A General Robust-Optimization Formulation for Nonlinear Programming

Most research in robust optimization has so far been focused on inequality-only, convex conic programming with simple linear models for uncertain parameters. Many practical optimization problems, however, are nonlinear and non-convex. Even in linear programming, coefficients may still be nonlinear functions of uncertain parameters. In this paper, we propose robust formulations (see (1) versus (5), and (2) versus (3), for example) that extend the robust-optimization approach to a general nonlinear programming setting with parameter uncertainty involving both equality and inequality constraints. The proposed robust formulations are valid in a neighborhood of a given nominal parameter value and are robust to the first-order, thus suitable for applications where reasonable parameter estimations are available and uncertain variations are moderate.