Sequential Approximate Optimization in an NLP Filter Framework

Nonlinear programming (NLP) filter methods are a recent development in trust region sequential quadratic programming (SQP) algorithms. The NLP filter is a bi-objective representation of the two competing aims to minimize the objective function and to satisfy the constraints. It replaces the penalty merit function as a criterion in trust region SQP for the acceptance or rejection of trial steps. The filter can also be used to the advantage of many a sequential approximate optimization (SAO) method in structural and multidisciplinary optimization. Accordingly, we cast gradient-based SAO algorithms in the filter-SQP algorithmic framework of Fletcher, Leyffer, and Toint. The resultant filter-SAO method is then applied to some well-known structural optimization test problems, using several popular engineering approximation functions, namely the linear, reciprocal, conservative, and spherical quadratic approximations. The test problems confirm the effectiveness of the filter for use in SAO.

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