Constructing the set of efficient objective values in multiple objective linear programs (Q918870)

The work is devoted to obtain proper descriptions for the set of all feasible objective values in finite vectorial multiple objective linear programs \[ (MOLP) \text{ ``maximize'' \(Cx\) subject to } x\in X \] where \(X=\{x\in R^ n:\) Ax\(\leq b\}\) and C is a linear mapping from \(R^ n\) to \(R^ k\) identified with a \(k\times n\) matrix (Proposition 3.1, Proposition 3.2) and to the elaboration of numerical algorithms for computing the range of C (Section 2), its efficient structure and the image of the polyhedron X by C (Section 3). The authors construct also a polyhedron which has the same efficient points as the set of objective values and all of its extreme points are Pareto-efficient. We note that it is not possible to transfer the results to infinite dimensional spaces.