Previous |  Up |  Next


convex optimization; marginal value formula; bi-convex mathematical model; regions of stability; Lagrange multiplier
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.
[1] I. I. Eremin N. N. Astafiev: Introduction to the Theory of Linear and Convex Programming. Nauka, Moscow, 1976. (In Russian.) MR 0475825
[2] V. G. Karmanov: Mathematical Programming. Nauka, Moscow, 1975. (In Russian.) MR 0411559 | Zbl 0349.90075
[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.
[5] S. Zlobec: Regions of stability for ill-posed convex programs. Aplikace Matematiky, 27 (1982), 176-191. MR 0658001 | Zbl 0482.90073
[6] S. Zlobec: Characterizing an optimal input in perturbed convex programming. Mathematical Programming, 25 (1983), 109-121. DOI 10.1007/BF02591721 | MR 0679256 | Zbl 0505.90077
[7] S. Zlobec: Characterizing an optimal input in perturbed convex programming: An addendum. (In preparation.)
[8] S. Zlobec: Input optimization: I. Optimal realizations of mathematical models. Mathematical Programming 31 (1985). DOI 10.1007/BF02591948 | MR 0783391 | Zbl 0589.90068
[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. MR 0548525
[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. MR 0652938
Partner of
EuDML logo