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Two-Point Step Size Gradient Methods
Etude de nouvelles methodes de descente suivant le gradient pour la solution approchee du probleme de minimisation sans contrainte. Analyse de la convergence
On Projection Algorithms for Solving Convex Feasibility Problems
A very broad and flexible framework is investigated which allows a systematic discussion of questions on behaviour in general Hilbert spaces and on the quality of convergence in convex feasibility problems.
Convex analysis and nonlinear optimization : theory and examples
Background * Inequality constraints * Fenchel duality * Convex analysis * Special cases * Nonsmooth optimization * The Karush-Kuhn-Tucker Theorem * Fixed points * Postscript: infinite versus finite…
Pi and the AGM: A Study in Analytic Number Theory and Computational Complexity
Complete Elliptic Integrals and the Arithmetic-Geometric Mean Iteration. Theta Functions and the Arithmetic-Geometric Mean Iteration. Jacobi's Triple-Product and Some Number Theoretic Applications.…
Duality relationships for entropy-like minimization problems
This paper considers the minimization of a convex integral functional over the positive cone of an $L_p $ space, subject to a finite number of linear equality constraints. Such problems arise in…
Modular Equations and Approximations to π
G n and g n can always be expressed as roots of algebraical equations when n is any rational number.
A smooth variational principle with applications to subdifferentiability and to differentiability of convex functions
We show that, typically, lower semicontinuous functions on a Banach space densely inherit lower subderivatives of the same degree of smoothness as the norm. In particular every continuous convex…
Partially finite convex programming, Part I: Quasi relative interiors and duality theory
The notion of the quasi relative interior of a convex set, an extension of the relative interior in finite dimensions, is developed and used in a constraint qualification for a fundamental Fenchel duality result.