Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics

Joint Seminars in Statistics & Biostatistics


Wednesday, February 26th, 2020

Time: 11:30-12:20 Place: Jeffery Hall 225

Speaker: Prof. Xiang Li (Queen's University, Dept. of Chemical Engineering)

Title: Decomposition Based Global Optimization

Abstract: Large-scale nonconvex optimization arises from a variety of scientific and engineering problems. Often such optimization problem is simplified into an easier convex or mixed-integer convex optimization problem, but the solution of the simplified problem is unlikely to be optimal or feasible for the original problem. Recent advances in decomposition based global optimization provides a promising way to solve large-scale nonconvex optimization problems within reason time. In this presentation, we will first discuss the principle of generalized Benders decomposition (GBD), including the reformulation into a master problem using strong Lagrangian duality, the construction of upper and lower bounding problems, and the finite convergence property. We also show how GBD can be applied to decompose multi-scenario problems. Then we introduce two variants of GBD. The first variant, called nonconvex generalized Benders decomposition (NGBD), is able to solve a class of nonconvex problems that GBD cannot solve. The second variant, called joint decomposition (JD), enhances GBD/NGBD via the integration of Lagrangian decomposition. Finally, we demonstrate the computational advantages of GBD, NGBD and JD via some engineering problems.