Semidefinite programming

By Christoph Helmberg. 2002

2,205 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Computer Graphics and Computer-Aided Design, Numerical Analysis

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Citations in the corpus

A Comprehensive Survey of Graph Embedding: Problems, Techniques, and Applications (2017, background): “Specifically, SDP [104] aims to find an inner product matrix that maximizes the pairwise distances between any two inputs which are not connected in the graph while preserving the nearest neighbors distances.”
A Comprehensive Survey on Transfer Learning (2019, background): “In this way, it avoids solving the SDP problem, which results in relatively low computational burden.”
Phase Retrieval with Application to Optical Imaging: A contemporary overview (2015, methodology): “ConjeCture: 4 N−4 generiC meAsurements Are suFFiCient [43] IEEE SIGNAL PROCESSING MAGAZINE [93] MAY 2015 " General Algorithms " section) and sparsity-based methods, i.e., techniques exploiting prior knowledge in the form of signal sparsity (see the " Sparsity-Based Algorithms " section).”
Minimax approaches to robust model predictive control (2003, methodology): “, 1995) and (Vandenberghe and Boyd, 1996) is an exact but possibly expensive method based on an eigenvalue decomposition of F (x), while the second approach is an approximate but hopefully efficient method based on Cholesky factorizations of F (x) and backtracking.”
Concave Quadratic Cuts for Mixed-Integer Quadratic Problems (2015, neutral): “This SDP can be solved using an interior point method in polynomial time, and in practice, the number of iterations required is constant and insensitive to the problem size, despite its worst-case complexity [VB96].”
Interior point methods 25 years later (2012, background): “The readers interested in nonlinear, semidefinite and second-order cone programming are referred to excellent surveys of Forsgren et al. [34], Vandenberghe and Boyd [101], and Lobo et al. [70], respectively.”
Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization (2000, background): “In the last few years, Linear Matrix Inequalities (LMIs, see [17, 91] for background material) have become very useful tools in control theory.”
Safety Verification of Hybrid Systems Using Barrier Certificates (2004, methodology): “The relaxation is provided by the sum of squares decomposition [18] and semidefinite programming [24], which we will describe now.”
Joint Transmit Beamforming for Multiuser MIMO Communications and MIMO Radar (2019, background): “The global optimum of (31) can be obtained in polynomial time with convex optimization toolboxes [62]–[65].”
Fifty Years of MIMO Detection: The Road to Large-Scale MIMOs (2015, background): “to the mathematical model of semidefinite programming (SDP) [323], [324], [494], which is a subfield of convex optimization theory [495].”
Dimensionality Reduction: A Comparative Review (2008, background): “Both the computational and the memory complexity of solving an SDP are cube in the number of constraints [19].”
Theory and Applications of Robust Optimization (2010, background): “We refer the reader to some of the standard optimization literature (e.g., Bertsimas and Tsitsiklis, [37], Boyd and Vandenberghe, [43]) and works on perturbation theory (e.g., Freund, [75], Renegar, [123]) for more on sensitivity analysis.”
Interior Methods for Nonlinear Optimization (2002, neutral): “, the surveys [65, 99, 101]).”