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In a second-order cone program (SOCP) a linear function is minimized over the intersection of an a ne set and the product of second-order (quadratic) cones. SOCPs are nonlinear convex problems that include linear and (convex) quadratic programs as special cases, but are less general than semide nite programs (SDPs). Several e cient primal-dual… (More)

Convex programming is a subclass of nonlinear programming (NLP) that unifies and generalizes least squares (LS), linear programming (LP), and convex quadratic programming (QP). This generalization is achieved while maintaining many of the important, attractive theoretical properties of these predecessors. Numerical algorithms for solving convex programs are… (More)

- Siddharth Joshi, Stephen Boyd
- IEEE Transactions on Signal Processing
- 2009

We consider the problem of choosing a set of k sensor measurements, from a set of m possible or potential sensor measurements, that minimizes the error in estimating some parameters. Solving this problem by evaluating the performance for each of the (<sub>m</sub> <sup>k</sup>) possible choices of sensor measurements is not practical unless m and k are… (More)

- Stephen Boyd, C. Barratt
- 1991

- Seung-Jean Kim, Kwangmoo Koh, Mitch Lustig, Stephen Boyd, Dimitry M. Gorinevsky
- IEEE Journal of Selected Topics in Signal…
- 2007

Recently, a lot of attention has been paid to regularization based methods for sparse signal reconstruction (e.g., basis pursuit denoising and compressed sensing) and feature selection (e.g., the Lasso algorithm) in signal processing, statistics, and related fields. These problems can be cast as -regularized least-squares programs (LSPs), which can be… (More)

- Sunil Kandukuri, Stephen Boyd
- IEEE Trans. Wireless Communications
- 2002

We propose a new method of power control for interference limited wireless networks with Rayleigh fading of both the desired and interference signals. Our method explictly takes into account the statistical variation of both the received signal and interference power, and optimally allocates power subject to constraints on the probability of fading induced… (More)

Recently, a lot of attention has been paid to l1 regularization based methods for sparse signal reconstruction (e.g., basis pursuit denoising and compressed sensing) and feature selection (e.g., the Lasso algorithm) in signal processing, statistics, and related fields. These problems can be cast as l1-regularized least squares programs (LSPs), which can be… (More)

CVXGEN is a software tool that takes a high level description of a convex optimization problem family, and automatically generates custom C code that compiles into a reliable, high speed solver for the problem family. The current implementation targets problem families that can be transformed, using disciplined convex programming techniques, to convex… (More)

This is a collection of additional exercises, meant to supplement those found in the book Convex Optimization, by Stephen Boyd and Lieven Vandenberghe. These exercises were used in several courses on convex optimization, EE364a (Stanford), EE236b (UCLA), or 6.975 (MIT), usually for homework, but sometimes as exam questions. Some of the exercises were… (More)

- Stephen Boyd
- 1985

Ahsfract-Using the notion of fading memory we prove very strong versions of two folk theorems. The first is that any time-inuariant (TZ) con~inuou.r nonlinear operator can be approximated by a Volterra series operator, and the second is that the approximating operator can be realized as a finiiedimensional linear dynamical system with a nonlinear readout… (More)