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

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

2006-09-07

arxiv.org/abs/math/0609218v1

EUROMECH 442, Colloquium on Computer-Aided Optimization of Mechanical System, 2003

Mathematics

Optimization and Control

12 pages

Scientific paper

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.

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