Variational Inclusions Research Articles

New iterative algorithms for solving split variational inclusions

New iterative algorithms for solving split variational inclusions

Nonmonotone Spectral Analysis for Variational Inclusions

Gradient descent algorithms perform well in convex optimization but can get tied for finding local minima in non-convex optimization. A robust method that combines a spectral approach with nonmonotone line search strategy for solving variational inclusion problems is proposed. Spectral properties using eigenvalues information are used for accelerating the convergence. Nonmonotonic behaviour is exhibited to relax descent property and escape local minima. Nonmonotone spectral conditions leverage adaptive search directions and global convergence for the proposed spectral subgradient algorithm.

Refined Iterative Method for a Common Variational Inclusion and Common Fixed-Point Problem with Practical Applications

This paper introduces a novel parallel method for solving common variational inclusion and common fixed-point (CVI-CFP) problems. The proposed algorithm provides a strong convergence theorem established under specific conditions associated with the CVI-CFP problem. Numerical simulations demonstrate the algorithm’s efficacy in the context of signal recovery problems involving various types of blurred filters. The results highlight the algorithm’s potential for practical applications in image processing and other fields.

On split equality monotone variational inclusion and fixed point problems in reflexive Banach spaces

In this paper, motivated by the works of Akbar and Shahrosvand [Filomat {\bf 32} (2018), no.\ 11, 3917-3932], Ogbuisi and Izuchukwu [Numer. Funct. Anal. Optim. {\bf 41} (2020), no.\ 2, 322-343], and some other related results in the literature, we introduce a Halpern iterative algorithm and employ a Bregman distance approach for approximating a solution of split equality monotone variational inclusion problem and fixed point problem of Bregman relatively nonexpansive mapping in reflexive Banach spaces. Under suitable condition, we state and prove a strong convergence result for approximating a common solution of the aforementioned problems. Furthermore, we give an application of our main result to variational inequality problems and provide some numerical examples to illustrate the convergence behavior of our result. The result presented in this paper extends and complements many related results in literature.

Modi ed inertia Halpern method for split null point problem in Banach spaces

Abstract. In this paper, we study split null point problem in reflexive Banach spaces. Using the Bregman technique together with a modified inertial Halpern method, we approximate a solution of split null point problem. Also, we establish a strong convergence result for approximating the solution of the aforementioned problems. It is worth mentioning that the iterative algorithm employ in this study is design in such a way that it does not require prior knowledge of operator norm. We display some numerical examples to illustrate the performance of the proposed iterative method. The result discuss in this paper extends and complements many related results in literature. Mathematics Subject Classification (2010): 47H06, 47H09, 47J05, 47J25. Keywords: Monotone variational inclusion problem, split feasibility problem, firmly nonexpansive-type mapping, fixed point problem, inertial method.

A new algorithm for approximating solutions of the common variational inclusion

A new algorithm for approximating solutions of the common variational inclusion

Parallel inertial forward–backward splitting methods for solving variational inequality problems with variational inclusion constraints

The inertial forward–backward splitting algorithm can be considered as a modified form of the forward–backward algorithm for variational inequality problems with monotone and Lipschitz continuous cost mappings. By using parallel and inertial techniques and the forward–backward splitting algorithm, in this paper, we propose a new parallel inertial forward–backward splitting algorithm for solving variational inequality problems, where the constraints are the intersection of common solution sets of a finite family of variational inclusion problems. Then, strong convergence of proposed iteration sequences is showed under standard assumptions imposed on cost mappings in a real Hilbert space. Finally, some numerical experiments demonstrate the reliability and benefits of the proposed algorithm.

Enhanced Double Inertial Forward–Backward Splitting Algorithm for Variational Inclusion Problems: Applications in Mathematical Integrated Skill Prediction

Enhanced Double Inertial Forward–Backward Splitting Algorithm for Variational Inclusion Problems: Applications in Mathematical Integrated Skill Prediction

Generalized Yosida inclusion problem involving multi-valued operator with XOR operation

Abstract In this article, we study a generalized Yosida variational inclusion problem involving multi-valued operator with XOR operation. It is shown that the generalized Yosida variational inclusion problem involving multi-valued operator with XOR operation is equivalent to a fixed point equation. We have proved that the generalized Yosida approximation operator is Lipschitz continuous. Finally, we prove an existence and convergence result for our problem.

