Bibliographic Details
| Title: |
Counterexample and an additional revealing poll step for a result of "analysis of direct searches for discontinuous functions". |
| Authors: |
Audet, Charles1 (AUTHOR), Bouchet, Pierre-Yves1 (AUTHOR) pierre-yves.bouchet@polymtl.ca, Bourdin, Loïc2 (AUTHOR) |
| Source: |
Mathematical Programming. Nov2024, Vol. 208 Issue 1/2, p411-424. 14p. |
| Subject Terms: |
*Mathematics, Discontinuous functions, Possibility |
| Abstract: |
This note provides a counterexample to a theorem announced in the last part of the paper (Vicente and Custódio Math Program 133:299–325, 2012). The counterexample involves an objective function f : R → R which satisfies all the assumptions required by the theorem but contradicts some of its conclusions. A corollary of this theorem is also affected by this counterexample. The main flaw revealed by the counterexample is the possibility that a directional direct search method (dDSM) generates a sequence of trial points (x k) k ∈ N converging to a point x ∗ where f is discontinuous, lower semicontinuous and whose objective function value f (x ∗) is strictly less than lim k → ∞ f (x k) . Moreover the dDSM generates trial points in only one of the continuity sets of f near x ∗ . This note also investigates the proof of the theorem to highlight the inexact statements in the original paper. Finally this work introduces a modification of the dDSM that allows, in usual cases, to recover the properties broken by the counterexample. [ABSTRACT FROM AUTHOR] |
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| Database: |
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