Generalized derivatives of computer programs

ABSTRACT

A method for evaluating lexicographical directional (LD)-derivatives of functional programs is presented, extending previous methods to programs containing conditional branches and loops. A language for imperative programs is given, and conditions under which LD-derivatives can be calculated automatically for conditional branches and loops are described, along with a full description of the source transformation procedures necessary.

Keywords:

• Generalized derivatives
• computer programs
• nondifferentiable functions
• lexicographic derivatives

2010 Mathematics Subject Classifications:

• 49J52 (nonsmooth analysis)
• 90C56 (generalized derivatives)
• 90C35 (network problems)

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Matthew R. Billingsley

Matthew R. Billingsley is a Ph.D. candidate at Massachusetts Institute of Technology, researching sensitivity analysis of nonsmooth systems and discontinuous dynamical systems. He received an M.S. in Chemical Engineering Practice from Massachusetts Institute of Technology in 2017 and B.S. degrees in Chemical Engineering and Mathematics from Rose-Hulman Institute of Technology in 2015.

Paul I. Barton

Paul I. Barton is the Lammot du Pont Professor of Chemical Engineering at the Massachusetts Institute of Technology. He received an M.Eng. (1988) and Ph.D. (1992) in Chemical Engineering from Imperial College, University of London.