NEW PRIMAL-DUAL PARTITION OF THE SPACE OF LINEAR SEMI-INFINITE CONTINUOUS OPTIMIZATION PROBLEMS

• Published in: Comptes rendus de l'Academie bulgare des Sciences Vol. 69; no. 10; p. 1263
• Main Authors: Barragan, Abraham B, Hernandez, Lidia A, Todorov, Maxim I
• Format: Journal Article
• Language: English
• Published: Bulgarian Academy of Sciences 01.01.2016
• ISSN: 1310-1331

In this paper we consider the set of all linear semi-infinite programming problems with a fixed compact set of indices and continuous right and left hand side coefficients. In the whole parameter space, the problems are classified in a different manner. F.i., in our case, consistent and inconsistent, solvable (with bounded optimal value and optimal set non-empty), unsolvable (with bounded optimal value and empty optimal set) and unbounded (i.e., with infinity optimal value), etc. Various different partitions have been considered in previous papers. In the majority of them, the classification is made for both the primal and the dual problems. Our classification generates a partition of the parameter space, which we call second general primal-dual partition. We have tried to characterize each cell of the partition by means of necessary and sufficient, and in some cases only necessary or sufficient conditions, which guarantee that the pair of problems (primal and dual) belongs to the cell. In addition, we show that each cell of the partition is non empty and with suitable examples we demonstrate that the conditions are only necessary or sufficient. Finally, we present a study of the stability of the presented partition.Key words: Linear semi-infinite programming, parameter space of continuous problems, primal-dual partition, stability properties2010 Mathematics Subject Classification: 90C05, 90C34, 90C31, 90C46