Wilke, DNKok, S2012-09-142012-09-142012-07Wilke, DN and Kok, S. Numerical sensitivity computation for discontinuous gradient-only optimization problems using the complex-step method. Proceedings of the 10th World Congress on Computational Mechanics (WCCM 2012), Sao Paulo, Brazil, 8-13 July 2012http://hdl.handle.net/10204/6094Proceedings of the 10th World Congress on Computational Mechanics (WCCM 2012), Sao Paulo, Brazil, 8-13 July 2012This study considers the numerical sensitivity calculation for discontinuous gradientonly optimization problems using the complex-step method. The complex-step method was initially introduced to differentiate analytical functions in the late 1960s, and is based on a Taylor series expansion using a pure imaginary step. The complex-step method is not subject to subtraction errors as with finite difference approaches when computing first order sensitivities and therefore allows for much smaller step sizes that ultimately yields accurate sensitivities. This study investigates the applicability of the complex-step method to numerically compute first order sensitivity information for discontinuous optimization problems. An attractive feature of the complex-step approach is that no real difference step is taken as with conventional finite difference approaches, since conventional finite differences are problematic when real steps are taken over a discontinuity. We highlight the benefits and disadvantages of the complex-step method in the context of discontinuous gradient-only optimization problems that result from numerically approximated (partial) differential equations.enComplex-step derivativeDiscontinuous functionGradient-only optimizationConference PresentationWilke, D., & Kok, S. (2012). Numerical sensitivity computation for discontinuous gradient-only optimization problems using the complex-step method. http://hdl.handle.net/10204/6094Wilke, DN, and S Kok. "Numerical sensitivity computation for discontinuous gradient-only optimization problems using the complex-step method." (2012): http://hdl.handle.net/10204/6094Wilke D, Kok S, Numerical sensitivity computation for discontinuous gradient-only optimization problems using the complex-step method; 2012. http://hdl.handle.net/10204/6094 .TY - Conference Presentation AU - Wilke, DN AU - Kok, S AB - This study considers the numerical sensitivity calculation for discontinuous gradientonly optimization problems using the complex-step method. The complex-step method was initially introduced to differentiate analytical functions in the late 1960s, and is based on a Taylor series expansion using a pure imaginary step. The complex-step method is not subject to subtraction errors as with finite difference approaches when computing first order sensitivities and therefore allows for much smaller step sizes that ultimately yields accurate sensitivities. This study investigates the applicability of the complex-step method to numerically compute first order sensitivity information for discontinuous optimization problems. An attractive feature of the complex-step approach is that no real difference step is taken as with conventional finite difference approaches, since conventional finite differences are problematic when real steps are taken over a discontinuity. We highlight the benefits and disadvantages of the complex-step method in the context of discontinuous gradient-only optimization problems that result from numerically approximated (partial) differential equations. DA - 2012-07 DB - ResearchSpace DP - CSIR KW - Complex-step derivative KW - Discontinuous function KW - Gradient-only optimization LK - https://researchspace.csir.co.za PY - 2012 T1 - Numerical sensitivity computation for discontinuous gradient-only optimization problems using the complex-step method TI - Numerical sensitivity computation for discontinuous gradient-only optimization problems using the complex-step method UR - http://hdl.handle.net/10204/6094 ER -