132,280 research outputs found
New Douglas-Rachford algorithmic structures and their convergence analyses
In this paper we study new algorithmic structures with Douglas- Rachford (DR)
operators to solve convex feasibility problems. We propose to embed the basic
two-set-DR algorithmic operator into the String-Averaging Projections (SAP) and
into the Block-Iterative Pro- jection (BIP) algorithmic structures, thereby
creating new DR algo- rithmic schemes that include the recently proposed cyclic
Douglas- Rachford algorithm and the averaged DR algorithm as special cases. We
further propose and investigate a new multiple-set-DR algorithmic operator.
Convergence of all these algorithmic schemes is studied by using properties of
strongly quasi-nonexpansive operators and firmly nonexpansive operators.Comment: SIAM Journal on Optimization, accepted for publicatio
A von Neumann Alternating Method for Finding Common Solutions to Variational Inequalities
Modifying von Neumann's alternating projections algorithm, we obtain an
alternating method for solving the recently introduced Common Solutions to
Variational Inequalities Problem (CSVIP). For simplicity, we mainly confine our
attention to the two-set CSVIP, which entails finding common solutions to two
unrelated variational inequalities in Hilbert space.Comment: Nonlinear Analysis Series A: Theory, Methods & Applications, accepted
for publicatio
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