A novel approach in uncertain programming. II: A class of constrained nonlinear programming problems with interval objective functions (Q874446)

[For part I see ibid. 2, No.~4, 351--371 (2006; Zbl 1115.65050).] The authors investigate a nonlinear programming problem of the form \(\max\sum_iC_if_i(x)\) subject to \(x\in X\subset \mathbb R^n\), where \(C_i\) are compact real intervals and \(f_i\) are real functions \((i=1,\ldots,m)\). Thus the objective is interval-valued and its values are compared using a special order \(\preceq/{}_{t_0,t_1}\) between intervals. In the main result of the paper it is shown that the set of optimal solutions of this problem can be characterized by two nonlinear programming problems with real (not interval) data. Several examples are given.