at low SFRs. On the other hand, variations in the IMF in the high mass regime can be easily dominated by variations in the slope of the ICLMF. We compare our results of the metallicity and SFR-dependent IGIMF to a sample of Milky Way ultra-faint dwarf (UFD) satellite galaxies that have available metallicity measurements. The present-day stellar mass function of these galaxies is a good analog to the IGIMF at the time their overall population of stars formed. We show that the slope of the stellar mass function of the UFD galaxies measured for stars in the mass range [0.4, 0.8] M⊙ can only be reproduced when IMF variations of the same order as those measured in the present-day Milky Way are included. Our results suggest that the inclusion of IMF variations in models of galaxy formation and evolution is of vital importance in order to improve our understanding of star formation and star formation feedback effects on galactic scales.

A new system of generalized nonlinear variational inclusion problems in semi-inner product spaces

In this work we reflect a new system of generalized nonlinear variational inclusion problems in 2-uniformly smooth Banach spaces. By using resolvent operator technique, we offer an iterative algorithm for figuring out the approximate solution of the said system. The motive of this paper is to review the convergence analysis of a system of generalized nonlinear variational inclusion problems in 2-uniformly smooth Banach spaces. The proposition used in this paper can be considered as an extension of propositions for examining the existence of solution for various classes of variational inclusions considered and studied by many authors in 2-uniformly smooth Banach spaces.