965 research outputs found
Generic identifiability and second-order sufficiency in tame convex optimization
We consider linear optimization over a fixed compact convex feasible region
that is semi-algebraic (or, more generally, "tame"). Generically, we prove that
the optimal solution is unique and lies on a unique manifold, around which the
feasible region is "partly smooth", ensuring finite identification of the
manifold by many optimization algorithms. Furthermore, second-order optimality
conditions hold, guaranteeing smooth behavior of the optimal solution under
small perturbations to the objective
Directed Subdifferentiable Functions and the Directed Subdifferential without Delta-Convex Structure
We show that the directed subdifferential introduced for differences of
convex (delta-convex, DC) functions by Baier and Farkhi can be constructed from
the directional derivative without using any information on the DC structure of
the function. The new definition extends to a more general class of functions,
which includes Lipschitz functions definable on o-minimal structure and
quasidifferentiable functions.Comment: 30 pages, 3 figure
\L ojasiewicz-type inequalities and global error bounds for nonsmooth definable functions in o-minimal structures
In this paper, we give some {\L}ojasiewicz-type inequalities and a nonsmooth
slope inequality on non-compact domains for continuous definable functions in
an o-minimal structure. We also give a necessary and sufficicent condition for
which global error bound exists. Moreover, we point out the relationship
between the Palais-Smale condition and this global error bound.Comment: 14 page
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