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» Geometric optimization and sums of algebraic functions
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SODA
2010
ACM
163views Algorithms» more  SODA 2010»
14 years 2 months ago
Geometric optimization and sums of algebraic functions
We present a new optimization technique that yields the first FPTAS for several geometric problems. These problems reduce to optimizing a sum of non-negative, constant description...
Antoine Vigneron
ACCV
2007
Springer
13 years 11 months ago
Conic Fitting Using the Geometric Distance
We consider the problem of fitting a conic to a set of 2D points. It is commonly agreed that minimizing geometrical error, i.e. the sum of squared distances between the points and...
Peter F. Sturm, Pau Gargallo
ISSAC
1997
Springer
194views Mathematics» more  ISSAC 1997»
13 years 9 months ago
The Minimised Geometric Buchberger Algorithm: An Optimal Algebraic Algorithm for Integer Programming
IP problems characterise combinatorial optimisation problems where conventional numerical methods based on the hill-climbing technique can not be directly applied. Conventional me...
Qiang Li, Yike Guo, Tetsuo Ida, John Darlington
ICC
2008
IEEE
130views Communications» more  ICC 2008»
13 years 12 months ago
A Polynomial-Time Approximation Algorithm for Weighted Sum-Rate Maximization in UWB Networks
— Scheduling in an ad hoc wireless network suffers from the non-convexity of the cost function, caused by the interference between communication links. In previous optimization t...
Gyouhwan Kim, Qiao Li, Rohit Negi
MP
2010
150views more  MP 2010»
13 years 5 days ago
The algebraic degree of semidefinite programming
Given a generic semidefinite program, specified by matrices with rational entries, each coordinate of its optimal solution is an algebraic number. We study the degree of the minima...
Jiawang Nie, Kristian Ranestad, Bernd Sturmfels