Outer Approximation for Mixed-Integer Nonlinear Robust Optimization

Abstract Currently, few approaches are available for mixed-integer nonlinear robust optimization. Those that do exist typically either require restrictive assumptions on the problem structure or not guarantee protection. In this work, we develop an algorithm convex optimization problems where a key feature is method does rely specific of inner worst-case (adversarial) and allows latter to be non-convex. A major challenge such general setting ensuring protection, as calls global solution non-convex adversarial problem. Our able achieve up tolerance, by requiring evaluations only certain precision. For example, necessary can met approximating via piecewise relaxations solving resulting any requested error linear our approach, model nonsmooth tackle it outer approximation requires inexact function values subgradients. To deal with arising subproblems, render adaptive bundle applicable extend generate cutting planes, which valid known Relying its convergence approximate critical points, prove, consequence, finite algorithm. As application, study gas transport under uncertainties in demand physical parameters realistic instances provide computational results demonstrating efficiency method.