Analysis of the sensitivity of an efficient solution of a vector Boolean problem of the minimization of projections of linear functions onto \(\mathbb R_+\) and \(\mathbb R_-\). (Russian) Zbl 1249.90165

Emelichev, V. A.; Kuz’min, K. G.

Diskretn. Anal. Issled. Oper., Ser. 2 12, No. 2, 24-43 (2005).

Summary: We consider the vector Boolean problem of finding a Pareto set for which both positive and negative linear cut-off functions are treated as partial criteria. We prove a formula for the limit level of perturbations in the parameter space of these functions equipped with the \(l_1\)-metric that preserve the efficiency (i.e., Pareto optimality) of the solution. As a consequence, we obtain necessary and sufficient conditions for the problem to be stable.

MSC:

90C09

Boolean programming

Keywords:

Pareto set; nonpositive orthant