Vietnam Journal of Mathematics

, Volume 43, Issue 2, pp 471–486

# The Adaptive Parameter Control Method and Linear Vector Optimization

Article

## Abstract

The question of constructing a set of equidistant points, with a given small approximate distance, in the efficient and weakly efficient frontiers of a linear vector optimization problem of a general form, is considered in this paper. It is shown that the question can be solved by combining Pascoletti–Serafini’s scalarization method (1984) and Eichfelder’s adaptive parameter control method (2009) with a sensitivity analysis formula in linear programming, which was obtained by J. Gauvin (2001). Our investigation shows that one can avoid the strong second-order sufficient condition used by G. Eichfelder, which cannot be imposed on linear vector optimization problems.

## Keywords

Vector optimization Linear vector optimization Pascoletti–Serafini’s scalarization method Eichfelder’s adaptive parameter control method Sensitivity analysis in linear programming

## Mathematics Subject Classification (2010)

90C29 90C31 90C05

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