31 May 2013 Use of formal derivative for extremizing real-valued functions of complex variables
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Abstract
The extremum of a real-valued nonanalytic function of a complex variable that defies Cauchy-Riemann equations can be found using formal derivatives. This letter shows how the first and second derivative tests can be recast via formal gradient and formal Hessian. The elegance of the method is illustrated with examples.
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Sudarshan R. Nelatury, Sudarshan R. Nelatury, Charles W. Nelatury, Charles W. Nelatury, Charles F. Nelatury, Charles F. Nelatury, } "Use of formal derivative for extremizing real-valued functions of complex variables", Proc. SPIE 8720, Photonic Applications for Aerospace, Commercial, and Harsh Environments IV, 87200H (31 May 2013); doi: 10.1117/12.2016270; https://doi.org/10.1117/12.2016270
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