Semidefinite Optimization and Convex Algebraic Geometry

By Grigoriy Blekherman, Pablo A. Parrilo, Rekha R. Thomas. 2012

724 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/1bca7277d1b418a51f59fa7581f0416400105294

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Citations in the corpus

Convex Formulations for Fair Principal Component Analysis (2018, background): “Note that (16) can be rewritten as SDP constraints using a standard reformulation for the spectral norm (Boyd et al., 1994; Blekherman et al., 2012).”
Application of the Moment-SOS Approach to Global Optimization of the OPF Problem (2013, background): “We first review some theoretical aspects of the moment-sos approach (a nice short account can be found in [25], and more in [26] and [27]).”
Amoebas, nonnegative polynomials and sums of squares supported on circuits (2014, background): “For an overview and proofs of the previous facts, see [3,32].”
Sample Path Generation for Probabilistic Demand Forecasting (2018, background): “Using the fact that the set of all possible covariance matrices is a convex set (see [3]), we only need to consider a single point inside C - let us denote this point by Σ∗ and define the shrinkage estimator Σ as:”
Learning algebraic varieties from samples (2018, methodology): “The second array [8,8,8,8] selects the 8 largest barcodes for each dimension.”
Dilations, Linear Matrix Inequalities, the Matrix Cube Problem and Beta Distributions (2014, background): “The book [BPR13] gives an overview of the substantial theory of LMIs and spectrahedra and the connection to real algebraic geometry.”
Graduated Non-Convexity for Robust Spatial Perception: From Non-Minimal Solvers to Global Outlier Rejection (2019, methodology): “We benchmark GNC-GM and GNC-TLS against (i) Zhou’s method [15], (ii) RANSAC with 100 maximum iterations and 99% confidence using a 4-point minimal solver (we use our SOS solver as minimal solver), and (iii) ADAPT [27].”