Lectures on modern convex optimization - analysis, algorithms, and engineering applications

By Aharon Ben-Tal, Arkadiaei Semenovich Nemirovskiaei. 2001

2,978 citations recorded by the source corpus.

Subfields: Aerospace Engineering, Computational Theory and Mathematics, Numerical Analysis

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Citations in the corpus

The Price of Fair PCA: One Extra Dimension (2018, methodology): “5 log(1 /(cid:15) )) runtime of an SDP solver that is commonly implemented with the interior point method [Ben-Tal and Nemirovski, 2001], our algorithm may be faster or slower depending on n, (cid:15) .”
Group sparse regularization for deep neural networks (2016, background): “For a convex loss in (2), standard arguments from duality theory show that the problem can be reformulated as follows [37]: where µ λ is a scalar whose precise value depends on λ , and whose existence is guaranteed thanks to the absence of duality gap.”
Outage Constrained Robust Transmit Optimization for Multiuser MISO Downlinks: Tractable Approximations by Conic Optimization (2011, methodology): “Moreover, using the -lemma [48], it can be shown that the semi-infinite constraint on the LHS of (12) is equivalent to the following system of LMIs:”
Three‐dimensional quasi‐static frictional contact by using second‐order cone linear complementarity problem (2006, methodology): “One of the reasons why SOCP and SDP have received larger attention is that the efficient algorithms, the so-called primal-dual interior-point methods [24, 25], have been proposed for these problems, and there exist several implementations of these algorithms that are well developed [26].”
Minimax approaches to robust model predictive control (2003, background): “This is a surprisingly expressive problem class with many applications, such as robust least squares, sumof-norms minimization and quadratically constrained quadratic programming, just to mention a few (Lobo et al., 1998; Ben-Tal and Nemirovski, 2001)”
A Primer on Monotone Operator Methods (2015, background): “Standard references on convex optimization and convex analysis (which contain far more than the reader needs) include [101, 14, 18, 86, 15, 110, 12, 16, 11, 13].”
Matrix Scaling and Balancing via Box Constrained Newton's Method and Interior Point Methods (2017, methodology): “These algorithms are based on interior point methods, with appropriately chosen barriers, commonly used in exponential programming [37].”
Sequential Semidefinite Program for Maximum Robustness Design of Structures under Load Uncertainty (2006, background): “We can see in Problem (21) that maximizing α is equivalent to maximizing α2, which concludes the proof.”
Mesh adaptive computation of upper and lower bounds in limit analysis (2008, background): “A particular class of convex problems are the so-called conic programs (CP) [26].”
Formulation and solution of some plasticity problems as conic programs (2007, background): “1 A fi approp K 1⁄4 K1 KN ð9Þ Conic programming rests of three key assumptions about each cone K (Ben-Tal and Nemirovski, 2001): K is closed : n; n0 2 K ) nþ n0 2 K K is a conic set : n 2 K; k P 0) kn 2 K K is pointed : K \ ð KÞ 1⁄4 0 ð10Þ”
Tractable Approximations to Robust Conic Optimization Problems (2006, background): “Since K is a closed, convex, pointed cone with nonempty interior, so is K∗ (see [5]).”
Direction-of-Arrival Estimation Using a Sparse Representation of Array Covariance Vectors (2011, background): “The DOA estimation in (13) can be efficiently worked out in the second-order cone (SOC) programming framework [10] , [15] .”
A Survey of the S-Lemma (2007, background): “This is the idea of the proof of the S-lemma in [11].”