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Direct multisearch for multiobjective optimization
Custódio, A. L.; Madeira, J. F. A.; Vaz, A. I. F.; Vicente, L. N.In practical applications of optimization it is common to have several conflicting objective functions to optimize. Frequently, these functions are subject to noise or can be of black-box type, preventing the use of derivative-based techniques. We propose a novel multiobjective derivative-free methodology, calling it direct multisearch (DMS), which does not aggregate any of the objective functions. Our framewor...
Analysis of direct searches for non-Lipschitzian functions
Vicente, L. N.; Custódio, A. L.It is known that the Clarke generalized directional derivative is nonnegative along the limit directions generated by directional direct-search methods at a limit point of certain subsequences of unsuccessful iterates, if the function being minimized is Lipschitz continuous near the limit point. In this paper we generalize this result for non-Lipschitzian functions using Rockafellar generalized directional deri...
Using simplex gradients of nonsmooth functions in direct search methods
Custódio, A. L.; Dennis Jr., John E.; Vicente, Luís NunesIt has been shown recently that the efficiency of direct search methods that use opportunistic polling in positive spanning directions can be improved significantly by reordering the poll directions according to descent indicators built from simplex gradients. The purpose of this paper is twofold. First, we analyze the properties of simplex gradients of nonsmooth functions in the context of direct search method...
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