id:"swepub:oai:gup.ub.gu.se/238192"
Search: id:"swepub:oai:gup.ub.gu.se/238192" > Ergodic, primal con...
- 1 of 1
- Previous record
- Next record
- To hitlist
Ergodic, primal convergence in dual subgradient schemes for convex programming, II: the case of inconsistent primal problems
-
- Önnheim, Magnus, 1985 (author)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences,Chalmers tekniska högskola,Chalmers University of Technology,University of Gothenburg,Chalmers, Sweden; University of Gothenburg, Sweden
-
- Gustavsson, Emil, 1987 (author)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences,University of Gothenburg,Chalmers tekniska högskola,Chalmers University of Technology,Chalmers, Sweden; University of Gothenburg, Sweden
-
- Strömberg, Ann-Brith, 1961 (author)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences,Chalmers tekniska högskola,Chalmers University of Technology,Chalmers, Sweden; University of Gothenburg, Sweden
- show more...
- show less...
- (creator_code:org_t)
- 2016-07-28
- 2017
- English.
- In: Mathematical programming. - : Springer Science and Business Media LLC. - 0025-5610 .- 1436-4646. ; 163:1, s. 57-84
- Journal article (peer-reviewed)
Abstract
Subject headings
Close
- Consider the utilization of a Lagrangian dual method which is convergent for consistent optimization problems. When it is used to solve an infeasible optimization problem, its inconsistency will then manifest itself through the divergence of the sequence of dual iterates. Will then the sequence of primal subproblem solutions still yield relevant information regarding the primal program? We answer this question in the affirmative for a convex program and an associated subgradient algorithm for its Lagrange dual. We show that the primal–dual pair of programs corresponding to an associated homogeneous dual function is in turn associated with a saddle-point problem, in which—in the inconsistent case—the primal part amounts to finding a solution in the primal space such that the Euclidean norm of the infeasibility in the relaxed constraints is minimized; the dual part amounts to identifying a feasible steepest ascent direction for the Lagrangian dual function. We present convergence results for a conditional ε-subgradient optimization algorithm applied to the Lagrangian dual problem, and the construction of an ergodic sequence of primal subproblem solutions; this composite algorithm yields convergence of the primal–dual sequence to the set of saddle-points of the associated homogeneous Lagrangian function; for linear programs, convergence to the subset in which the primal objective is at minimum is also achieved.
Subject headings
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
Keyword
- inconsistent convex program
- Lagrange dual
- homogeneous Lagrangian function
- subgradient algorithm
- ergodic primal sequence
- subgradient algorithm
Publication and Content Type
- ref (subject category)
- art (subject category)
Find in a library
- Mathematical programming (Search for host publication in LIBRIS)
To the university's database
- 1 of 1
- Previous record
- Next record
- To hitlist
Find more in SwePub
- By the author/editor
- Önnheim, Magnus, ...
- Gustavsson, Emil ...
- Strömberg, Ann-B ...
- Patriksson, Mich ...
- Larsson, Torbjör ...
- About the subject
-
- NATURAL SCIENCES
- NATURAL SCIENCES
- and Mathematics
- and Computational Ma ...
- Articles in the publication
- Mathematical pro ...
- By the university
- University of Gothenburg
- Chalmers University of Technology
- Linköping University
Search outside SwePub
- Extend your search to:
- Google Book Search
- Google Scholar
Kungliga biblioteket hanterar dina personuppgifter i enlighet med EU:s dataskyddsförordning (2018), GDPR. Läs mer om hur det funkar här.
Så här hanterar KB dina uppgifter vid användning av denna tjänst.
- Copyright © LIBRIS - National Library Systems
- LIBRIS.kb.se
