Nondifferential optimization via adaptive smoothing

The problem of minimizing a nondifferential functionx f(x) (subject, possibly, to nondifferential constraints) is considered. Conventional algorithms are employed for minimizing a differential approximationf off (subject to differentiable approximations ofg). The parameter is adaptively reduced in such a way as to ensure convergence to points satisfying necessary conditions of optimality for the original problem.This research was supported by the UK Science and Engineering Research Council, the National Science Foundation under Grant No. ECS-8121149, and the Joint Services Electronics Program, Contract No. F49620-79-C-0178.