On the Convergence of the Concave-Convex Procedure

By Bharath K. Sriperumbudur, Gert R. G. Lanckriet. Neural Information Processing Systems, 2009

529 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/8aabf5ba342d37edc1ebd89ba898c70b0a4ca121

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Citations in the corpus

Learning Multi-View Neighborhood Preserving Projections (2011, methodology): “We choose the loss function as Li,j(w1, w2, xi, yj , Sxi) = (3) I[[yj∈Sxi ]] 2 × Li,j1 + ( 1− I[[yj∈Sxi ]] ) 2 × Li,j2 (4) with (5) Li,j1 = ‖g w1 1 (xi)− g w2 2 (yj)‖ 2 Fro (6) Li,j2 (βd) = − 12β 2 d + aλ2 2 , if 0 ≤ |βd| λ |βd|2−2aλ|βd|+a2λ2 2(a−1) , if λ ≤ |βd| ≤ aλ 0, if |βd| ≥ aλ, (7) where β”
Efficient Structured Prediction with Latent Variables for General Graphical Models (2012, methodology): “…instances of variational meth-ods discussed, e.g ., in (Jordan et al., 1999) like the concave-convex procedure (CCCP) (Yuille & Rangara-jan, 2003; Sriperumbudur & Lanckriet, 2009) by sepa-rating the cost function into two functions f 1 λ ) and f 3 ( d ), convex in their parameters and a bilinear…”
Hopfield Networks is All You Need (2020, methodology): “sidered with E 1 convex, E 2 convex, ccomponent-wise convex function, and dan afﬁne function. The CCCP algorithm solves this minimization problem by linearization of the concave part and is deﬁned in [57] as ˘t+1 2argmin ˘ E 1 (˘) + ˘Tr ˘E 2 ˘t (A32) s.t. c(˘) 60 ; d(˘) = 0 : We deﬁne the upper boun”
Content-Centric Sparse Multicast Beamforming for Cache-Enabled Cloud RAN (2015, background): “The convergence proof of CCP to critical points of the original problem for the differentiable case can be found in [26] and [32].”
Policy Evaluation and Optimization with Continuous Treatments (2018, background): “The global convergence of such a procedure remains an open question but it works well in practice [13].”
Variations and extension of the convex–concave procedure (2016, background): “A proof showing convergence to critical points of the original problem in the differentiable case can be found in (Lanckreit and Sriperumbudur, 2009).”
Learning with Augmented Class by Exploiting Unlabeled Data (2014, methodology): “CCCP is an algorithm which solves a difference of convex functions programming as a sequence of convex programming, and is proved to converge with both convex and non-convex constraints (Lanckriet and Sriperumbudur 2009).”
Disciplined convex-concave programming (2016, background): “The convex-concave procedure (CCP) [22], [23] is another heuristic algorithm for finding a local optimum of (1), which leverages our ability to efficiently solve convex optimization problems.”
Viewpoint-Aware Video Summarization (2018, background): “Please refer [20] for the convergence property of CCCP.”
Multitask Learning without Label Correspondences (2010, methodology): “This procedure is guaranteed to converge to a local optimum or saddle point [16].”
Self-Paced Learning for Latent Variable Models (2010, methodology): “This observation leads to a concave-convex procedure (CCCP) [24] outlined in Algorithm 2, which has been shown to converge to a local minimum or saddle point solution [19].”