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We present a hybrid algorithm for optimizing a convex, smooth function over the cone of positive semidefinite matrices. Our algorithm converges to the global optimal solution and can be used to solve general large-scale semidefinite programs and hence can be readily applied to a variety of machine learning problems. We show experimental results on three(More)
We consider parameterized convex optimization problems over the unit simplex, that depend on one parameter. We provide a simple and efficient scheme for maintaining an ε-approximate solution (and a corresponding ε-coreset) along the entire parameter path. We prove correctness and optimality of the method. Practically relevant instances of the(More)
13 Article history: 14 Available online xxxx 15 1 6 a b s t r a c t 17 In this paper, we present approximation algorithms for a variety of problems occurring in 18 the design of energy-efficient wireless communication networks. We first study the k-sta-19 tion network problem, where for a set S of stations and some constant k, one wants to 20 assign(More)
We consider an abstract class of optimization problems that are parameterized concavely in a single parameter, and show that the solution path along the parameter can always be approximated with accuracy ε > 0 by a set of size O(1/ √ ε). A lower bound of size Ω(1/ √ ε) shows that the upper bound is tight up to a constant factor. We also devise an algorithm(More)
Hyperbolic geo metry appears to be intrinsic in many large real networks. We construct and implement a new maximum likelihood estimation algorithm that embeds scale-free graphs in the hyperbolic space. All previous approaches of similar embedding algorithms require a runtime of Ω(n2). Our algorithm achieves quasilinear runtime, which makes it the first(More)
We devise a simple algorithm for computing an approximate solution path for parameter-ized semidefinite convex optimization problems that is guaranteed to be ε-close to the exact solution path. As a consequence, we can compute the entire regularization path for many regularized matrix completion and factorization approaches, as well as nuclear norm or(More)
We consider the problem of assigning powers to nodes of a wireless network in the plane such that a message from a source node s reaches all other nodes within a bounded number k of transmissions and the total amount of assigned energy is minimized. By showing the existence of a coreset of size O(` 1 ǫ ´ 4k) we are able to (1 + ǫ)-approximate the(More)