Equivalent displacement based formulations for maximum strength Truss topology design
IMPACT of Computing in Science and Engineering
Hidden convexity in some nonconvex quadratically constrained quadratic programming
Mathematical Programming: Series A and B
Multiple-load truss topology and sizing optimization: some properties of minimax compliance
Journal of Optimization Theory and Applications
On Extensions of the Frank-Wolfe Theorems
Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part II
Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Robust Truss Topology Design via Semidefinite Programming
SIAM Journal on Optimization
Optimal Truss Design by Interior-Point Methods
SIAM Journal on Optimization
An iterative working-set method for large-scale nonconvex quadratic programming
Applied Numerical Mathematics
Computational Optimization and Applications
Computational Optimization and Applications
New branch and bound approaches for truss topology design with discrete areas
AMERICAN-MATH'10 Proceedings of the 2010 American conference on Applied mathematics
Global optima for the Zhou---Rozvany problem
Structural and Multidisciplinary Optimization
Generalized Benders' Decomposition for topology optimization problems
Journal of Global Optimization
A new Branch and Bound method for a discrete truss topology design problem
Computational Optimization and Applications
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This two part paper considers the classical problem of finding a truss design with minimal compliance subject to a given external force and a volume bound. The design variables describe the cross-section areas of the bars. While this problem is well-studied for continuous bar areas, we treat here the case of discrete areas. This problem is of major practical relevance if the truss must be built from pre-produced bars with given areas. As a special case, we consider the design problem for a single bar area, i.e., a 0/1-problem. In contrast to heuristic methods considered in other approaches, Part I of the paper together with Part II present an algorithmic framework for the calculation of a global optimizer of the underlying large-scaled mixed integer design problem. This framework is given by a convergent branch-and-bound algorithm which is based on solving a sequence of nonconvex continuous relaxations. The main issue of the paper and of the approach lies in the fact that the relaxed nonlinear optimization problem can be formulated as a quadratic program (QP). Here the paper generalizes and extends the available theory from the literature. Although the Hessian of this QP is indefinite, it is possible to circumvent the non-convexity and to calculate global optimizers. Moreover, the QPs to be treated in the branch-and-bound search tree differ from each other just in the objective function. In Part I we give an introduction to the problem and collect all theory and related proofs for the treatment of the original problem formulation and the continuous relaxed problems. The implementation details and convergence proof of the branch-and-bound methodology and the large-scale numerical examples are presented in Part II.