publication . Article . Preprint . 2006

On Equivalence Between Optimality Criteria and Projected Gradient Methods with Application to Topology Optimization Problem

Ananiev, Sergey;
Open Access
  • Published: 07 Sep 2006 Journal: Multibody System Dynamics, volume 13, pages 25-38 (issn: 1384-5640, eissn: 1573-272X, Copyright policy)
  • Publisher: Springer Science and Business Media LLC
Abstract
The paper demonstrates the equivalence between the optimality criteria (OC) method, initially proposed by Bendsoe & Kikuchi for topology optimization problem, and the projected gradient method. The equivalence is shown using Hestenes definition of Lagrange multipliers. Based on this development, an alternative formulation of the Karush-Kuhn-Tucker (KKT) condition is suggested. Such reformulation has some advantages, which will be also discussed in the paper. For verification purposes the modified algorithm is applied to the design of tension-only structures.
Subjects
arXiv: Mathematics::Optimization and Control
free text keywords: Mechanical Engineering, Modelling and Simulation, Control and Optimization, Aerospace Engineering, Computer Science Applications, Karush–Kuhn–Tucker conditions, Constraint algorithm, Equivalence (measure theory), Lagrange multiplier, symbols.namesake, symbols, Topology optimization, Gradient method, Topology optimization problem, Mathematics, Mathematical optimization, Mathematics - Optimization and Control, 65K99
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