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R. H. Byrd and R. A. Waltz, “An Active-Set Algorith for Nonlinear Programming Using Parametric Linear Programming,” Department of Industrial and Systems Engineering, Uni-versity of Southern California, Los Angeles, 2007.

has been cited by the following article:

• TITLE: A Combined Probabilistic and Optimization Approach for Improved Chemical Mixing Systems Design

  AUTHORS: Matthew J. Opgenorth, William E. McDermott, Peter Laz, Corinne S. Lengsfeld

  KEYWORDS: Probabilistic Design, Optimization Design, Tolerance Design, Computer-Aided Design

  JOURNAL NAME: Engineering, Vol.3 No.6, June 23, 2011

  ABSTRACT: A design analysis of a mixing nozzle was performed using a combination of probabilistic and optimization techniques. A novel approach was utilized where probabilistic analysis was used to reduce the number of geometric constraints based on sensitivity factors. An optimization algorithm used only the most significant parameters to maximize mixing. A second probabilistic analysis was performed after optimization was com-plete in order to quantitatively predict the effects of manufacturing tolerances on mixing performance. This process for automated design is attractive over full parameter optimization techniques due to the computa-tional efficiency resulting from an intelligent reduction in evaluated variables.