## A note on error bounds for convex and nonconvex programs.(English)Zbl 1040.90546

Summary: Given a single feasible solution $$x_F$$ and a single infeasible solution $$x_I$$ of a mathematical program, we provide an upper bound to the optimal dual value. We assume that $$x_F$$ satisfies a weakened form of the Slater condition. We apply the bound to convex programs and we discuss its relation to Hoffman-like bounds. As a special case, we recover a bound due to O. L. Mangasarian [Math. Program. 83A, 187–194 (1998; Zbl 0920.90119)] on the distance of a point to a convex set specified by inequalities.

### MSC:

 90C31 Sensitivity, stability, parametric optimization 90C25 Convex programming 49K40 Sensitivity, stability, well-posedness

### Keywords:

convex programming; optimization duality; error bounds

Zbl 0920.90119
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