A mathematical view of interior-point methods in convex optimization

By J. Renegar. MPS-SIAM series on optimization, 2001

745 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/db69e32846a9e4e80e1b58cb930a0d2017803300

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In Numerical Analysis

Citations in the corpus

Cones and interior-point algorithms for structured convex optimization involving powers andexponentials (2009, neutral): “[52],[46],[55]).”
A second-order method for strongly convex ℓ1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell _1$$\end{document}-re (2013, background): “a quadratic approximation of the function f ˝ (x) at x q ˝ (y) := f ˝ (x) + rf ˝ (x) |(y x) + 1 2 (y x)|r2f ˝ (x)(y x); then jf ˝ (y) q ˝ (y)j 1 6 L f ˝ ky xk3: Proof Using corollary 1.5.3 in [19] and Lemma 5 we have jf ˝ (y) q ˝ (y)jky xk2 Z 1 0 Z t 0 kr2f ˝ (x+ s(y x)) r 2f ˝ (x)kdsdt ky xk2 Z 1 0”
Sums of Squares, Moment Matrices and Optimization Over Polynomials (2009, neutral): “[96, 117, 147, 150, 156].”
Pivotal estimation via square-root Lasso in nonparametric regression (2011, background): “gramming, 109(2-3):319–344, 2007. [21] Y. Nesterov and A Nemirovskii. Interior-PointPolynomialAlgorithmsinConvexProgramming. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, 1993. [22] J. Renegar. A Mathematical View of Interior-Point Methods in Convex Optimization. Society for I”
11-magic : Recovery of sparse signals via convex programming (2005, background): “The complete log-barrier implementation for each problem follows the outline: 1The choice of − log(−x) for the barrier function is not arbitrary, it has a property (termed self-concordance) that is very important for quick convergence of (7) to (6) both in theory and in practice (see the very nice e”
Square-Root Lasso: Pivotal Recovery of Sparse Signals via Conic Programming (2010, methodology): “the icecream cone). This formulation allows us to implement the estimator using eﬃcient algorithmic methods, such as interior point methods, which provide polynomial-time bounds on computational time [10, 11], and which have been recently extended to handle problems of a very large 12 BELLONI CHERNO”
Approximation of the Stability Number of a Graph via Copositive Programming (2002, background): “, [24]) gives the duality relations between (P ) and (D).”