A counter-example to ‘minimal distance between two non-convex surfaces’

Abstract

The aim of this note is to show that the main results in Gao and Yang [Minimal distance between two non-convex surfaces, Optimization 57 (2008), pp. 705–714] are false and to discuss the manner in which the minimization problem in this article is investigated while presenting in a particular case a thorough study of the mentioned optimization problem. To achieve our main goal we provide counter-examples.

Keywords:

• counter-example
• minimal distance
• total complementary function
• triality theory

AMS Subject Classifications::

• 90C30
• 90C46