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Global optimality c...
Global optimality conditions for discrete and nonconvex optimization-with applications to Lagrangian heuristics and column generation
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- Larsson, Torbjörn, 1957- (författare)
- Linköpings universitet,Tekniska högskolan,Optimeringslära
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- Patriksson, Michael (författare)
- Matematiska vetenskaper Chalmers tekniska högskola
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(creator_code:org_t)
- Institute for Operations Research and the Management Sciences (INFORMS), 2006
- 2006
- Engelska.
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Ingår i: Operations Research. - : Institute for Operations Research and the Management Sciences (INFORMS). - 0030-364X .- 1526-5463. ; 54:3, s. 436-453
- Relaterad länk:
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https://urn.kb.se/re...
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visa fler...
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https://doi.org/10.1...
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Abstract
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- The well-known and established global optimality conditions based on the Lagrangian formulation of an optimization problem are consistent if and only if the duality gap is zero. We develop a set of global optimality conditions that are structurally similar but are consistent for any size of the duality gap. This system characterizes a primal-dual optimal solution by means of primal and dual feasibility, primal Lagrangian ε-optimality, and, in the presence of inequality constraints, a relaxed complementarity condition analogously called δ-complementarity. The total size ε + δ of those two perturbations equals the size of the duality gap at an optimal solution. Further, the characterization is equivalent to a near-saddle point condition which generalizes the classic saddle point characterization of a primal-dual optimal solution in convex programming. The system developed can be used to explain, to a large degree, when and why Lagrangian heuristics for discrete optimization are successful in reaching near-optimal solutions. Further, experiments on a set-covering problem illustrate how the new optimality conditions can be utilized as a foundation for the construction of new Lagrangian heuristics. Finally, we outline possible uses of the optimality conditions in column generation algorithms and in the construction of core problems. © 2006 INFORMS.
Ämnesord
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Nyckelord
- MATHEMATICS
- MATEMATIK
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