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New pre­print on sur­ro­ga­te-ba­sed mul­ti­ob­jec­ti­ve op­ti­mi­za­ti­on al­go­rithms with non­li­ne­ar cons­traints

We have just published a preprint on a "Multi-Objective Trust-Region Filter Method for Nonlinear Constraints using Inexact Gradients". In this article, we build on previous work to present an optimization algorithm for nonlinearly constrained multi-objective optimization problems. The algorithm combines a surrogate-assisted derivative-free trust-region approach with the filter method known from single-objective optimization. Instead of the true objective and constraint functions, so-called fully linear models are employed and we show how to deal with the gradient inexactness in the composite step setting, adapted from single-objective optimization as well. Under standard assumptions, we prove convergence of a subset of iterates to a quasi-stationary point and if constraint qualifications hold, then the limit point is also a KKT-point of the multi-objective problem.

The paper can be downloaded from the arXiv.