A Benders Decomposition Method for Discretely-Constrained Mathematical Programs with Equilibrium Constraints with Applications in Energy

Event Sponsor: 
Mathematics and Computer Science Division Seminar
Start Date: 
Dec 1 2008 (All day)
Building 221 Conference Room A216
Argonne National Laboratory
Yohan Shim
Speaker(s) Title: 
University of Maryland
Sven Leyffer and Todd Munson

I will present a new variant of Benders method combined with a domain decomposition heuristic to solve discretely-constrained mathematical programs with equilibrium constraints (DC-MPECs). These bi-level, integer-constrained problems are important for a variety of areas involving infrastructure planning (e.g., energy) although they are computationally challenging. The numerical difficulties arise in that one must treat a lower-level optimization or complimentarily problem as well as the discrete nature of the upper-level planning variables. Thus, we combine both integer programming and equilibrium modeling. Lastly, we provide numerical evidence that the proposed new method works; the domain decomposition heuristic has been implemented with MATLAB-TOMLAB interfacing for small-size problems and MATLAB-GAMS interfacing for large-size problems.

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