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- Title
Informative lagrange Multipliers in nonlinear parametric programming models.
- Authors
Jie, Tao; Yan, Gao
- Abstract
The minimum norm Lagrange multiplier, as a type of informative Lagrange multiplier, is proposed to replace the classical shadow price when the later fails to exist. This kind of multiplier expresses the rate of cost improvement when the right-hand side of the constraints are permitted to slightly violated. However, the minimum norm Lagrange multiplier may fail to be informative in fully parametric optimization problems. In this paper, we extend the classical constraint violation condition to a general formulation, which captures the characteristics of the problem structure of nonlinear parametric programming models. Based on the generalized constraint violation condition, we provide sufficient conditions for the minimum norm Lagrange multiplier to be informative. Furthermore, we propose a kind of penalty function method to derive the informative Lagrange multiplier in fully parametric programming models, which means that the perturbations are not only on the right-hand side of the constraints. Finally, we use examples to support our theoretic results.
- Subjects
NONLINEAR programming; LAGRANGE multiplier; PARAMETRIC modeling; PRICES; NONLINEAR equations
- Publication
Journal of Industrial & Management Optimization, 2024, Vol 20, Issue 4, p1
- ISSN
1547-5816
- Publication type
Article
- DOI
10.3934/jimo.2023134