@inproceedings{9227,
abstract = {In the multiway cut problem we are given a weighted undirected graph G=(V,E) and a set T⊆V of k terminals. The goal is to find a minimum weight set of edges E′⊆E with the property that by removing E′ from G all the terminals become disconnected. In this paper we present a simple local search approximation algorithm for the multiway cut problem with approximation ratio 2−2k . We present an experimental evaluation of the performance of our local search algorithm and show that it greatly outperforms the isolation heuristic of Dalhaus et al. and it has similar performance as the much more complex algorithms of Calinescu et al., Sharma and Vondrak, and Buchbinder et al. which have the currently best known approximation ratios for this problem.},
author = {Bloch-Hansen, Andrew and Samei, Nasim and Solis-Oba, Roberto},
booktitle = {Conference on Algorithms and Discrete Applied Mathematics},
isbn = {9783030678982},
issn = {1611-3349},
location = {Rupnagar, India},
pages = {346--358},
publisher = {Springer Nature},
title = {{Experimental evaluation of a local search approximation algorithm for the multiway cut problem}},
doi = {10.1007/978-3-030-67899-9_28},
volume = {12601},
year = {2021},
}
@article{9315,
abstract = {We consider inertial iteration methods for Fermat–Weber location problem and primal–dual three-operator splitting in real Hilbert spaces. To do these, we first obtain weak convergence analysis and nonasymptotic O(1/n) convergence rate of the inertial Krasnoselskii–Mann iteration for fixed point of nonexpansive operators in infinite dimensional real Hilbert spaces under some seemingly easy to implement conditions on the iterative parameters. One of our contributions is that the convergence analysis and rate of convergence results are obtained using conditions which appear not complicated and restrictive as assumed in other previous related results in the literature. We then show that Fermat–Weber location problem and primal–dual three-operator splitting are special cases of fixed point problem of nonexpansive mapping and consequently obtain the convergence analysis of inertial iteration methods for Fermat–Weber location problem and primal–dual three-operator splitting in real Hilbert spaces. Some numerical implementations are drawn from primal–dual three-operator splitting to support the theoretical analysis.},
author = {Iyiola, Olaniyi S. and Shehu, Yekini},
issn = {14209012},
journal = {Results in Mathematics},
number = {2},
publisher = {Springer Nature},
title = {{New convergence results for inertial Krasnoselskii–Mann iterations in Hilbert spaces with applications}},
doi = {10.1007/s00025-021-01381-x},
volume = {76},
year = {2021},
}
@article{9365,
abstract = {In this paper, we propose a new iterative method with alternated inertial step for solving split common null point problem in real Hilbert spaces. We obtain weak convergence of the proposed iterative algorithm. Furthermore, we introduce the notion of bounded linear regularity property for the split common null point problem and obtain the linear convergence property for the new algorithm under some mild assumptions. Finally, we provide some numerical examples to demonstrate the performance and efficiency of the proposed method.},
author = {Ogbuisi, Ferdinard U. and Shehu, Yekini and Yao, Jen Chih},
issn = {10294945},
journal = {Optimization},
publisher = {Taylor and Francis},
title = {{Convergence analysis of new inertial method for the split common null point problem}},
doi = {10.1080/02331934.2021.1914035},
year = {2021},
}
@article{9469,
abstract = {In this paper, we consider reflected three-operator splitting methods for monotone inclusion problems in real Hilbert spaces. To do this, we first obtain weak convergence analysis and nonasymptotic O(1/n) convergence rate of the reflected Krasnosel'skiĭ-Mann iteration for finding a fixed point of nonexpansive mapping in real Hilbert spaces under some seemingly easy to implement conditions on the iterative parameters. We then apply our results to three-operator splitting for the monotone inclusion problem and consequently obtain the corresponding convergence analysis. Furthermore, we derive reflected primal-dual algorithms for highly structured monotone inclusion problems. Some numerical implementations are drawn from splitting methods to support the theoretical analysis.},
author = {Iyiola, Olaniyi S. and Enyi, Cyril D. and Shehu, Yekini},
issn = {10294937},
journal = {Optimization Methods and Software},
publisher = {Taylor and Francis},
title = {{Reflected three-operator splitting method for monotone inclusion problem}},
doi = {10.1080/10556788.2021.1924715},
year = {2021},
}
@article{8817,
abstract = {The paper introduces an inertial extragradient subgradient method with self-adaptive step sizes for solving equilibrium problems in real Hilbert spaces. Weak convergence of the proposed method is obtained under the condition that the bifunction is pseudomonotone and Lipchitz continuous. Linear convergence is also given when the bifunction is strongly pseudomonotone and Lipchitz continuous. Numerical implementations and comparisons with other related inertial methods are given using test problems including a real-world application to Nash–Cournot oligopolistic electricity market equilibrium model.},
author = {Shehu, Yekini and Iyiola, Olaniyi S. and Thong, Duong Viet and Van, Nguyen Thi Cam},
issn = {14325217},
journal = {Mathematical Methods of Operations Research},
number = {2},
pages = {213--242},
publisher = {Springer Nature},
title = {{An inertial subgradient extragradient algorithm extended to pseudomonotone equilibrium problems}},
doi = {10.1007/s00186-020-00730-w},
volume = {93},
year = {2021},
}