Design and multi-body dynamic analysis of inline and offset track configuration in deep-sea mining vehicles for enhanced traction in soft seabed

The deep sea polymetallic nodule mining vehicle maneuverability depends on the vehicle track parameters and track configuration. The traction force offered by the deep sea soil is very limited for the mining vehicle during dynamic operating conditions on the seabed and it is very critical to maneuver against the external resistances. The present study strives to arrive at optimum track parameters for enhancing the traction of the vehicle for the pre-determined seabed conditions. The efficacy of the four tracks in Inline and Offset track configurations on the soft soil has been compared. To improve the traction force estimation, the existing mathematical model was modified with the inclusion of dynamic variation of shear stress-shear displacement characteristics and variation in shear residual displacement concerning the track parameters. The modified mathematical model was solved in a well-established mathematical tool and found that there are 30 percent improvements in the traction force generation for the offset configuration over inline track configuration. The optimum track length to width ratio (L/b) was also estimated for the given contact area to configure the vehicle track for improvement of the traction. Further, a Multi-Body Dynamic (MBD) analysis has been carried out in commercially available soil-machine interaction tool for the inline and offset track configurations with actual measured seabed soil parameters. The MBD analysis proved that the sinkage and vehicle gradient is significantly increased in the inline track configuration due to disturbance created by the front tracks. The simulation results confirm that the offset track configuration is suitable for the deep sea soil conditions for handling the higher payload of a deep sea mining vehicle.

Solving split equality equilibrium and fixed point problems in Banach spaces

In this paper, we introduce a new algorithm for approximating a common solution of Split Equality Generalised Mixed Equilibrium Problem (SEGMEP) and Split Equality Fixed Point Problem (SEFPP) for two infinite families of closed uniformly Li-Lipschitz continuous and Ki-Lipschitz continuous and uniformly quasi-ϕ-asymptotically nonexpansive mappings (i ∈ N and ϕ is the Lyapunov functional) in Banach spaces. Under standard and mild assumption of monotonicity and lower semicontinuity of the SEGMEP associated mappings, we establish the strong convergence of the scheme without imposing any compactness type conditions on either the operators or the spaces considered. We apply our result to approximate the solution of Split Equality Convex Minimization Problem (SECMP) and Split Equality Variational Inclusion Problem (SEVIP). A numerical example is presented to illustrate the performance and implementability of our method. Our results extend, generalize and complement several related works in the literature.

Scaled forward-backward algorithm and the modified superiorized version for solving the split monotone variational inclusion problem

In this paper, we propose an inexact scaled forward-backward algorithm to solve the split monotone variational inclusion problem in a real Hilbert space and prove the strong convergence of it under appropriate conditions. Based on this, we discuss the bounded perturbation resilience of the exact algorithm for introducing the corresponding superiorized version and the superiorization algorithm with restarted perturbations. The numerical experiments illustrate that the proposed algorithms perform well and the superiorization version with restarted perturbations has advantage in decreasing the number of the iterations.

Modified splitting algorithms for approximating solutions of split variational inclusions in Hilbert spaces

Modified splitting algorithms for approximating solutions of split variational inclusions in Hilbert spaces

Extending the CWM approach to intraspecific trait variation: how to deal with overly optimistic standard tests?

Community weighted means (CWMs) are widely used to study the relationship between community-level functional traits and environment. For certain null hypotheses, CWM-environment relationships assessed by linear regression or ANOVA and tested by standard parametric tests are prone to inflated Type I error rates. Previous research has found that this problem can be solved by permutation tests (i.e., the max test). A recent extension of the CWM approach allows the inclusion of intraspecific trait variation (ITV) by the separate calculation of fixed, site-specific, and intraspecific CWMs. The question is whether the same Type I error rate inflation exists for the relationship between environment and site-specific or intraspecific CWM. Using simulated and real-world community datasets, we show that site-specific CWM-environment relationships have also inflated Type I error rate, and this rate is negatively related to the relative ITV magnitude. In contrast, for intraspecific CWM-environment relationships, standard parametric tests have the correct Type I error rate, although somewhat reduced statistical power. We introduce an ITV-extended version of the max test, which can solve the inflation problem for site-specific CWM-environment relationships and, without considering ITV, becomes equivalent to the "original" max test used for the CWM approach. We show that this new ITV-extended max test works well across the full possible magnitude of ITV on both simulated and real-world data. Most real datasets probably do not have intraspecific trait variation large enough to alleviate the problem of inflated Type I error rate, and published studies possibly report overly optimistic significance results.

