TY - CHAP

T1 - Some Extragradient Methods for Solving Variational Inequalities Using Bregman Projection and Fixed Point Techniques in Reflexive Banach Spaces

AU - Olakunle Jolaoso, Lateef

N1 - Publisher Copyright:
© 2021, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

PY - 2021

Y1 - 2021

N2 - In this chapter, we introduce some extragradient methods for solving variational inequalities using Bregman projections and a fixed point technique in reflexive Banach spaces. These algorithms are extensions of the prototypes which have been studied extensively in real Hilbert and 2-uniformly convex Banach spaces. We emphasize that there are some applicable examples (most especially in mechanics) which can be modelled as variational inequalities in reflexive Banach spaces outside Hilbert and 2-uniformly convex Banach spaces. Moreover, the usage of Bregman projections allows the consideration of more general structures of the feasible set. The convergence analysis of the algorithms are given using Bregman distance and fixed point techniques. More so, we present some computational examples to illustrate the effects of various type of convex functions on the proposed algorithm.

AB - In this chapter, we introduce some extragradient methods for solving variational inequalities using Bregman projections and a fixed point technique in reflexive Banach spaces. These algorithms are extensions of the prototypes which have been studied extensively in real Hilbert and 2-uniformly convex Banach spaces. We emphasize that there are some applicable examples (most especially in mechanics) which can be modelled as variational inequalities in reflexive Banach spaces outside Hilbert and 2-uniformly convex Banach spaces. Moreover, the usage of Bregman projections allows the consideration of more general structures of the feasible set. The convergence analysis of the algorithms are given using Bregman distance and fixed point techniques. More so, we present some computational examples to illustrate the effects of various type of convex functions on the proposed algorithm.

UR - http://www.scopus.com/inward/record.url?scp=85122462204&partnerID=8YFLogxK

U2 - 10.1007/978-981-16-4896-0_8

DO - 10.1007/978-981-16-4896-0_8

M3 - Chapter

AN - SCOPUS:85122462204

T3 - Forum for Interdisciplinary Mathematics

SP - 159

EP - 183

BT - Forum for Interdisciplinary Mathematics

PB - Springer

ER -