A sequential parametric convex approximation method with applications to nonconvex truss topology design problems |
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Authors: | Amir Beck Aharon Ben-Tal Luba Tetruashvili |
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Institution: | (1) Institute of Applied Mathematics, University of Dortmund, Vogelpothsweg 87, 44221 Dortmund, Germany;(2) Department of Mathematics, Technical University of Denmark, Matematiktorvet Building 303 S, 2800 Kgs. Lyngby, Denmark |
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Abstract: | We describe a general scheme for solving nonconvex optimization problems, where in each iteration the nonconvex feasible set
is approximated by an inner convex approximation. The latter is defined using an upper bound on the nonconvex constraint functions.
Under appropriate conditions, a monotone convergence to a KKT point is established. The scheme is applied to truss topology
design (TTD) problems, where the nonconvex constraints are associated with bounds on displacements and stresses. It is shown
that the approximate convex problem solved at each inner iteration can be cast as a conic quadratic programming problem, hence
large scale TTD problems can be efficiently solved by the proposed method. |
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Keywords: | |
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