Erratum: Validated Linear Relaxations and Preprocessing: Some Experiments

This is a correction to R. B. Kearfott and S. Hongthong’s article [SIAM J. Optim., 16 (2005), pp. 418–433]. DOI. 10.1137/100816080 There are errors in column 4 (entitled “Under / over estimators”) of rows 3, 4, and 5 of Table 4.1, on p. 426 of [1]. As a consequence, references to those entries in the table on lines 1 and 2 below the table (on page 426) and on lines 5, 6, 7, and 8 of section 4.1 are incorrect, and the last line of that paragraph should be deleted. The error occurred by using the wrong enclosure range. For example, the midpoint of the enclosure range [−3, 1] for v4, namely v4 = −1, should have been used in the tangent line for row 3, whereas the midpoint of the enclosure range for v5 = v2 4 had been used instead. Similar errors occurred in rows 4 and 5. Table 4.1 should therefore be corrected to read as follows: Operation Enclosures Under/over estimators Convexity 1 v3 ← x1 + x2 [−2, 2] x1 + x2 − v3 = 0 linear 2 v4 ← v3 − 1 [−3, 1] v3 − 1 − v4...

• Type: Journal
• Year: 2011
• Where: SIAMJO
• Authors: R. Baker Kearfott
• Keywords: Enclosure Range, Linear, SIAMJO 2011, Software Engineering, Tangent Line