A derivative-free algorithm for systems of nonlinear inequalities |
| |
Authors: | G Liuzzi S Lucidi |
| |
Institution: | (1) CNR - Consiglio Nazionale delle Ricerche, IASI - Istituto di Analisi dei Sistemied Informatica “A. Ruberti”, Viale Manzoni 30, 00185 Rome, Italy;(2) Dipartimento di Informatica e Sistemistica “Antonio Ruberti”, Università di Roma “La Sapienza”, via Ariosto, 25, 00185 Rome, Italy |
| |
Abstract: | Recently a new derivative-free algorithm has been proposed for the solution of linearly constrained finite minimax problems.
This derivative-free algorithm is based on a smoothing technique that allows one to take into account the non-smoothness of
the max function. In this paper, we investigate, both from a theoretical and computational point of view, the behavior of
the minmax algorithm when used to solve systems of nonlinear inequalities when derivatives are unavailable. In particular,
we show an interesting property of the algorithm, namely, under some mild conditions regarding the regularity of the functions
defining the system, it is possible to prove that the algorithm locates a solution of the problem after a finite number of
iterations. Furthermore, under a weaker regularity condition, it is possible to show that an accumulation point of the sequence
generated by the algorithm exists which is a solution of the system. Moreover, we carried out numerical experimentation and
comparison of the method against a standard pattern search minimization method. The obtained results confirm that the good
theoretical properties of the method correspond to interesting numerical performance. Moreover, the algorithm compares favorably
with a standard derivative-free method, and this seems to indicate that extending the smoothing technique to pattern search
algorithms can be beneficial. |
| |
Keywords: | Derivative-free methods Nonlinear inequality systems |
本文献已被 SpringerLink 等数据库收录! |
|