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Weak sharp minima revisited. III: Error bounds for differentiable convex inclusions. (English) Zbl 1163.90016
The term weak sharp minima is coined by Ferris in the late 1980’s to describe an extension of the notion of sharp minima to include the possibility of a non-unique solution set. It unifies a number of important ideas in optimization and many authors have studied this notion extensively. The notion of weak sharp minima is also an important tool in the analysis of the perturbation behavior of certain classes of optimization problems as well as in the convergence analysis of algorithms designed to solve these problems. This is the third paper in this series. Part I of this work [Control Cybern. 31, No. 3, 439–469 (2002; Zbl 1105.90356)] provides the foundation for the theory of weak sharp minima. The basic results on weak sharp minima in Part I are applied to a number of important problems in convex programming. In Part II [Math. Program. 104, No. 2–3 (B), 235–261 (2005; Zbl 1124.90349)], the applications to the linear regularity and bounded linear regularity of a finite collection of convex sets as well as global error bounds in convex programming are studied. In Part III, the authors continue their study of weak sharp minima by focusing on applications to error bounds for differentiable convex inclusions. A number of standard constraint qualifications for such inclusions are also examined.
MSC:
90C25Convex programming
90C31Sensitivity, stability, parametric optimization
49J52Nonsmooth analysis (other weak concepts of optimality)
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