TY - JOUR
AB - 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.
AU - Shehu, Yekini
AU - Iyiola, Olaniyi S.
AU - Thong, Duong Viet
AU - Van, Nguyen Thi Cam
ID - 8817
IS - 2
JF - Mathematical Methods of Operations Research
SN - 14322994
TI - An inertial subgradient extragradient algorithm extended to pseudomonotone equilibrium problems
VL - 93
ER -
TY - CONF
AB - 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.
AU - Bloch-Hansen, Andrew
AU - Samei, Nasim
AU - Solis-Oba, Roberto
ID - 9227
SN - 0302-9743
T2 - Conference on Algorithms and Discrete Applied Mathematics
TI - Experimental evaluation of a local search approximation algorithm for the multiway cut problem
VL - 12601
ER -
TY - JOUR
AB - In this paper, we present two new inertial projection-type methods for solving multivalued variational inequality problems in finite-dimensional spaces. We establish the convergence of the sequence generated by these methods when the multivalued mapping associated with the problem is only required to be locally bounded without any monotonicity assumption. Furthermore, the inertial techniques that we employ in this paper are quite different from the ones used in most papers. Moreover, based on the weaker assumptions on the inertial factor in our methods, we derive several special cases of our methods. Finally, we present some experimental results to illustrate the profits that we gain by introducing the inertial extrapolation steps.
AU - Izuchukwu, Chinedu
AU - Shehu, Yekini
ID - 9234
IS - 2
JF - Networks and Spatial Economics
KW - Computer Networks and Communications
KW - Software
KW - Artificial Intelligence
SN - 1566-113X
TI - New inertial projection methods for solving multivalued variational inequality problems beyond monotonicity
VL - 21
ER -
TY - JOUR
AB - 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.
AU - Iyiola, Olaniyi S.
AU - Shehu, Yekini
ID - 9315
IS - 2
JF - Results in Mathematics
SN - 14226383
TI - New convergence results for inertial Krasnoselskii–Mann iterations in Hilbert spaces with applications
VL - 76
ER -
TY - JOUR
AB - 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.
AU - Ogbuisi, Ferdinard U.
AU - Shehu, Yekini
AU - Yao, Jen Chih
ID - 9365
JF - Optimization
SN - 02331934
TI - Convergence analysis of new inertial method for the split common null point problem
ER -