A bipolar theorem for L
A compact convex set with no extreme points
A Geometrical Characterization of Choquet Simplexes.
A new series of conjectures and open questions in optimization and matrix analysis
We present below a new series of conjectures and open problems in the fields of (global) Optimization and Matrix analysis, in the same spirit as our recently published paper [J.-B. Hiriart-Urruty, Potpourri of conjectures and open questions in Nonlinear analysis and Optimization. SIAM Review 49 (2007) 255–273]. With each problem come a succinct presentation, a list of specific references, and a view on the state of the art of the subject.
A new series of conjectures and open questions in optimization and matrix analysis
We present below a new series of conjectures and open problems in the fields of (global) Optimization and Matrix analysis, in the same spirit as our recently published paper [J.-B. Hiriart-Urruty, Potpourri of conjectures and open questions in Nonlinear analysis and Optimization. SIAM Review49 (2007) 255–273]. With each problem come a succinct presentation, a list of specific references, and a view on the state of the art of the subject.
A note on formal power series
In this note we investigate a relationship between the boundary behavior of power series and the composition of formal power series. In particular, we prove that the composition domain of a formal power series is convex and balanced which implies that the subset consisting of formal power series which can be composed by a formal power series possesses such properties. We also provide a necessary and sufficient condition for the superposition operator to map into itself or to map into...
A note on infinite dimensional convex sets.
A note on separation by linear mappings
A simple geometrie proof of a theorem for starshaped unions of convex sets
Absolutely linear relations.
Absolutely linear relations (Short Communication).
Algebraic and geometric approach to the classification of semispaces.
Approximation under an arc length constraint.
Approximation under an arc length constraint. (Short Communiaction).
Asymptotes and Projections of Convex Sets.
Central points of convex sets
Closures of faces of compact convex sets
This paper gives necessary and sufficient conditions for the closure of a face in a compact convex set to be again a face. As applications of these results, several theorems scattered in the literature are proved in an economical and uniform manner.
Compacts de fonctions de première classe
Continuous Convex Sets.
Convessità in dimensione finita