Stability theory for linear inequality systems

SIAM Journal on Matrix Analysis and Applications

Volumn 17, Issue 4, 1996, Pages 730-743

  Goberna, M A ^a   Lopez, M A ^a   Todorov, M ^b  

^a UNIVERSITY OF ALICANTE   (Spain)

^b BULGARIAN ACADEMY OF SCIENCES   (Bulgaria)

Author keywords

Linear inequality systems; Semicontinuity; Stability

Indexed keywords

EID: 0030506537     PISSN: 08954798     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895479895259766     Document Type: Article

References (18)

1. E. J. ANDERSON AND P. NASH, Linear Programming in Infinite Dimensional Spaces, Wiley, New York, 1987.
2. B. BROSOWSKI, Parametric Semi-Infinite Optimization, Verlag Peter Lang, Frankfurt am Main, 1982.
3. _, Parametric semi-infinite linear programming I. Continuity of the feasible set and the optimal value, Math. Programming Study, 21 (1984), pp. 18-42.
4. G. CHRISTOV AND M. TODOROV, Semi-infinite optimization: Existence and uniqueness of the solution, Math. Balkanica, 2 (1988), pp. 182-191.
5. J. W. DANIEL, On perturbations in systems of linear inequalities, SIAM J. Numer. Anal., 10 (1973), pp. 299-307.
6. _, Remarks on perturbations in linear inequalities, SIAM J. Numer. Anal., 12 (1975), pp. 770-772.
7. I. I. EREMIN, Methods of parametrization in the analysis of improper mathematical programming problems, in Mathematical Research No. 35, Akademie-Verlag, Berlin, 1987, pp. 82-94.
8. T. FISCHER, Contributions to semi-infinite linear optimization, in Methoden und Verfahren der mathematischen Physik, Band 27, Verlag Peter Lang, Berlin, 1983, pp. 175-199.
9. M. A. GOBERNA AND M. A. LÓPEZ, A theory of the linear inequality systems, Linear Algebra Appl., 106 (1988), pp. 77-115.
10. M. A. GOBERNA, M. A. LÓPEZ, J. A. MIRA, AND J. VALLS, On the existence of solutions for linear inequality systems. J. Math. Anal. Appl., 192 (1995), pp. 133-150.
11. M. A. GOBERNA, M. A. LÓPEZ, AND J. T. PASTOR, Farkas-Minkowski systems in semi-infinite programming. Appl. Math. Optim., 7 (1981), pp. 295-308.
12. H. J. GREENBERG AND W. P. PIERSKALLA, Stability theorems for infinitely constrained mathematical programs, J. Opt. Theory Appl., 16 (1975), pp. 409-428.
13. S. HELBIG, Stability in disjunctive linear optimization I: Continuity of the feasible set, Optimization, 21 (1990), pp. 855-869.
14. S. M. ROBINSON. Normed convex processes, Trans. Amer. Math. Soc., 174 (1972), pp. 127-140.
15. _, Stability theory for systems of inequalities. Part I: Linear systems, SIAM J. Numer. Anal., 12 (1975), pp. 754-769.
16. R. T. ROCKAFELLAR, Convex Analysis, Princeton University Press, Princeton, NJ, 1970.
17. M. TODOROV, Generic existence and uniqueness of the solution set to linear semi-infinite optimization problems, Numer. Funct. Anal. Optim., 8 (1985-1986), pp. 541-556.
18. H. TUY, Stability property of a system of inequalities, Math. Operationsforsch. Statist. Optim., 8 (1977), pp. 27-39.