Figure 3 - available via license: Creative Commons Attribution 4.0 International
Content may be subject to copyright.
Source publication
In this paper, we propose an adaptive algorithm with multi-step inertia for solving a convex bilevel optimization problem. Under suitable parameter conditions, we prove that our algorithm converges strongly to some solution of the problem, which is the unique solution of some variational inequality problem. The effectiveness of the proposed algorit...
Similar publications
![Figure 1. Graphical error of our method with [12, 13] when solving system 1](profile/Sabo-John-2/publication/379509295/figure/fig1/AS:11431281233756448@1712111895023/Graphical-error-of-our-method-with-12-13-when-solving-system-1_Q320.jpg)
![Relationship of block algorithm with [12, 13] for solving system 1](profile/Sabo-John-2/publication/379509295/figure/tbl3/AS:11431281233727478@1712111895659/Relationship-of-block-algorithm-with-12-13-for-solving-system-1_Q320.jpg)
The numerical application of higher order linear block method for the direct solution of fourth order initial value problems was proposed using the linear block algorithm, where the methods applied in block form. The method is zero-stabile, consistent and convergent when analyzing the properties of the method. The mathematical example solved using...
Exact penalty methods are one of the effective tools to solve nonlinear programming problems with inequality constraints. In this study, a new class of exact penalty functions is defined and a new family of smoothing techniques to exact penalty functions is introduced. Error estimations are presented among the original, non-smooth exact penalty and...
We study the homogenization limit of the renewal equation with heterogeneous external constraints by means of the two-scale convergence theory. We prove that the homogenized limit satisfies an equation involving non-local terms, which are the consequence of the oscillations in the birth and death terms. We have moreover shown that the numerical app...
A family of fifth-order iterative methods is proposed for solving nonlinear equations using the weight function technique. This family offers flexibility through its structure and the choice of weight functions, resulting in a wide range of new specific schemes. It is demonstrated that this proposed family includes several well-known and recent met...
In this paper, a quadratic B-spline collocation method is developed to solve a singularly perturbed semilinear reaction–diffusion problem with a discontinuous source term. The discontinuous source term leads to a jump in the second-order derivative of the exact solution at the discontinuous point. A quadratic B-spline collocation method on a Shishk...
