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On the convergence of conditional e-subgradient methods for convex programs and convex-concave saddle-point problems
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .ORCID iD: 0000-0003-2094-7376
2003 (English)In: European Journal of Operational Research, ISSN 0377-2217, E-ISSN 1872-6860, Vol. 151, no 3, 461-473 p.Article in journal (Refereed) Published
Abstract [en]

The paper provides two contributions. First, we present new convergence results for conditional e-subgradient algorithms for general convex programs. The results obtained here extend the classical ones by Polyak [Sov. Math. Doklady 8 (1967) 593, USSR Comput. Math. Math. Phys. 9 (1969) 14, Introduction to Optimization, Optimization Software, New York, 1987] as well as the recent ones in [Math. Program. 62 (1993) 261, Eur. J. Oper. Res. 88 (1996) 382, Math. Program. 81 (1998) 23] to a broader framework. Secondly, we establish the application of this technique to solve non-strictly convex-concave saddle point problems, such as primal-dual formulations of linear programs. Contrary to several previous solution algorithms for such problems, a saddle-point is generated by a very simple scheme in which one component is constructed by means of a conditional e-subgradient algorithm, while the other is constructed by means of a weighted average of the (inexact) subproblem solutions generated within the subgradient method. The convergence result extends those of [Minimization Methods for Non-Differentiable Functions, Springer-Verlag, Berlin, 1985, Oper. Res. Lett. 19 (1996) 105, Math. Program. 86 (1999) 283] for Lagrangian saddle-point problems in linear and convex programming, and of [Int. J. Numer. Meth. Eng. 40 (1997) 1295] for a linear-quadratic saddle-point problem arising in topology optimization in contact mechanics.

Place, publisher, year, edition, pages
2003. Vol. 151, no 3, 461-473 p.
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Mathematics
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URN: urn:nbn:se:liu:diva-22333DOI: 10.1016/S0377-2217(02)00629-XLocal ID: 1534OAI: oai:DiVA.org:liu-22333DiVA: diva2:242646
Available from: 2009-10-07 Created: 2009-10-07 Last updated: 2017-12-13

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Larsson, Torbjörn

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