Besides other treasures, late Professor M. J. D. Powell left us five derivative-free optimization solvers that he coded in Fortran, namely COBYLA (1992), UOBYQA (2000), NEWUOA (2004), BOBYQA (2009), and LINCOA (2013). Professor Powell devised these solvers to tackle general nonlinear optimization problems of continuous variables with or without constraints using only function values but not derivatives of the objective function or nonlinear constraint functions. In practice, such functions are often black boxes defined by simulations, and the corresponding optimization problems are often categorized as black-box optimization or simulation-based optimization. Problems of this kind occur frequently in industrial and engineering applications, including circuit design, aircraft design, and machine learning. We will introduce the basic ideas of Powell's solvers, and present the PDFO package, which provides interfaces for calling these solvers from MATLAB and Python. This talk is based on the PDFO project conducted by Tom M. Ragonneau and Dr. Zaikun Zhang funded by the Hong Kong Ph.D. Fellowship Scheme (PF18-24698) and the Hong Kong RGC Early Career Scheme (PolyU 253012/17P).
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