On dual vector optimization and shadow prices

Letizia Pellegrini

RAIRO - Operations Research (2010)

  • Volume: 38, Issue: 4, page 305-317
  • ISSN: 0399-0559

Abstract

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In this paper we present the image space analysis, based on a general separation scheme, with the aim of studying Lagrangian duality and shadow prices in Vector Optimization. Two particular kinds of separation are considered; in the linear case, each of them is applied to the study of sensitivity analysis, and it is proved that the derivatives of the perturbation function can be expressed in terms of vector Lagrange multipliers or shadow prices.

How to cite

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Pellegrini, Letizia. "On dual vector optimization and shadow prices." RAIRO - Operations Research 38.4 (2010): 305-317. <http://eudml.org/doc/105317>.

@article{Pellegrini2010,
abstract = { In this paper we present the image space analysis, based on a general separation scheme, with the aim of studying Lagrangian duality and shadow prices in Vector Optimization. Two particular kinds of separation are considered; in the linear case, each of them is applied to the study of sensitivity analysis, and it is proved that the derivatives of the perturbation function can be expressed in terms of vector Lagrange multipliers or shadow prices. },
author = {Pellegrini, Letizia},
journal = {RAIRO - Operations Research},
keywords = {Vector Optimization; image space; Lagrangian duality; shadow prices.; vector optimization; shadow prices},
language = {eng},
month = {3},
number = {4},
pages = {305-317},
publisher = {EDP Sciences},
title = {On dual vector optimization and shadow prices},
url = {http://eudml.org/doc/105317},
volume = {38},
year = {2010},
}

TY - JOUR
AU - Pellegrini, Letizia
TI - On dual vector optimization and shadow prices
JO - RAIRO - Operations Research
DA - 2010/3//
PB - EDP Sciences
VL - 38
IS - 4
SP - 305
EP - 317
AB - In this paper we present the image space analysis, based on a general separation scheme, with the aim of studying Lagrangian duality and shadow prices in Vector Optimization. Two particular kinds of separation are considered; in the linear case, each of them is applied to the study of sensitivity analysis, and it is proved that the derivatives of the perturbation function can be expressed in terms of vector Lagrange multipliers or shadow prices.
LA - eng
KW - Vector Optimization; image space; Lagrangian duality; shadow prices.; vector optimization; shadow prices
UR - http://eudml.org/doc/105317
ER -

References

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  1. S. Bolintineanu and B.D. Craven, Linear multicriteria sensitivity and shadow costs. Optimization26 (1992) 115–127.  Zbl0817.90087
  2. M. Ehrgott, Multicriteria Optimization. Springer, Lect. Not. Econom. Math. Syst.491 (2000).  Zbl0956.90039
  3. F. Giannessi, Theorems of the alternative, quadratic programs and complementarity problems, in Variational Inequalities and Complementarity Problems, edited by R.W. Cottle et al. J. Wiley (1980) 151–186.  Zbl0484.90081
  4. F. Giannessi, Theorems of the alternative and optimality conditions. J. Optim. Theor. Appl.42 (1984) 331–365.  Zbl0504.49012
  5. F. Giannessi, G. Mastroeni and L. Pellegrini, On the theory of vector optimization and variational inequalities. Image space analysis and separation, in Vector Variational Inequalities and Vector Equilibria. Mathematical Theories, edited by F. Giannessi. Kluwer Acad. Publ. (2000) 153–215.  Zbl0985.49005
  6. H. Isermann, On some relations between a dual pair of multiple objective linear programs. Z. Oper. Res.22 (1978) 33–41.  Zbl0375.90049
  7. O.L. Mangasarian, Nonlinear Programming. SIAM Classics Appl. Math.10 (1994).  
  8. L. Pellegrini, On Lagrangian duality in vector optimization. Optimization. Submitted.  Zbl1114.90117
  9. T. Tanino, Sensitivity analysis in multiobjective optimization. J. Optim. Theor. Appl.56 (1988) 479–499.  Zbl0619.90073
  10. W. Song, Duality for vector optimization of set valued functions. J. Math. Anal. Appl.201 (1996) 212–225.  Zbl0851.90110

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