Calmness in optimization problems with equality constraints (Q1842072)

The paper is devoted to the study of the calmness condition, first introduced by \textit{F. H. Clarke} [Math. Oper. Res. 1, 165-173 (1976; Zbl 0404.90100)] (this condition is one of the weakest constraint qualifications). First, the authors give two counterexamples to illustrate that an optimization problem with equality constraints need not be calm almost everywhere. Then, some conditions are presented that insure calmness at local solutions and also conditions that insure that a problem is calm at local solutions almost everywhere.