scholarly journals Solving common nonmonotone equilibrium problems using an inertial parallel hybrid algorithm with Armijo line search with applications to image recovery

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Suthep Suantai ◽  
Damrongsak Yambangwai ◽  
Watcharaporn Cholamjiak
Keyword(s):  
Hybrid Algorithm ◽  
Line Search ◽  
Equilibrium Problems ◽  
Common Solution ◽  
Parallel Hybrid ◽  
Armijo Line Search ◽  
Weak Convergence Theorem ◽  
The Common ◽  
Convexity Assumptions

AbstractIn this work, we modify the inertial hybrid algorithm with Armijo line search using a parallel method to approximate a common solution of nonmonotone equilibrium problems in Hilbert spaces. A weak convergence theorem is proved under some continuity and convexity assumptions on the bifunction and the nonemptiness of the common solution set of Minty equilibrium problems. Furthermore, we demonstrate the quality of our inertial parallel hybrid algorithm by using image restoration, as well as its superior efficiency when compared with previously considered parallel algorithms.

scholarly journals A Parallel-Viscosity-Type Subgradient Extragradient-Line Method for Finding the Common Solution of Variational Inequality Problems Applied to Image Restoration Problems

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 248 ◽  
Author(s):  
Suthep Suantai ◽  
Pronpat Peeyada ◽  
Damrongsak Yambangwai ◽  
Watcharaporn Cholamjiak
Keyword(s):  
Variational Inequality ◽  
Hilbert Spaces ◽  
Hybrid Algorithm ◽  
Variational Inequality Problems ◽  
Strong Convergence Theorem ◽  
Infinite Dimensional ◽  
Common Solution ◽  
Line Method ◽  
The Common ◽  
Monotone Hybrid Algorithm

In this paper, we study a modified viscosity type subgradient extragradient-line method with a parallel monotone hybrid algorithm for approximating a common solution of variational inequality problems. Under suitable conditions in Hilbert spaces, the strong convergence theorem of the proposed algorithm to such a common solution is proved. We then give numerical examples in both finite and infinite dimensional spaces to justify our main theorem. Finally, we can show that our proposed algorithm is flexible and has good quality for use with common types of blur effects in image recovery.

scholarly journals STRONG CONVERGENCE OF A NEW HYBRID ALGORITHM FOR FIXED POINT PROBLEMS AND EQUILIBRIUM PROBLEMS

2018 ◽  
Vol 24 (1) ◽  
pp. 1-19 ◽  
Author(s):  
Dang Van Hieu
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Hybrid Algorithm ◽  
Equilibrium Problems ◽  
Extragradient Method ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Mann Iteration ◽  
Common Solution ◽  
Mild Conditions

The paper considers the problem of finding a common solution of a pseudomonotone and Lipschitz-type equilibrium problem and a fixed point problem for a quasi nonexpansive mapping in a Hilbert space. A new hybrid algorithm is introduced for approximating a solution of this problem. The presented algorithm can be considered as a combination of the extragradient method (two-step proximal-like method) and a modified version of the normal Mann iteration. It is well known that the normal Mann iteration has the weak convergence, but in this paper we has obtained the strong convergence of the new algorithm under some mild conditions on parameters. Several numerical experiments are reported to illustrate the convergence of the algorithm and also to show the advantages of it over existing methods.

scholarly journals Optimization Based Methods for Solving the Equilibrium Problems with Applications in Variational Inequality Problems and Solution of Nash Equilibrium Models

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 822 ◽  
Author(s):  
Habib ur Rehman ◽  
Poom Kumam ◽  
Ioannis K. Argyros ◽  
Meshal Shutaywi ◽  
Zahir Shah
Keyword(s):  
Variational Inequality ◽  
Practical Reason ◽  
Line Search ◽  
Equilibrium Problems ◽  
Convergence Result ◽  
Proximal Methods ◽  
Search Procedure ◽  
Equilibrium Models ◽  
Convergence Results ◽  
Weak Convergence Theorem

In this paper, we propose two modified two-step proximal methods that are formed through the proximal-like mapping and inertial effect for solving two classes of equilibrium problems. A weak convergence theorem for the first method and the strong convergence result of the second method are well established based on the mild condition on a bifunction. Such methods have the advantage of not involving any line search procedure or any knowledge of the Lipschitz-type constants of the bifunction. One practical reason is that the stepsize involving in these methods is updated based on some previous iterations or uses a stepsize sequence that is non-summable. We consider the well-known Nash–Cournot equilibrium models to support our well-established convergence results and see the advantage of the proposed methods over other well-known methods.

scholarly journals A Weak Convergence Self-Adaptive Method for Solving Pseudomonotone Equilibrium Problems in a Real Hilbert Space

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1165 ◽  
Author(s):  
Pasakorn Yordsorn ◽  
Poom Kumam ◽  
Habib ur Rehman ◽  
Abdulkarim Hassan Ibrahim
Keyword(s):  
Hilbert Space ◽  
Weak Convergence ◽  
Line Search ◽  
Equilibrium Problems ◽  
Real Hilbert Space ◽  
Extragradient Method ◽  
Adaptive Method ◽  
Type Condition ◽  
Computational Performance ◽  
Weak Convergence Theorem

In this paper, we presented a modification of the extragradient method to solve pseudomonotone equilibrium problems involving the Lipschitz-type condition in a real Hilbert space. The method uses an inertial effect and a formula for stepsize evaluation, that is updated for each iteration based on some previous iterations. The key advantage of the algorithm is that it is achieved without previous knowledge of the Lipschitz-type constants and also without any line search procedure. A weak convergence theorem for the proposed method is well established by assuming mild cost bifunction conditions. Many numerical experiments are presented to explain the computational performance of the method and to equate them with others.

