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Given a real-analytic function f : Rn â†’ R and a critical point a âˆˆ Rn, the Lojasiewicz inequality asserts that there exists Î¸ âˆˆ [ 1 2 , 1) such that the function |f âˆ’ f(a)|Î¸ â€–âˆ‡fâ€–âˆ’1 remains boundedâ€¦ (More)

- JÃ©rÃ´me Bolte, Aris Daniilidis, Adrian S. Lewis, Masahiro Shiota
- SIAM Journal on Optimization
- 2007

We establish the following result: if the graph of a lower semicontinuous real-extendedvalued function f : Rn â†’ R âˆª {+âˆž} admits a Whitney stratification (so in particular if f is a semialgebraicâ€¦ (More)

The classical Lojasiewicz inequality and its extensions for partial differential equation problems (Simon) and to o-minimal structures (Kurdyka) have a considerable impact on the analysis ofâ€¦ (More)

- JÃ©rÃ´me Bolte, Aris Daniilidis, Adrian S. Lewis
- SIAM Journal on Optimization
- 2007

Given a real-analytic function f : Rn â†’ R and a critical point a âˆˆ Rn, the Lojasiewicz inequality asserts that there exists Î¸ âˆˆ [ 1 2 , 1) such that the function |f âˆ’ f(a)|Î¸ â€–âˆ‡fâ€–âˆ’1 remains boundedâ€¦ (More)

- Michele Conforti, GÃ©rard CornuÃ©jols, Aris Daniilidis, Claude LemarÃ©chal, JÃ©rÃ´me Malick
- Math. Oper. Res.
- 2015

We consider the separation problem for sets X that are inverse images of a given set S by a linear mapping. Classical examples occur in integer programming, complementarity problems and otherâ€¦ (More)

- Aris Daniilidis, Jeffrey C. H. Pang
- J. London Math. Society
- 2011

Continuity of set-valued maps is hereby revisited: after recalling some basic concepts of variational analysis and a short description of the State-of-the-Art, we obtain as by-product two Sard typeâ€¦ (More)

- Bernard Brogliato, Aris Daniilidis, Claude LemarÃ©chal, Vincent Acary
- Systems & Control Letters
- 2006

In this note, we prove the equivalence, under appropriate conditions, between several dynamical formalisms: projected dynamical systems, two types of differential inclusions, and a class ofâ€¦ (More)

- Aris Daniilidis, Dmitriy Drusvyatskiy, Adrian S. Lewis
- SIAM J. Matrix Analysis Applications
- 2014

Orthogonally invariant functions of symmetric matrices often inherit properties from their diagonal restrictions: von Neumannâ€™s theorem on matrix norms is an early example. We discuss the example ofâ€¦ (More)

It is shown that a locally Lipschitz function is approximately convex if, and only if, its Clarke subdifferential is a submonotone operator. Consequently, in finite dimensions, the class of locallyâ€¦ (More)

- Aris Daniilidis, Claude LemarÃ©chal
- Math. Program.
- 2005