An outer-approximation algorithm for a class of mixed-integer nonlinear programs
Mathematical Programming: Series A and B
Solving mixed integer nonlinear programs by outer approximation
Mathematical Programming: Series A and B
SIAM Review
SIAM Journal on Optimization
Robust Truss Topology Design via Semidefinite Programming
SIAM Journal on Optimization
Optimal Design of Truss Structures by Logic-Based Branch and Cut
Operations Research
Numerical Analysis in Modern Scientific Computing: An Introduction
Numerical Analysis in Modern Scientific Computing: An Introduction
A survey on benders decomposition applied to fixed-charge network design problems
Computers and Operations Research
Structural Topology Optimization with Eigenvalues
SIAM Journal on Optimization
Global optimization of truss topology with discrete bar areas--Part I: theory of relaxed problems
Computational Optimization and Applications
Accelerating Benders Decomposition by Local Branching
INFORMS Journal on Computing
Material interpolation schemes for unified topology and multi-material optimization
Structural and Multidisciplinary Optimization
Journal of Global Optimization
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This article considers the non-linear mixed 0---1 optimization problems that appear in topology optimization of load carrying structures. The main objective is to present a Generalized Benders' Decomposition (GBD) method for solving single and multiple load minimum compliance (maximum stiffness) problems with discrete design variables to global optimality. We present the theoretical aspects of the method, including a proof of finite convergence and conditions for obtaining global optimal solutions. The method is also linked to, and compared with, an Outer-Approximation approach and a mixed 0---1 semi definite programming formulation of the considered problem. Several ways to accelerate the method are suggested and an implementation is described. Finally, a set of truss topology optimization problems are numerically solved to global optimality.