Steffen Rebennack – Optimization Online

Spatial branch-and-bound for nonconvex separable piecewise linear optimization

Published: 2024/05/02

(Mixed) Integer Linear Programming, Global Optimization branching strategies, convex underestimators, lower semicontinuous functions, piecewise linear functions, spatial branch and bound

Nonconvex separable piecewise linear functions (PLFs) frequently appear in applications and to approximate nonlinearitites. The standard practice to formulate nonconvex PLFs is from the perspective of discrete optimisation, using special ordered sets and mixed integer linear programs (MILPs). In contrast, we take the viewpoint of global continuous optimization and present a spatial branch-and-bound algorithm (sBB) … Read more

Stochastic Dual Dynamic Programming And Its Variants – A Review

Published: 2021/01/19, Updated: 2023/05/24

Christian Füllner

Steffen Rebennack

Stochastic Programming global optimization, large-scale optimization, linear programming, multistage stochastic programming, nested benders decomposition, nonconvex optimization, sampling-based optimization, stochastic dual dynamic programming

We provide a tutorial-type review on stochastic dual dynamic programming (SDDP), as one of the state-of-the-art solution methods for large-scale multistage stochastic programs. Since introduced about 30 years ago for solving large-scale multistage stochastic linear programming problems in energy planning, SDDP has been applied to practical problems from several fields and is enriched by various … Read more