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The present article is related to [1][2][3][4][5][6][7], and it examines stability of vector optimization problems of the form (C, X) : "max" { Cx: x E X}, is the number of criteria, X is a bounded set of arbitrary structure (possibly discrete) in R n. Sec. 1 presents the necessary definitions and notation. Here stability and P-stability are understood in the sense of Hausdorff upper semicontinuity of certain set-valued mappings.See. 2 proves that our problem is P-stable in the decision space under changes of the criterion coefficients. Necessary and sufficient conditions of stab!lity under changes of criterion coefficients are proved, and simple sufficient condkions are given. For the problem with an unperturbed feasible region in the initial-data space, we identify the set of initial-data matrices for which the problem is stable in the decision space under changes in the criterion coefficients. We show that this set is everywhere dense in the initial-data space.See. 3 examines the equivalence of the concepts of stability in the decision space and in the space of alternatives. We show that for the vector mixed-integer optimization problem these concepts are not equivalent. Some sufficient conditions of their equivalence are given. We also prove necessary and sufficient condkions of stability of problem (1) in the space of alternatives under changes in the criterion coefficients.See. 4 considers yet another definition of stability (/-stability), which is based on Hausdorff lower semicontinuity. In particular we show that the set of initial-data matrices C E R Lxn for which the problem (C, X 0) is not/-stable in the decision space under changes of criterion coefficients is of measure zero for L _> n.

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