On a Class of Nonconvex Problems Where all Local Minima are Global

Leo Liberti

Displaying similar documents to “On a Class of Nonconvex Problems Where all Local Minima are Global”

On the points of non-differentiability of convex functions

David Pavlica (2004)

Commentationes Mathematicae Universitatis Carolinae

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We characterize sets of non-differentiability points of convex functions on $ℝ^{n}$ . This completes (in $ℝ^{n}$ ) the result by Zajíček [2] which gives a characterization of the magnitude of these sets.

Compensated convexity and its applications

Kewei Zhang (2008)

Annales de l'I.H.P. Analyse non linéaire

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Injectivity onto a star-shaped set for local homeomorphisms in n-space

Gianluca Gorni, Gaetano Zampieri (1994)

Annales Polonici Mathematici

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We provide a number of either necessary and sufficient or only sufficient conditions on a local homeomorphism defined on an open, connected subset of the n-space to be actually a homeomorphism onto a star-shaped set. The unifying idea is the existence of "auxiliary" scalar functions that enjoy special behaviours along the paths that result from lifting the half-lines that radiate from a point in the codomain space. In our main result this special behaviour is monotonicity, and the auxiliary...

On the separation of parametric convex polyhedral sets with application in MOLP

Milan Hladík (2010)

Applications of Mathematics

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We investigate diverse separation properties of two convex polyhedral sets for the case when there are parameters in one row of the constraint matrix. In particular, we deal with the existence, description and stability properties of the separating hyperplanes of such convex polyhedral sets. We present several examples carried out on PC. We are also interested in supporting separation (separating hyperplanes support both the convex polyhedral sets at given faces) and permanent separation...