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Constructive, experimental, and nonlinear analysis
Michel Théra
- 01 Jan 2000
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TL;DR: In this paper, the authors consider a class of dynamical systems with a convex Lyapunov function, and they give dual characterizations of optimality for convex semidefinite programming.
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Abstract: Fejer monotonicity and weak convergence of an accelerated method of projections by H. H. Bauschke, F. Deutsch, H. Hundal, and S.-H. Park General "squeeze theorems" in nonsmooth analysis by J. Benoist and J.-B. Hiriart-Urruty Ramanujan's short unpublished manuscript on integrals and series related to Euler's constant by B. C. Berndt and D. C. Bowman An efficient algorithm for the Riemann zeta function by P. Borwein On periods of elements from real quadratic number fields by E. B. Burger and A. J. van der Poorten Vector-valued perturbed minimization principles by R. Deville and C. Finet Continued fractions, comparison algorithms, and fine structure constants by P. Flajolet and B. Vallee A class of dynamical systems with a convex Lyapunov function by M. Gabour, S. Reich, and A. J. Zaslavski On a convergence of lower semicontinuous functions linked with the graph convergence of their subdifferentials by M. Geoffroy and M. Lassonde Rotundity related to Lipschitz separation by J. R. Giles and J. D. Vanderwerff Codirectional compactness, metric regularity and subdifferential calculus by A. Ioffe Complete dual characterizations of optimality for convex semidefinite programming by V. Jeyakumar and M. J. Nealon A second-welfare theorem in nonconvex economies by A. Jofre Auxiliary problem and the approximation of variational inequalities with non-symmetric multi-valued operators by A. Kaplan and R. Tichatschke Dynamic emission tomography-Regularization and inversion by J. Maeght, D. Noll, and S. Boyd Semi-spaces and bases on convexity systems in complete lattices by J. E. Martinez-Legaz and I. Singer On variational characterizations of Asplund spaces by B. S. Mordukhovich and B. Wang Transposition of relations by J.-P. Penot On a classical existence theorem for nonlinear elliptic equations by B. Ricceri Limiting convex subdifferential calculus with applications to integration and maximal monotonicity of subdifferential by L. Thibault.
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Citations
Quasi-Fejérian Analysis of Some Optimization Algorithms
TL;DR: A quasi-Fejer sequence is a sequence which satisfies the standard Fejer monotonicityproperty to within an additional error term and is shown to provide a powerful framework to analyze the convergence of a wide range of optimization algorithms in a systematic fashion.
Set-valued optimization in welfare economics
Truong Q. Bao,Boris S. Mordukhovich +1 more
- 01 Jan 2010
TL;DR: In this paper, a variational approach has been developed to obtain new necessary conditions for various types of local optimal solutions to constrained multiobjective problems and to derive from them new versions of the second welfare theorem applied to Pareto as well as weak, strict, and strong optimal allocations of nonconvex economies under certain qualification conditions developed in the paper.
Variational Stability and Marginal Functions via Generalized Differentiation
TL;DR: An approach to variational stability based on generalized differentiation is developed, which derives efficient conditions ensuring the preservation of Lipschitzian and related properties for set-valued mappings under various operations, with the exact bound/modulus estimates.
Noncommutative algebra, multiple harmonic sums and applications in discrete probability
TL;DR: This theorem enables one to give an explicit form to generalized Euler constants associated with the divergent harmonic sums, and therefore, to get a very efficient algorithm to compute the asymptotic expansion of any H"s(N) as N->+~.
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Codifferential Calculus
Shengjie Li,Jean-Paul Penot,Xiaowei Xue +2 more
- 01 Dec 2011
TL;DR: In this article, exact calculus rules are obtained for calculating the coderivatives of the composition of two multivalued maps, including contingent, Frechet and limiting coderive.
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