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Keywords:
parametric optimization; point-to-set mappings; regions of stability; input optimization; optimality conditions; Lagrange multipliers; marginal value
parametric optimization; point-to-set mappings; regions of stability; input optimization; optimality conditions; Lagrange multipliers; marginal value
Summary:
using point-to-set mappings we identify two new regions of stability in input optimization. Then we extend various results from the literature on optimality conditions, continuity of Lagrange multipliers, and the marginal value formula over the new and some old regions of stability.
References:
[1] B. Bank J. Guddat D. Klatte B. Kummer K. Tammer: Nonlinear Parametric Optimization. Akademie-Verlag, Berlin, 1982. MR 0701243
[2] A. Ben-Israel A. Ben-Tal S. Zlobec: Optimality in Nonlinear Programming: A Feasible Directions Approach. Wiley-Interscience, New York, 1981. MR 0607673
[3] C. Berge: Espace Topologiques, fonctions multivogues. Dunod, Paris, 1959. MR 0105663
[4] I. Cojocaru: Regions de stabilité dans la programmation linéaire. An. Univ. Bucuresti Mat. 34 (1985), 12-21. MR 0808044 | Zbl 0584.90054
[5] I. I. Eremin N. N. Astafiev: Introduction to the Theory of Linear and Convex Programming. Nauka, Moscow, 1976. (In Russian.) MR 0475825
[6] W. W. Hogan: Point-to-set maps in mathematical programming. SIAM Review 15 (1973), 591-603. DOI 10.1137/1015073 | MR 0345641 | Zbl 0256.90042
[7] D. Klatte: On the lower semicontinuity of optimal sets in convex parametric optimization. Mathematical Programming Studies 10 (1979), 104-109. DOI 10.1007/BFb0120847 | MR 0527061 | Zbl 0404.90087
[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 10.1007/BFb0121216 | MR 0751248 | Zbl 0562.90088
[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 0841542
[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 10.1007/BF01582236 | MR 0839610
[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 0917933
[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 0839610
[15] C. Zidaroiu: Regions of stability for random decision systems with complete connections. An. Univ. Bucuresti Mat. 34 (1985), 87-97. MR 0808053 | Zbl 0573.93077
[16] S. Zlobec: Regions of stability for ill-posed convex programs. Aplikace Matematiky 27 (1982), 176-191. MR 0658001 | Zbl 0482.90073
[17] 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
[18] S. Zlobec: Input optimization: I. Optimal realizations of mathematical models. Mathematical Programming 31 (1985), 245-268. DOI 10.1007/BF02591948 | MR 0783391 | Zbl 0589.90068
[19] S. Zlobec: Regions of stability for ill-posed convex programs: An addendum. Aplikace Matematiky 31 (1968), 109-117. MR 0837472
[20] S. Zlobec: Characterizing an optimal input in perturbed convex programming: Corrigendum. Mathematical Programming 35 (1986), 368-371. DOI 10.1007/BF01580887 | MR 0850381 | Zbl 0606.90109
[21] S. Zlobec: Input optimization: III. Optimal realizations of multi-objective models. Optimization 17 (1986), 429-445. DOI 10.1080/02331938608843153 | MR 0843034
[22] S. Zlobec: Survey of input optimization. Optimization 18 (1987), 309-348. DOI 10.1080/02331938708843243 | MR 0882514 | Zbl 0633.90077
[23] S. Zlobec: An index condition in input optimization. Utilitas Mathematica 33 (1988), 183-192. MR 0936175 | Zbl 0655.90075
[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 0405.90071
[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 0652938
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