Optimal Values’ Approximate Range of Convex Interval NonLinear Programming Problems

Uncertainty frequently appears in real-world optimization problems and is often represented using interval data. This paper studies Convex Interval Nonlinear Programming (CINLP) problems in which the objective function and constraints contain interval coefficients, while the decision variables remain deterministic and bounded. We focus on problems with interval linear objectives and [Formula: see text]-type interval constraints. To estimate the approximate optimal range of the objective function, we extend the classical Cutting Plane Method (CPM) to the interval setting and solve the problem from two complementary perspectives. Knowing this optimal interval provides managers with essential risk-related insights. Numerical examples are presented to demonstrate the practical necessity of CINLP models and to evaluate the performance of the proposed algorithms. Additional examples are used to illustrate sufficient conditions for the convergence of the method.