Scienti c activity report for the research grant Regularity and sensitivity in multicriteria optimization PN-II-ID-PCE-2011-3-0084, nr. 239/05.10.2011

Error bounds for vector-linear programming (documentation) Metric regularity and constraint quali\u85cation conditions (documentation) Concerning the \u85rst objective, i.e., Error bounds for vector-linear programming, we \u85rstly mention a celebrated result of Ho¤man (1952) which considers the system of linear inequalities and equations: Ay a By = b where A;B are l n; m n real matrices and a 2 Rl; b 2 Rm: When the solution set S of the above system is nonempty, it is proved that there exists some > 0 such that d(y; S) (k(Ay a)+k+ kBy bk) 8y 2 Rn; i.e. a global error bound was found for the violation of the constraints. The Ho¤mans fundamental result was further extended by several authors in many nonlinear settings which involve convexity and/or set-valued maps. We intend to extend the study of the error bounds for vector-linear programming. Since it is known to exist strong links between the general topic of error bounds and the study of sharp minima (see, for instance, [1]) we shall concentrate on both of these questions in vectoria