Topology optimization of microstructures with perturbation analysis and penalty methods

Topology Optimization by Penalty (TOP) Method

1. Abstract In traditional structural topology optimization (TO), the material properties of continuum finite elements of fixed form and coupling are varied to find the optimal topology that satisfies the design problem. We develop an alternative, fundamental formulation where the design space search is dependent on the coupling, and the goal of the topology optimization by penalty (TOP) method...

Two-Scale Topology Optimization with Microstructures: Supplemental Material

1 DISCRETE SAMPLING OF MICROSTRUCTURES Given a set of microstructures, a new population of microstructures is generated using the Stochastically-Ordered Sequential Monte Carlo (SOSMC) method introduced by Ritchie et al. (2015). In our implementation, the samples (or particles) are our microstructures, i.e. binary assignments of the base materials, and the desired distribution is the one that ma...

Penalty and Barrier Methods for Constrained Optimization

A Unified Analysis of Nonconvex Optimization Duality and Penalty Methods with General Augmenting Functions

In this paper, we study a unifying framework for the analysis of duality schemes and penalty methods constructed using augmenting functions that need not be nonnegative or bounded from below. We consider two geometric optimization problems that are dual to each other and characterize primal-dual problems for which the optimal values of the two problems are equal. To establish this, we show that...

Steering Exact Penalty Methods for Optimization

This paper reviews, extends and analyzes a new class of penalty methods for nonlinear optimization. These methods adjust the penalty parameter dynamically; by controlling the degree of linear feasibility achieved at every iteration, they promote balanced progress toward optimality and feasibility. In contrast with classical approaches, the choice of the penalty parameter ceases to be a heuristi...