Name
Abstract | ||
|---|---|---|
This paper concerns with convergence properties of the classical proximal point algorithm for finding zeroes of maximal monotone operators in an infinite-dimensional Hilbert space. It is well known that the proximal point algorithm converges weakly to a solution un- der very mild assumptions. However, it was shown by Guler (11) that the iterates may fail to converge strongly in the infinite-dimensional case. We propose a new proximal-type algorithm which does converge strongly, provided the problem has a solution. Moreover, our algorithm solves proximal point subproblems inexactly, with a constructive stopping criterion introduced in (31). Strong convergence is forced by combining proximal point iterations with simple pro- jection steps onto intersection of two halfspaces containing the solution set. Additional cost of this extra projection step is essentially negligible since it amounts, at most, to solving a linear system of two equations in two unknowns. |
Year | DOI | Venue |
|---|---|---|
2000 | 10.1007/s101079900113 | Math. Program. |
Keywords | Field | DocType |
Key words: proximal point algorithm – Hilbert spaces – weak convergence – strong convergence Mathematics Subject Classification (1991): 49M45,90C25,90C33 | Hilbert space,Convergence (routing),Weak convergence,Mathematical optimization,Linear system,Mathematical analysis,Operator (computer programming),Solution set,Iterated function,Monotone polygon,Mathematics | Journal |
Volume | Issue | ISSN |
87 | 1 | 0025-5610 |
Citations | PageRank | References |
39 | 10.29 | 9 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| M. V. Solodov | 1 | 600 | 72.47 |
| B. F. Svaiter | 2 | 608 | 72.74 |