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Sensitivity analysis in linear semi-infinite programming via partitions
- Publication Year :
- 2009
- Publisher :
- INFORMS (Institute for Operations Research and Management Sciences), 2009.
-
Abstract
- This paper provides sufficient conditions for the optimal value function of a given linear semi-infinite programming (LSIP) problem to depend linearly on the size of the perturbations, when these perturbations involve either the cost coefficients or the right-hand side function or both, and they are sufficiently small. Two kinds of partitions are considered. The first concerns the effective domain of the optimal value as a function of the cost coefficients and consists of maximal regions on which this value function is linear. The second class of partitions considered in this paper concerns the index set of the constraints through a suitable extension of the concept of optimal partition from ordinary to LSIP. These partitions provide convex sets, in particular, segments, on which the optimal value is a linear function of the size of the perturbations, for the three types of perturbations considered in this paper. Research of the first author was supported by MEC and FEDER, Grant MTM2005-08572-C03-01; the second author was supported by NSERC, MITACS, the Canada Research Chair Program, and a grant from Lehigh University; the third author was partially supported by CONACyT of MX.Grant 55681.
- Subjects :
- Mathematical optimization
Linear programming
General Mathematics
Regular polygon
Linear semi-infinite programming
Management Science and Operations Research
Semi-infinite programming
Computer Science Applications
Linear-fractional programming
Effective domain
Optimal value function
Bellman equation
Estadística e Investigación Operativa
Applied mathematics
Partition (number theory)
Sensitivity analysis
Mathematics
Subjects
Details
- Language :
- Spanish; Castilian
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....046995899ab90006acee6f6b91887ed3