Hidden invariant convexity for global and conic-intersection optimality guarantees in discrete-time optimal control

Abstract Non-convex discrete-time optimal control problems in, e.g. , water or power systems, typically involve a large number of variables related through nonlinear equality constraints. The ideal goal is to find globally solution, and numerical experience indicates that algorithms aiming for Karush–Kuhn–Tucker points often solutions are indistinguishable from global optima. In our paper, we provide theoretical underpinning this phenomenon, showing on broad class the objective can be shown an invariant convex function ( invex function) decision when state eliminated using implicit theory. way, optimality guarantees obtained, exact nature which depends position solution within feasible set. example, show how high-quality obtained with local search river problem where invexity holds.