Modified Tseng's extragradient methods with self-adaptive step size for solving bilevel split variational inequality problems

Optimization ◽  
2020 ◽  
pp. 1-28
Author(s):  
Pham Van Huy ◽  
Le Huynh My Van ◽  
Nguyen Duc Hien ◽  
Tran Viet Anh
Keyword(s):  
Variational Inequality ◽  
Variational Inequality Problems ◽  
Step Size ◽  
Adaptive Step Size ◽  
Extragradient Methods ◽  
Split Variational Inequality ◽  
Adaptive Step ◽  
Self Adaptive

scholarly journals Improved inertial projection and contraction method for solving pseudomonotone variational inequality problems

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ming Tian ◽  
Gang Xu
Keyword(s):  
Variational Inequality ◽  
Real Hilbert Space ◽  
Lipschitz Constant ◽  
Variational Inequality Problems ◽  
Iterative Sequence ◽  
Step Size ◽  
Contraction Method ◽  
Projection And Contraction Method ◽  
Inertial Algorithm ◽  
Adaptive Step

AbstractThe objective of this article is to solve pseudomonotone variational inequality problems in a real Hilbert space. We introduce an inertial algorithm with a new self-adaptive step size rule, which is based on the projection and contraction method. Only one step projection is used to design the proposed algorithm, and the strong convergence of the iterative sequence is obtained under some appropriate conditions. The main advantage of the algorithm is that the proof of convergence of the algorithm is implemented without the prior knowledge of the Lipschitz constant of cost operator. Numerical experiments are also put forward to support the analysis of the theorem and provide comparisons with related algorithms.

scholarly journals Inertial shrinking projection algorithm with self-adaptive step size for split generalized equilibrium and fixed point problems for a countable family of nonexpansive multivalued mappings

2021 ◽  
Vol 54 (1) ◽  
pp. 47-67
Author(s):  
Musa A. Olona ◽  
Timilehin O. Alakoya ◽  
Abd-semii O.-E. Owolabi ◽  
Oluwatosin T. Mewomo
Keyword(s):  
Countable Family ◽  
Projection Algorithm ◽  
Common Element ◽  
Multivalued Mappings ◽  
Strong Convergence Theorem ◽  
Step Size ◽  
Adaptive Step Size ◽  
Generalized Equilibrium ◽  
Adaptive Step ◽  
Self Adaptive

Abstract In this paper, we introduce a shrinking projection method of an inertial type with self-adaptive step size for finding a common element of the set of solutions of a split generalized equilibrium problem and the set of common fixed points of a countable family of nonexpansive multivalued mappings in real Hilbert spaces. The self-adaptive step size incorporated helps to overcome the difficulty of having to compute the operator norm, while the inertial term accelerates the rate of convergence of the proposed algorithm. Under standard and mild conditions, we prove a strong convergence theorem for the problems under consideration and obtain some consequent results. Finally, we apply our result to solve split mixed variational inequality and split minimization problems, and we present numerical examples to illustrate the efficiency of our algorithm in comparison with other existing algorithms. Our results complement and generalize several other results in this direction in the current literature.

scholarly journals An Inertial Generalized Viscosity Approximation Method for Solving Multiple-Sets Split Feasibility Problems and Common Fixed Point of Strictly Pseudo-Nonspreading Mappings

Axioms ◽  
2020 ◽  
Vol 10 (1) ◽  
pp. 1
Author(s):  
Hammed Anuoluwapo Abass ◽  
Lateef Olakunle Jolaoso
Keyword(s):  
Fixed Point ◽  
Approximation Method ◽  
Feasibility Problem ◽  
Viscosity Approximation Method ◽  
Viscosity Approximation ◽  
Step Size ◽  
Adaptive Step Size ◽  
Adaptive Step ◽  
Split Feasibility ◽  
Self Adaptive

In this paper, we propose a generalized viscosity iterative algorithm which includes a sequence of contractions and a self adaptive step size for approximating a common solution of a multiple-set split feasibility problem and fixed point problem for countable families of k-strictly pseudononspeading mappings in the framework of real Hilbert spaces. The advantage of the step size introduced in our algorithm is that it does not require the computation of the Lipschitz constant of the gradient operator which is very difficult in practice. We also introduce an inertial process version of the generalize viscosity approximation method with self adaptive step size. We prove strong convergence results for the sequences generated by the algorithms for solving the aforementioned problems and present some numerical examples to show the efficiency and accuracy of our algorithm. The results presented in this paper extends and complements many recent results in the literature.

Accelerated Cuckoo Search With Extended Diversification and Intensification

2021 ◽  
Vol 12 (3) ◽  
pp. 125-148
Author(s):  
Deepak Garg ◽  
Pardeep Kumar
Keyword(s):  
Cuckoo Search ◽  
Search Performance ◽  
Step Size ◽  
Adaptive Step Size ◽  
Adaptive Parameters ◽  
Objective Parameter ◽  
Discovery Probability ◽  
Good Neighbor ◽  
Adaptive Step ◽  
Self Adaptive

Metaheuristics have been great to solve NP-hard class problems in the deterministic time, but due to so many parameter settings, they lack in generality (i.e., not easy to implement on all types of problems) and also lack in global search. But the cuckoo search (CS) algorithm has only one parameter as input and also has a good reachable probability to global solution due to Levy flight. But this algorithm lacks self-adaptive parameters and extended strategies. In this paper, a deep study and improvement of cuckoo search performance has been done by introducing self-adaptive step size, extended alien egg discovery replacement (on each dimension with the use of good neighbor study), and adaptive discovery probability, and it has been named accelerated cuckoo search (ACS). Then this ACS has been utilized as an example in the load balancing problem in cloud with minimum makespan time as an objective parameter to evaluate the performance of ACS over CS. Furthermore, to validate ACS superiority over CS in all problems, these have been successfully compared on a few benchmark functions.

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