On variable-step relaxed projection algorithm for variational inequalities

By Qingzhi Yang. 2005

117 citations recorded by the source corpus.

Projection algorithms are practically useful for solving variational inequalities (VI). However some among them require the knowledge related to VI in advance, such as Lipschitz constant. Usually it is impossible in practice. This paper studies the variable-step basic projection algorithm and its relaxed version under weakly co-coercive condition. The algorithms discussed need not know constant/function associated with the co-coercivity or weak co-coercivity and the step-size is varied from one iteration to the next. Under certain conditions the convergence of the variable-step basic projection algorithm is established. For the practical consideration, we also give the relaxed version of this algorithm, in which the projection onto a closed convex set is replaced by another projection at each iteration and latter is easy to calculate. The convergence of relaxed scheme is also obtained under certain assumptions. Finally we apply these two algorithms to the Split Feasibility Problem (SFP).

Subfields: Computational Mechanics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/47d23dca705f70b2aa3db411a01527b7f3dc0e6b

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In Computational Mechanics

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

An iterative regularization method for the solution of the split feasibility problem in Banach spaces (2008, methodology): “Relaxed projections have e.g. also been used by Byrne [20], Censor et al [22, 25], Qu and Xiu [44] and Yang [52, 53].”
Solving the split feasibility problem without prior knowledge of matrix norms (2012, background): “In fact, Yang [37] used this way and considered the following stepsize: τn := ρn ‖∇ f (xn)‖ , (1.”
Perturbed projections and subgradient projections for the multiple-sets split feasibility problem (2007, unknown): “…[9,10], where the linear split feasibility problem is studied, in Qu and Xiu [23] who modify algorithms by adopting Armijo-like searches, in Yang [29] where algorithms that do not depend on the calculation of the spectral radius of the matrix A T A are derived, in Yang and Zhao [30] where the…”