Thermo-convection driven Sodium Alginate-based Darcy–Forchheimer EMHD Williamson hybrid nanofluid flow with varying thermal distribution

A computational investigation is furnished to explore the responses of a Darcy–Forchheimer EMHD Williamson flow of a Sodium Alginate [Formula: see text]-based Ag-Al2O3 hybrid nanofluid passing over a vertically exponentially stretching cylinder emerged through a porous region. The prime focus of this research is to encompass the inclusion of nonlinear variations in heat distribution, Newtonian boundary heating (NBH) effects, and the influence of thermo-convection alongside suction effects. Key parameters, including thermal buoyancy, Darcy porous medium effects, heat source/sink effects, Biot number, variable thermal index, and thermal convection factor, are comprehensively analyzed as these combining factors can play a crucial role in optimizing the efficacy of several systems such as heat exchanger, material processing and geothermal system that involve the concept of thermo-transportation mechanism. The physical flow dynamics are modeled, employing suitable similarity transformations, and subsequently translated into a dimensionless form. The ensuing collection of modified nonlinear ordinary differential equations is solved by employing the Bvp4c solver bundled into the MATLAB program. Several parameters are scrutinized through graphical presentations to elucidate their impacts on the velocity curve, temperature curve, skin friction coefficient, and Nusselt index. It is worth mentioning that the heat distribution profile significantly escalated for the rising values of several factors such as electric field parameter, varying thermal index, Biot number and shape factor, but the reverse is the pattern with suction and thermo-convection effect. Also, the thermal transportation rate at the proximity of the vertical cylindrical wall appears to exhibit an increment of about an average of 47% in SA-based Williamson hybrid nanofluid compared to Williamson fluid for thermo-convective effect, NBH, and thermal buoyancy. Furthermore, the proximate shear stress rate appears to be amplified by approximately 39% in Williamson hybrid nanofluid when contrasted with Williamson fluid for electric field parameter and thermo-convection effect alongside the raised Darcy–Forchheimer factor.

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.

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.

A machine learning model for the early diagnosis of bloodstream infection in patients admitted to the pediatric intensive care unit.

Bloodstream infection (BSI) is associated with increased morbidity and mortality in the pediatric intensive care unit (PICU) and high healthcare costs. Early detection and appropriate treatment of BSI may improve patient's outcome. Data on machine-learning models to predict BSI in pediatric patients are limited and neither study included time series data. We aimed to develop a machine learning model to predict an early diagnosis of BSI in patients admitted to the PICU. This was a retrospective cohort study of patients who had at least one positive blood culture result during stay at a PICU of a tertiary-care university hospital, from January 1st to December 31st 2019. Patients with positive blood culture results with growth of contaminants and those with incomplete data were excluded. Models were developed using demographic, clinical and laboratory data collected from the electronic medical record. Laboratory data (complete blood cell counts with differential and C-reactive protein) and vital signs (heart rate, respiratory rate, blood pressure, temperature, oxygen saturation) were obtained 72 hours before and on the day of blood culture collection. A total of 8816 data from 76 patients were processed by the models. The machine committee was the best-performing model, showing accuracy of 99.33%, precision of 98.89%, sensitivity of 100% and specificity of 98.46%. Hence, we developed a model using demographic, clinical and laboratory data collected on a routine basis that was able to detect BSI with excellent accuracy and precision, and high sensitivity and specificity. The inclusion of vital signs and laboratory data variation over time allowed the model to identify temporal changes that could be suggestive of the diagnosis of BSI. Our model might help the medical team in clinical-decision making by creating an alert in the electronic medical record, which may allow early antimicrobial initiation and better outcomes.

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.