Regions of stability for ill-posed convex programs: An addendum

Sanjo Zlobec

Aplikace matematiky (1986)

  • Volume: 31, Issue: 2, page 109-117
  • ISSN: 0862-7940

Abstract

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The marginal value formula in convex optimization holds in a more restrictive region of stability than that recently claimed in the literature. This is due to the fact that there are regions of stability where the Lagrangian multiplier function is discontinuous even for linear models.

How to cite

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Zlobec, Sanjo. "Regions of stability for ill-posed convex programs: An addendum." Aplikace matematiky 31.2 (1986): 109-117. <http://eudml.org/doc/15441>.

@article{Zlobec1986,
abstract = {The marginal value formula in convex optimization holds in a more restrictive region of stability than that recently claimed in the literature. This is due to the fact that there are regions of stability where the Lagrangian multiplier function is discontinuous even for linear models.},
author = {Zlobec, Sanjo},
journal = {Aplikace matematiky},
keywords = {convex optimization; marginal value formula; bi-convex mathematical model; regions of stability; Lagrange multiplier; convex optimization; marginal value formula; bi-convex mathematical model; regions of stability; Lagrange multiplier},
language = {eng},
number = {2},
pages = {109-117},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Regions of stability for ill-posed convex programs: An addendum},
url = {http://eudml.org/doc/15441},
volume = {31},
year = {1986},
}

TY - JOUR
AU - Zlobec, Sanjo
TI - Regions of stability for ill-posed convex programs: An addendum
JO - Aplikace matematiky
PY - 1986
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 31
IS - 2
SP - 109
EP - 117
AB - The marginal value formula in convex optimization holds in a more restrictive region of stability than that recently claimed in the literature. This is due to the fact that there are regions of stability where the Lagrangian multiplier function is discontinuous even for linear models.
LA - eng
KW - convex optimization; marginal value formula; bi-convex mathematical model; regions of stability; Lagrange multiplier; convex optimization; marginal value formula; bi-convex mathematical model; regions of stability; Lagrange multiplier
UR - http://eudml.org/doc/15441
ER -

References

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  1. I. I. Eremin N. N. Astafiev, Introduction to the Theory of Linear and Convex Programming, Nauka, Moscow, 1976. (In Russian.) (1976) MR0475825
  2. V. G. Karmanov, Mathematical Programming, Nauka, Moscow, 1975. (In Russian.) (1975) Zbl0349.90075MR0411559
  3. J. Semple S. Zlobec, Continuity of the Lagrangian multiplier function in input optimization, Mathematical Programming, (forthcoming). 
  4. L. I. Trudzik, Optimization in Abstract Spaces, Ph. D. Thesis, University of Melbourne, 1983. (1983) 
  5. S. Zlobec, Regions of stability for ill-posed convex programs, Aplikace Matematiky, 27 (1982), 176-191. (1982) Zbl0482.90073MR0658001
  6. S. Zlobec, 10.1007/BF02591721, Mathematical Programming, 25 (1983), 109-121. (1983) Zbl0505.90077MR0679256DOI10.1007/BF02591721
  7. S. Zlobec, Characterizing an optimal input in perturbed convex programming: An addendum, (In preparation.) 
  8. S. Zlobec, 10.1007/BF02591948, Mathematical Programming 31 (1985). (1985) Zbl0589.90068MR0783391DOI10.1007/BF02591948
  9. S. Zlobec, Input optimization: II. A numerical method, (In preparation.) 
  10. S. Zlobec A. Ben-Israel, Perturbed convex programming: Continuity of optimal solutions and optimal values, Operations Research Verfahren XXXI (1979), 737-749. (1979) MR0548525
  11. S. Zlobec R. Gardner A. Ben-Israel, Regions of stability for arbitrarily perturbed convex programs, in: Mathematical Programming with Data Perturbations I (A. Fiacco, editor), M. Dekker, New York (1982), 69-89. (1982) MR0652938

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