Some remarks concerning Gao–Strang's complementary gap function

Abstract

The aim of this note is to analyse the results in the paper by D.Y. Gao and G. Strang [Geometric nonlinearity: Potential energy, complementary energy, and the gap function, Quart. Appl. Math. 47 (1989), pp. 487–504] where, according to D.Y. Gao, the complementary gap function was first introduced, and several flaws, mistakes, and inconsistencies are present, and to discuss the mathematical manner in which the mentioned paper presents itself, especially from the point of view of convex analysis.

Keywords:

• complementary gap function
• counter-example

AMS Subject Classifications::

• 49S05
• 74B20
• 90C30