Almost Every Convex or Quadratic Programming Problem Is Well Posed
Alexander Davidovich Ioffe, Roberto Lucchetti, J. P. Revalski · Mathematics of Operations Research · 2004
We provide an abstract principle aimed at proving that classes of optimization problems are typically well posed in the sense that the collection of ill-posed problems within each class is σ-porous. As a consequence, we establish typical well-posedness in the above sense for unconstrained minimization of certain classes of functions (e.g., convex and quasi-convex continuous), as well as of convex programming with inequality constraints. We conclude the paper by showing that the collection of consistent ill-posed problems of quadratic programming of any fixed size has Lebesgue measure zero in the corresponding Euclidean space.