scholarly journals A New Hybrid Projection Algorithm for System of Equilibrium Problems and Variational Inequality Problems and Two Finite Families of Quasi-ϕ-Nonexpansive Mappings

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Pongrus Phuangphoo ◽  
Poom Kumam
Keyword(s):  
Variational Inequality ◽  
Iterative Procedure ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Finite Family ◽  
Variational Inequality Problems ◽  
Projection Algorithm ◽  
Common Solution ◽  
The Common ◽  
System Of Equilibrium Problems

We introduce a modified Mann’s iterative procedure by using the hybrid projection method for solving the common solution of the system of equilibrium problems for a finite family of bifunctions satisfying certain condition, the common solution of fixed point problems for two finite families of quasi-ϕ-nonexpansive mappings, and the common solution of variational inequality problems for a finite family of continuous monotone mappings in a uniformly smooth and strictly convex real Banach space. Then, we prove a strong convergence theorem of the iterative procedure generated by some mild conditions. Our result presented in this paper improves and generalizes some well-known results in the literature.

The concept of motivation for effective credit risk management

2020 ◽  
Vol 26 (11) ◽  
pp. 2567-2593
Author(s):  
M.V. Pomazanov
Keyword(s):  
Risk Management ◽  
Economic Modeling ◽  
Type I ◽  
Credit Risk Management ◽  
Curve Modeling ◽  
Business Functions ◽  
The Common ◽  
Lending Decisions ◽  
The One

Subject. The study addresses the improvement of risk management efficiency and the quality of lending decisions made by banks. Objectives. The aim is to present the bank management with a fair algorithm for risk management motivation on the one hand, and the credit management (business) on the other hand. Within the framework of the common goal to maximize risk-adjusted income from loans, this algorithm will provide guidelines for ‘risk management’ and ‘business’ functions on how to improve individual and overall efficiency. Methods. The study employs the discriminant analysis, type I and II errors, Lorentz curve modeling, statistical analysis, economic modeling. Results. The paper offers a mechanism for assessing the quality of risk management decisions as opposed to (or in support of) decisions of the lending business when approving transactions. The mechanism rests on the approach of stating type I and II errors and the corresponding classical metric of the Gini coefficient. On the ‘business’ side, the mechanism monitors the improvement or deterioration of the indicator of changes in losses in comparison with the market average. Conclusions. The study substantiates the stimulating ‘rules of the game’ between the ‘business’ and ‘risk management’ to improve the efficiency of the entire business, to optimize interactions within the framework of internal competition. It presents mathematical tools to calculate corresponding indicators of the efficiency of internally competing entities.

scholarly journals Common Solution for a Finite Family of Equilibrium Problems, Quasi-Variational Inclusion Problems and Fixed Points on Hadamard Manifolds

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1161
Author(s):  
Jinhua Zhu ◽  
Jinfang Tang ◽  
Shih-sen Chang ◽  
Min Liu ◽  
Liangcai Zhao
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Equilibrium Problems ◽  
Fixed Point Problem ◽  
Finite Family ◽  
Variational Inclusion ◽  
Point Problem ◽  
Hadamard Manifolds ◽  
Inclusion Problems ◽  
Common Solution

In this paper, we introduce an iterative algorithm for finding a common solution of a finite family of the equilibrium problems, quasi-variational inclusion problems and fixed point problem on Hadamard manifolds. Under suitable conditions, some strong convergence theorems are proved. Our results extend some recent results in literature.

scholarly journals Development of a Multidisciplinary Aerodigestive Program: An Institutional Experience

Children ◽  
2021 ◽  
Vol 8 (7) ◽  
pp. 535
Author(s):  
Seung Kim ◽  
Mireu Park ◽  
Eunyoung Kim ◽  
Ga Eun Kim ◽  
Jae Hwa Jung ◽  
...  
Keyword(s):  
Quality Of Life ◽  
Chart Review ◽  
Retrospective Chart Review ◽  
Multidisciplinary Management ◽  
Neurologic Disease ◽  
Institutional Experience ◽  
Swallowing Difficulty ◽  
The Common ◽  
Chronic Comorbidities

We share our experience on the implementation of a multidisciplinary aerodigestive program comprising an aerodigestive team (ADT) so as to evaluate its feasibility. We performed a retrospective chart review of the patients discussed at the monthly ADT meetings and analyzed the data. A total of 98 children were referred to the ADT during the study period. The number of cases increased steadily from 3.5 cases per month in 2019 to 8.5 cases per month in 2020. The median age of patients was 34.5 months, and 55% were male. Among the chronic comorbidities, neurologic disease was the most common (85%), followed by respiratory (36%) and cardiac (13%) disorders. The common reasons for consultation were suspected aspiration (56%), respiratory difficulty (44%), drooling/stertor (30%), regurgitation/vomiting (18%), and feeding/swallowing difficulty (17%). Following discussions, 58 patients received active interventions, including fundoplication, gastrostomy, laryngomicrosurgery, tracheostomy, and primary dilatation of the airway. According to the questionnaire of the caregiver, the majority agreed that the main symptoms and quality of life of patients had improved (88%), reducing the burden on caregivers (77%). Aerodigestive programs may provide comprehensive and multidisciplinary management for children with complex airway and digestive tract disorders.

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