Journal of Nonlinear Analysis and Optimization: Theory & Applications (JNAO)

STRONG CONVERGENCE THEOREMS FOR SYSTEM OF ITERATIVE METHODS OF STRONGLY NONLINEAR NONCONVEX VARIATIONAL INEQUALITIES

2024-04-22T14:58:37+07:00

The article was found to contain errors and has been retracted at the request of Authors and the Editor in Chief. The Publisher apologizes for any inconvenience this may cause.

ACCELERATED FIXED POINT ALGORITHM FOR CONVEX BI-LEVEL OPTIMIZATION PROBLEMS IN HILBERT SPACES WITH APPLICATIONS

2024-04-22T15:06:18+07:00

In this thesis, we propose and analyze a new accelerated algorithm for solving bi-level convex optimization problems in Hilbert spaces in the form of the minimization of smooth and strongly convex function over the optimal solutions set which is the set
of all minimizers of the sum of smooth and nonsmooth functions. In addition, we apply our algorithms to solve regression and classification problems by using machine learning models. Our experiments show that our proposed machine learning algorithm has a better convergence behaviour than the others.

A MODIFIED ITERATIVE ALGORITHM FOR PREŠIĆ TYPE NONEXPANSIVE OF MAPPING IN HADAMARD SPACES

2024-04-22T15:13:13+07:00

In this paper, we introduce a modified iterative method tailored for Prešić nonexpansive mappings in Hadamard spaces. Furthermore, we establish a Δ-convergence theorem aimed at approximating fixed points through the proposed iterative algorithm
under mild conditions. Our findings not only enhance existing results in the field but also offer a broader applicability within the literature.

MODIFIED INERTIAL SUBGRADIENT EXTRAGRADIENT ALGORITHM WITH SELF-ADAPTIVE STEP SIZES FOR SOLVING SPLIT EQUILIBRIUM PROBLEMS

2024-04-22T15:18:01+07:00

In this paper, we introduce a modified inertial subgradient extragradient algorithm featuring self-adaptive step sizes. Our focus is on solving split equilibrium problems that involve pseudomonotone bifunctions satisfying Lipschitz-type continuity within real Hilbert spaces. We demonstrate a strong convergence theorem for the proposed algorithm, requiring neither prior knowledge of the operator norm of the bounded linear operator nor the Lipschitz constants of bifunctions. This convergence holds under certain constraint qualifications of the scalar sequences.