Global regularity theorems. (English) Zbl 0655.90059

Auslender, A. A.; Crouzeix, J.-P.

Math. Oper. Res. 13, No. 2, 243-253 (1988).

Let C be the nonempty set defined by means of nondifferentiable proper convex functions and some linear functions. The authors give the best bound for the quotient of the distance of an infeasible point from C and the norm of the residual vector. It is claimed that the results of O. L. Mangasarian [Math. Oper. Res. 10, 175-179 (1985; Zbl 0565.90059)] are improved in several directions. Applications to stability theory are also mentioned.

Reviewer: R.N.Kaul

MSC:

90C25

Convex programming

Keywords:

convex inequalities; condition number; residual error; nondifferentiable proper convex functions; stability

Citations:

Zbl 0565.90059