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A tutorial on geometric programming
Abstract A geometric program (GP) is a type of mathematical optimization problem characterized by objective and constraint functions that have a special form. Recently developed solution methods canExpand
An Interior-Point Method for Large-Scale $\ell_1$-Regularized Least Squares
TLDR
A specialized interior-point method for solving large-scale -regularized LSPs that uses the preconditioned conjugate gradients algorithm to compute the search direction and can solve large sparse problems, with a million variables and observations, in a few tens of minutes on a PC. Expand
1 Trend Filtering
TLDR
This paper proposes a variation on Hodrick-Prescott (H-P) filtering, a widely used method for trend estimation that substitutes a sum of absolute values for the sum of squares used in H-P filtering to penalize variations in the estimated trend. Expand
Distributed average consensus with least-mean-square deviation
TLDR
The problem of finding the (symmetric) edge weights that result in the least mean-square deviation in steady state is considered and it is shown that this problem can be cast as a convex optimization problem, so the global solution can be found efficiently. Expand
An Interior-Point Method for Large-Scale l1-Regularized Logistic Regression
TLDR
This paper describes an efficient interior-point method for solving large-scale l1-regularized logistic regression problems, and shows how a good approximation of the entire regularization path can be computed much more efficiently than by solving a family of problems independently. Expand
Optimal kernel selection in Kernel Fisher discriminant analysis
TLDR
This paper considers the problem of finding the optimal kernel, over a given convex set of kernels, and shows that this optimal kernel selection problem can be reformulated as a tractable convex optimization problem which interior-point methods can solve globally and efficiently. Expand
A game-theoretic approach to power allocation in frequency-selective gaussian interference channels
This paper defines a rate maximization power allocation game in a frequency selective Gaus- sian interference channel, after assuming a suboptimal but pragmatic multi-user coding scheme. We show thatExpand
Tractable approximate robust geometric programming
Abstract The optimal solution of a geometric program (GP) can be sensitive to variations in the problem data. Robust geometric programming can systematically alleviate the sensitivity problem byExpand
Digital Circuit Optimization via Geometric Programming
TLDR
A method for digital circuit optimization based on formulating the problem as a geometric program or generalized geometric program (GGP), which can be transformed to a convex optimization problem and then very efficiently solved. Expand
Robust Fisher Discriminant Analysis
TLDR
It is shown that with general convex uncertainty models on the problem data, robust Fisher LDA can be carried out using convex optimization using a certain type of product form uncertainty model at a cost comparable to standard Fisher L DA. Expand
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