Matrix analysis
Derivatives and perturbations of eigenvectors
SIAM Journal on Numerical Analysis
SIAM Journal on Matrix Analysis and Applications
Matrix scaling, entropy minimization, and conjugate duality (II): the dual problem
Mathematical Programming: Series A and B
Optimization: algorithms and consistent approximations
Optimization: algorithms and consistent approximations
The anatomy of a large-scale hypertextual Web search engine
WWW7 Proceedings of the seventh international conference on World Wide Web 7
Authoritative sources in a hyperlinked environment
Journal of the ACM (JACM)
The stochastic approach for link-structure analysis (SALSA) and the TKC effect
Proceedings of the 9th international World Wide Web conference on Computer networks : the international journal of computer and telecommunications netowrking
Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Consistent Approximations and Approximate Functions and Gradients in Optimal Control
SIAM Journal on Control and Optimization
A new paradigm for ranking pages on the world wide web
WWW '03 Proceedings of the 12th international conference on World Wide Web
Google's PageRank and Beyond: The Science of Search Engine Rankings
Google's PageRank and Beyond: The Science of Search Engine Rankings
Numerical Optimization: Theoretical and Practical Aspects (Universitext)
Numerical Optimization: Theoretical and Practical Aspects (Universitext)
Pagerank optimization in polynomial time by stochastic shortest path reformulation
ALT'10 Proceedings of the 21st international conference on Algorithmic learning theory
Survey A survey of computational complexity results in systems and control
Automatica (Journal of IFAC)
Spectrum Management in Multiuser Cognitive Wireless Networks: Optimality and Algorithm
IEEE Journal on Selected Areas in Communications
Nonlinear Programming: Theory and Algorithms
Nonlinear Programming: Theory and Algorithms
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In the last years, Google@?s PageRank optimization problems have been extensively studied. In that case, the ranking is given by the invariant measure of a stochastic matrix. In this paper, we consider the more general situation in which the ranking is determined by the Perron eigenvector of a nonnegative, but not necessarily stochastic, matrix, in order to cover Kleinberg@?s HITS algorithm. We also give some results for Tomlin@?s HOTS algorithm. The problem consists then in finding an optimal outlink strategy subject to design constraints and for a given search engine. We study the relaxed versions of these problems, which means that we should accept weighted hyperlinks. We provide an efficient algorithm for the computation of the matrix of partial derivatives of the criterion, that uses the low rank property of this matrix. We give a scalable algorithm that couples gradient and power iterations and gives a local minimum of the Perron vector optimization problem. We prove convergence by considering it as an approximate gradient method. We then show that optimal linkage strategies of HITS and HOTS optimization problems satisfy a threshold property. We report numerical results on fragments of the real web graph for these search engine optimization problems.