SIAM J. on Optimization

Keyword
DOI
Citation
Advanced Search

Search Content Type

article doi:

Citation:

Journal Description

Publication Info

ISSN info
Print: 1052-6234
Electronic: 1095-7189
Coden: SJOPE8

The SIAM Journal on Optimization contains research articles on the theory and practice of optimization. The areas addressed include linear and quadratic programming, convex programming, nonlinear programming, complementarity problems, stochastic optimization, combinatorial optimization, integer programming, and convex, nonsmooth and variational analysis. Contributions may emphasize optimization theory, algorithms, software, computational practice, applications, or the links between these subjects.

Featured Article

Fixed Points of Averages of Resolvents: Geometry and Algorithms

To provide generalized solutions if a given problem admits no actual solution is an important task in mathematics and the natural sciences. It has a rich history dating back to the early 19th century, when Carl Friedrich Gauss developed the method of least squares of a system of linear equations—its solutions can be viewed as fixed points of averaged projections onto hyperplanes. A powerful generalization of this problem is to find fixed points of averaged resolvents (i.e., firmly nonexpansive mappings). This paper concerns the relationship between the set of fixed points of averaged resolvents and certain fixed point sets of compositions of resolvents. It partially extends recent work for two mappings on a question of C. Byrne. The analysis suggests a reformulation in a product space. Algorithmic consequences are also presented.

SIAM J. Optim. 22, pp. 24-40