Non-convex nested Benders decomposition

Abstract We propose a new decomposition method to solve multistage non-convex mixed-integer (stochastic) nonlinear programming problems (MINLPs). call this algorithm nested Benders (NC-NBD). NC-NBD is based on solving dynamically improved linear outer approximations of the MINLP, obtained by piecewise relaxations functions. Those MILPs are solved global optimality using an enhancement decomposition, in which regularization, refined binary state variables and Lagrangian cut techniques combined generate Lipschitz continuous value then used decide whether approximating MILP has be order compute feasible solutions for original MINLP. prove that converges $$\varepsilon $$ ε -optimal solution finite number steps. provide promising computational results some unit commitment moderate size.