On the conditional acceptance of iterates in SAO algorithms based on convex separable approximations

Abstract

We reflect on the convergence and termination of optimization algorithms based on convex and separable approximations using two recently proposed strategies, namely a trust region with filtered acceptance of the iterates, and conservatism. We then propose a new strategy for convergence and termination, denoted f iltered conservatism, in which the acceptance or rejection of an iterate is determined using the nonlinear acceptance filter. However, if an iterate is rejected, we increase the conservatism of every unconservative approximation, rather than reducing the trust region. Filtered conservatism aims to combine the salient features of trust region strategies with nonlinear acceptance filters on the one hand, and conservatism on the other. In filtered conservatism, the nonlinear acceptance filter is used to decide if an iterate is accepted or rejected. This allows for the acceptance of infeasible iterates, which would not be accepted in a method based on conservatism. If however an iterate is rejected, the trust region need not be decreased; it may be kept constant. Convergence is than effected by increasing the conservatism of only the unconservative approximations in the (large, constant) trust region, until the iterate becomes acceptable to the filter. Numerical results corroborate the accuracy and robustness of the method.Based on the paper entitled 'Globally convergent SAO algorithms for large scale simulation-based optimization', presented at the 8th World

An adaptive quadratic approximation for structural and topology optimization

“…This problem was initially proposed by Fleury [34] and is also studied by Groenwold [1,35,36]. This so-called Fleury's weight like minimization problem is then extended by Siddiqui et al [37] for an arbitrary given number of design variables as follows:…”

On sequential approximate simultaneous analysis and design in classical topology optimization

“…In order to deal with potential infeasibility of subproblem P Q P [ k ], evidently because too much material is removed from the design domain in areas required to connect the load to the fixing position, we employ the convergent ‘trust region filter’ algorithm by Fletcher et al . A simpler version of the algorithm can be found in Reference . The idea is that the feasibility of the sequence of points x { k } , k = 1,2,3,… may be maintained, to some extent, by the conditional acceptance of iterates, pending the satisfaction of descent and feasibility measures .…”

“…A simpler version of the algorithm can be found in Reference . The idea is that the feasibility of the sequence of points x { k } , k = 1,2,3,… may be maintained, to some extent, by the conditional acceptance of iterates, pending the satisfaction of descent and feasibility measures . The various parameters are set at values in agreement with those suggested in Reference – details can be found in Reference .…”

First-order sequential convex programming using approximate diagonal QP subproblems

“…A globally convergent algorithm may be obtained by casting dual subproblems P D [k] in a framework of variable conservatism, or in a trust region framework, see Groenwold et al (2009) and Groenwold and Etman (2010a).…”