Keywords: parametric optimization; point-to-set mappings; regions of stability; input optimization; optimality conditions; Lagrange multipliers; marginal value
@article{10_21136_AM_1988_104325,
author = {Huang, Sheng and Zlobec, Sanjo},
title = {New regions of stability in input optimization},
journal = {Applications of Mathematics},
pages = {470--486},
year = {1988},
volume = {33},
number = {6},
doi = {10.21136/AM.1988.104325},
mrnumber = {0973241},
zbl = {0664.90085},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1988.104325/}
}
TY - JOUR AU - Huang, Sheng AU - Zlobec, Sanjo TI - New regions of stability in input optimization JO - Applications of Mathematics PY - 1988 SP - 470 EP - 486 VL - 33 IS - 6 UR - http://geodesic.mathdoc.fr/articles/10.21136/AM.1988.104325/ DO - 10.21136/AM.1988.104325 LA - en ID - 10_21136_AM_1988_104325 ER -
Huang, Sheng; Zlobec, Sanjo. New regions of stability in input optimization. Applications of Mathematics, Tome 33 (1988) no. 6, pp. 470-486. doi: 10.21136/AM.1988.104325
[1] B. Bank J. Guddat D. Klatte B. Kummer K. Tammer: Nonlinear Parametric Optimization. Akademie-Verlag, Berlin, 1982. | MR
[2] A. Ben-Israel A. Ben-Tal S. Zlobec: Optimality in Nonlinear Programming: A Feasible Directions Approach. Wiley-Interscience, New York, 1981. | MR
[3] C. Berge: Espace Topologiques, fonctions multivogues. Dunod, Paris, 1959. | MR
[4] I. Cojocaru: Regions de stabilité dans la programmation linéaire. An. Univ. Bucuresti Mat. 34 (1985), 12-21. | MR | Zbl
[5] I. I. Eremin N. N. Astafiev: Introduction to the Theory of Linear and Convex Programming. Nauka, Moscow, 1976. (In Russian.) | MR
[6] W. W. Hogan: Point-to-set maps in mathematical programming. SIAM Review 15 (1973), 591-603. | DOI | MR | Zbl
[7] D. Klatte: On the lower semicontinuity of optimal sets in convex parametric optimization. Mathematical Programming Studies 10 (1979), 104-109. | DOI | MR | Zbl
[8] D. Klatte: A sufficient condition for lower semicontinuity of solution sets of systems of convex inequalities. Mathematical Programming Study 21 (1984), 139-149. | DOI | MR | Zbl
[9] D. Klatte: On stability of local and global optimal solutions in parametric problems of nonlinear programming. In: Parametric Optimization and Methods of Approximation for Ill-posed Problems in Mathematical Programming. Academy of Sciences U.S.S.R. The Ural Scientific Institute (1985), 120-132. (In Russian.) | MR
[10] F. Nožička J. Guddat H. Hollatz B. Bank: Theorie der linearen parametrischen Optimierung. Akademie-Verlag, Berlin, 1974.
[11] J. Petrič S. Zlobec: Nonlinear Programming. Naučna Knjiga, Belgrade, 1983. (In Serbo-Croatian.)
[12] J. Semple S. Zlobec: Continuity of a Lagrangian multiplier function in input optimization. Mathematical Programming 34 (1986), 362-269. | DOI | MR
[13] J. Semple S. Zlobec: On a necessary condition for stability in perturbed linear and convex programming. Zeitschrift für Operations Research, Series A: Theory 31 (1987) 161-172. | MR
[14] J. Semple S. Zlobec: Continuity of "non-standard" Lagrange multiplier functions in input optimization. UNISA Report 34/86 (14), June 1986. (To be published.) | MR
[15] C. Zidaroiu: Regions of stability for random decision systems with complete connections. An. Univ. Bucuresti Mat. 34 (1985), 87-97. | MR | Zbl
[16] S. Zlobec: Regions of stability for ill-posed convex programs. Aplikace Matematiky 27 (1982), 176-191. | MR | Zbl
[17] S. Zlobec: Characterizing an optimal input in perturbed convex programming. Mathematical Programming 25 (1983), 109-121. | DOI | MR | Zbl
[18] S. Zlobec: Input optimization: I. Optimal realizations of mathematical models. Mathematical Programming 31 (1985), 245-268. | DOI | MR | Zbl
[19] S. Zlobec: Regions of stability for ill-posed convex programs: An addendum. Aplikace Matematiky 31 (1968), 109-117. | MR
[20] S. Zlobec: Characterizing an optimal input in perturbed convex programming: Corrigendum. Mathematical Programming 35 (1986), 368-371. | DOI | MR | Zbl
[21] S. Zlobec: Input optimization: III. Optimal realizations of multi-objective models. Optimization 17 (1986), 429-445. | DOI | MR
[22] S. Zlobec: Survey of input optimization. Optimization 18 (1987), 309-348. | DOI | MR | Zbl
[23] S. Zlobec: An index condition in input optimization. Utilitas Mathematica 33 (1988), 183-192. | MR | Zbl
[24] S. Zlobec. A. Ben-Israel: Perturbed convex programs: Continuity of optimal solutions and optimal values. In: Methods of Operations Research (Proceedings of the III Symposium on Operations Research). Verlag Athenaum/Hain/Scriptor/Hanstein 31 (1979), 739-749. | Zbl
[25] S. Zlobec R. Gardner A. Ben-Israel: Regions of stability for arbitrarily perturbed convex programs. In: Mathematical Programming with Data Perturbations. M. Dekker, New York (1981), 69-89. | MR
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