Two Optimal Value Functions in Parametric Conic Linear Programming
We consider the conic linear program given by a closed convex cone in an Euclidean space and a matrix, where vector on the right-hand-side of the constraint system and the vector defining the objective function are subject to change. Using the strict feasibility condition, we prove the locally Lipsc...
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| Main Authors | , , |
|---|---|
| Format | Journal Article |
| Language | English |
| Published |
16.12.2020
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| Subjects | |
| Online Access | Get full text |
| DOI | 10.48550/arxiv.2012.09330 |
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| Abstract | We consider the conic linear program given by a closed convex cone in an
Euclidean space and a matrix, where vector on the right-hand-side of the
constraint system and the vector defining the objective function are subject to
change. Using the strict feasibility condition, we prove the locally Lipschitz
continuity and obtain some differentiability properties of the optimal value
function of the problem under right-hand-side perturbations. For the optimal
value function under linear perturbations of the objective function, similar
differentiability properties are obtained under the assumption saying that both
primal problem and dual problem are strictly feasible. |
|---|---|
| AbstractList | We consider the conic linear program given by a closed convex cone in an
Euclidean space and a matrix, where vector on the right-hand-side of the
constraint system and the vector defining the objective function are subject to
change. Using the strict feasibility condition, we prove the locally Lipschitz
continuity and obtain some differentiability properties of the optimal value
function of the problem under right-hand-side perturbations. For the optimal
value function under linear perturbations of the objective function, similar
differentiability properties are obtained under the assumption saying that both
primal problem and dual problem are strictly feasible. |
| Author | Yen, Nguyen Dong Luan, Nguyen Ngoc Kim, Do Sang |
| Author_xml | – sequence: 1 givenname: Nguyen Ngoc surname: Luan fullname: Luan, Nguyen Ngoc – sequence: 2 givenname: Do Sang surname: Kim fullname: Kim, Do Sang – sequence: 3 givenname: Nguyen Dong surname: Yen fullname: Yen, Nguyen Dong |
| BackLink | https://doi.org/10.48550/arXiv.2012.09330$$DView paper in arXiv |
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| Snippet | We consider the conic linear program given by a closed convex cone in an
Euclidean space and a matrix, where vector on the right-hand-side of the
constraint... |
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| SubjectTerms | Mathematics - Optimization and Control |
| Title | Two Optimal Value Functions in Parametric Conic Linear Programming |
| URI | https://arxiv.org/abs/2012.09330 |
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