A direct search method for constrained optimization via the rounded $l_1$ penalty function.

Abstract: This talk looks at the constrained optimization problem when the objective and constraints are Lipschitz continuous black box functions. The approach uses a sequence of smoothed and offset $\ell_1$ penalty functions. The method generates an approximate minimizer to each penalty function, and then adjusts the offsets and other parameters. The smoothing is steadily reduced, ultimately revealing the $\ell_1$ exact penalty function. The method preferentially uses a discrete quasi-Newton step, backed up by a global direction search. Theoretical convergence results are given for the smooth and non-smooth cases subject to relevant conditions. Numerical results are presented on a variety of problems with non-smooth objective or constraint functions. These results show the method is effective in practice.

optimization and control

Audience: researchers in the topic

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