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- Önnheim, Magnus,1985Gothenburg 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 (author)
Ergodic, primal convergence in dual subgradient schemes for convex programming, II: the case of inconsistent primal problems
- Article/chapterEnglish2017
Publisher, publication year, extent ...
- 2016-07-28
- Springer Science and Business Media LLC,2017
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- LIBRIS-ID:oai:gup.ub.gu.se/238192
- https://gup.ub.gu.se/publication/238192URI
- https://doi.org/10.1007/s10107-016-1055-xDOI
- https://research.chalmers.se/publication/238192URI
- https://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-137082URI
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- Language:English
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- Funding Agencies|Swedish Natural Science Research Council (NFR); Swedish Energy Agency, Chalmers University of Technology, University of Gothenburg; Linkoping University
- 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 and genre
- NATURVETENSKAP Matematik Beräkningsmatematik hsv//swe
- NATURAL SCIENCES Mathematics Computational Mathematics hsv//eng
- inconsistent convex program
- Lagrange dual
- homogeneous Lagrangian function
- subgradient algorithm
- ergodic primal sequence
- subgradient algorithm
Added entries (persons, corporate bodies, meetings, titles ...)
- Gustavsson, Emil,1987Gothenburg 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(Swepub:cth)emilg (author)
- Strömberg, Ann-Brith,1961Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences,Chalmers tekniska högskola,Chalmers University of Technology,Chalmers, Sweden; University of Gothenburg, Sweden(Swepub:cth)anstr (author)
- Patriksson, Michael,1964Gothenburg 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(Swepub:cth)mipat (author)
- Larsson, TorbjörnLinköpings universitet,Optimeringslära,Tekniska fakulteten(Swepub:liu)torla64 (author)
- Göteborgs universitetInstitutionen för matematiska vetenskaper (creator_code:org_t)
Related titles
- In:Mathematical programming: Springer Science and Business Media LLC163:1, s. 57-840025-56101436-4646
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- https://link.springer.com/content/pdf/10.1007%2Fs10107-016-1055-x.pdf
- https://research.chalmers.se/publication/238192/file/238192_Fulltext.pdfFULLTEXT
- https://liu.diva-portal.org/smash/get/diva2:1093282/FULLTEXT01.pdffulltext:print
- https://gup.ub.gu.se/publication/238192
- https://doi.org/10.1007/s10107-016-1055-x
- https://research.chalmers.se/publication/238192
- https://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-137082
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