On stability of an efficient solution of a vector Boolean problem of maximisation of absolute values of linear functions

Abstract

We consider a vector (multicriteria) problem of Boolean programming in the case where the partial criteria are the absolute values of linear functions. We study the limit level of disturbances of the coefficients of criterion functions in the space with metrics l 1 which preserves the Pareto optimality of the solution. We obtain a necessary and sufficient condition for the stability radius of such a solution to be infinite.

Multicriterial investment problem in conditions of uncertainty and risk

“…Similar to [6,8,10,13,14] the stability radius of the efficient portfolio is the number where The set is called the set of perturbing matrices.…”

“…Earlier studies of quantitative characteristics of stability of efficient solutions were performed mainly for linear multicriterial problems, such as Boolean [6,7] and integer [8][9][10] programming, finite games [11,12], and a number of Boolean problems with nonlinear criteria [13][14][15].…”

Finite cooperative games: parametrisation of the concept of equilibrium (from Pareto to Nash) and stability of the efficient situation in the Hölder metric

“…By analogy with [12][13][14][15], by the radius of stability of a situation x 2 Q n .C; I 1 ; : : : ; I n / in the Hölder metric l p , 1 p 1, is meant where ‚ D f" > 0W 8B 2 ‰ p . "/ .x 2 Q n .C C B; I 1 ; I 2 ; : : : ; I s //g:…”