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New ground is broken in our understanding of objective functions' ability to capture Pareto solutions for multiobjective design optimization problems. It is explained why widely used objective functions fail to capture Pareto solutions when the Pareto frontier is not convex in objective space, and the means to avoid this limitation, when possible, is provided.These conditionsare developed and presented in the general context of n-dimensionalobjective space, and numerical examples are provided.doi:10.2514/2.1071 fatcat:n2gnvevxrvdujmsavu5mhom5we