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Contribution Details
| Type | Journal Article |
| Scope | Discipline-based scholarship |
| Title | Projection-Based Local and Global Lipschitz Moduli of the Optimal Value in Linear Programming |
| Organization Unit | |
| Authors |
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| Item Subtype | Original Work |
| Refereed | Yes |
| Status | Published in final form |
| Language |
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| Journal Title | Journal of Optimization Theory and Applications |
| Publisher | Springer |
| Geographical Reach | international |
| ISSN | 1573-2878 |
| Volume | 193 |
| Number | 1-3 |
| Page Range | 280 - 299 |
| Date | 2022 |
| Abstract Text | In this paper, we use a geometrical approach to sharpen a lower bound given in [5] for the Lipschitz modulus of the optimal value of (finite) linear programs under tilt perturbations of the objective function. The key geometrical idea comes from orthogonally projecting general balls on linear subspaces. Our new lower bound provides a computable expression for the exact modulus (as far as it only depends on the nominal data) in two important cases: when the feasible set has extreme points and when we deal with the Euclidean norm. In these two cases, we are able to compute or estimate the global Lipschitz modulus of the optimal value function in different perturbations frameworks. |
| Digital Object Identifier | 10.1007/s10957-021-01948-2 |
| Other Identification Number | merlin-id:23118 |
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| Keywords | Applied Mathematics, Management Science and Operations Research, Control and Optimization |