Applications of second-order cone programming
TLDR
In this paper, an efficient primal-dual interior-point method for solving second-order cone programs (SOCP) is presented. But it is not a generalization of interior point methods for convex problems.About:
This article is published in Linear Algebra and its Applications.The article was published on 1998-11-15 and is currently open access. It has received 2215 citations till now. The article focuses on the topics: Second-order cone programming & Conic optimization.read more
Citations
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Journal ArticleDOI
Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones
TL;DR: This paper describes how to work with SeDuMi, an add-on for MATLAB, which lets you solve optimization problems with linear, quadratic and semidefiniteness constraints by exploiting sparsity.
Book ChapterDOI
Graph Implementations for Nonsmooth Convex Programs
Michael C. Grant,Stephen Boyd +1 more
TL;DR: Graph implementations as mentioned in this paper is a generic method for representing a convex function via its epigraph, described in a disciplined convex programming framework, which allows a very wide variety of smooth and nonsmooth convex programs to be easily specified and efficiently solved.
Journal ArticleDOI
A sparse signal reconstruction perspective for source localization with sensor arrays
TL;DR: This work presents a source localization method based on a sparse representation of sensor measurements with an overcomplete basis composed of samples from the array manifold that has a number of advantages over other source localization techniques, including increased resolution, improved robustness to noise, limitations in data quantity, and correlation of the sources.
Journal ArticleDOI
An Interior-Point Method for Large-Scale $\ell_1$ -Regularized Least Squares
TL;DR: In this paper, the preconditioned conjugate gradients (PCG) algorithm is used to compute the search direction for sparse least-squares programs (LSPs), which can be reformulated as convex quadratic programs, and then solved by several standard methods such as interior-point methods.
Proceedings ArticleDOI
Multiple kernel learning, conic duality, and the SMO algorithm
TL;DR: Experimental results are presented that show that the proposed novel dual formulation of the QCQP as a second-order cone programming problem is significantly more efficient than the general-purpose interior point methods available in current optimization toolboxes.
References
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Journal ArticleDOI
Semidefinite programming
Lieven Vandenberghe,Stephen Boyd +1 more
TL;DR: A survey of the theory and applications of semidefinite programs and an introduction to primaldual interior-point methods for their solution are given.
Journal ArticleDOI
Robust Convex Optimization
Aharon Ben-Tal,Arkadi Nemirovski +1 more
TL;DR: If U is an ellipsoidal uncertainty set, then for some of the most important generic convex optimization problems (linear programming, quadratically constrained programming, semidefinite programming and others) the corresponding robust convex program is either exactly, or approximately, a tractable problem which lends itself to efficientalgorithms such as polynomial time interior point methods.
Book
Primal-Dual Interior-Point Methods
TL;DR: This chapter discusses Primal Method Primal-Dual Methods, Path-Following Algorithm, and Infeasible-Interior-Point Algorithms, and their applications to Linear Programming and Interior-Point Methods.
Book
Introduction to approximation theory
TL;DR: In this paper, Tchebycheff polynomials and other linear families have been used for approximating least-squares approximations to systems of equations with one unknown solution.
Book
Linear Programming: Foundations and Extensions
TL;DR: The Simplex Method in Matrix Notation and Duality Theory, and Applications: Foundations of Convex Programming.