The Concave-Convex Procedure (CCCP)

By Alan L. Yuille, Anand Rangarajan. Neural Information Processing Systems, 2001

547 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/f0bf18fc90674fbef616e8c54bdefb3adc237e4d

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Citations in the corpus

Large Scale Transductive SVMs (2006, methodology): “We propose to solve this non convex problem using the “Concave-Convex Procedure” (CCCP) (Yuille and Rangarajan, 2002).”
Nonconvex Nonsmooth Low Rank Minimization via Iteratively Reweighted Nuclear Norm (2015, background): “NONCONVEX NONSMOOTH LOW RANK MINIMIZATION In this section, we show how to solve the general problem (3), which is a concave-convex problem [36].”
Hopfield Networks is All You Need (2020, background): “(A20) is the Concave-Convex Procedure (CCCP) for minimizing the energy E.”
Multiple instance learning for sparse positive bags (2007, methodology): “... achieve this is by augmenting the optimization formulation with a constraint |w �(x)+b| � 1 �x on the value of the decision function for every unlabeled instance x. Recently, Collobert et al. (2006) have given an approximation method for solving the resulting non-convex optimization problem, in ”
Spectral Algorithms for Computing Fair Support Vector Machines (2017, methodology): “Thus, the constrained convex-concave procedure [Tuy, 1995, Yuille and Rangarajan, 2002, Smola et al., 2005] can be used to design an algorithm.”
Modeling Occlusion by Discriminative AND-OR Structures (2013, methodology): “We use the concave-convex procedure (CCCP) [33] to solve our problem, where the details can be found in [33, 32, 34].”
Trading convexity for scalability (2006, methodology): “The Concave-Concave Procedure (CCCP) [23, 20] solves a sequence of convex problems and has no difficult parameters to tune.”
Multiple instance learning for soft bags via top instances (2015, unknown): “This is a latentSVM learning problem [10] min w 1 2 ||w||2 + C ∑NT i=1 max ( 0, 1− yifw(XBi) ) .”
Cosegmentation of Image Pairs by Histogram Matching - Incorporating a Global Constraint into MRFs (2006, methodology): “This method was inspired by concave-convex procedure for minimizing functions of continuous variables [22].”
Fully Connected Deep Structured Networks (2015, methodology): “Hence the concave-convex procedure (CCCP) [40] is directly applicable.”
Dynamic Pooling for Complex Event Recognition (2013, methodology): “In this work, we adopt the concave-convex procedure (CCCP) of [29].”
Viewpoint-Aware Video Summarization (2018, methodology): “We utilized a well-known CCCP (concave convex procedure) algorithm [40, 41] to solve it.”
Video Pop-up: Monocular 3D Reconstruction of Dynamic Scenes (2014, background): “Although exact optimisation of either of these costs is straightforward, optimising both together is challenging, and we make use of the convex-concave procedure (CCP) [43], [24], and find an optimisable cost that is tight at the current location, but an overestimate elsewhere.”
Semi-supervised learning by disagreement (2010, unknown): “…annealing approach, which decomposes the original optimization problem into a series of convex optimization problems, from easy to hard, and solves them sequentially [65] [66]; employing the convex-concave procedure (CCCP) [77] to directly optimize the non-convex loss function [25], etc.”
Derivative-Free Optimization via Classification (2016, methodology): “We set the total number of calls to the objective function to be 40n for all algorithms except for CCCP, while CCCP runs until it converges.”
Enhancing one-class support vector machines for unsupervised anomaly detection (2013, background): “The relaxation yields an objective that has a convex and a concave part, which makes the iterative approach a generalization of a concave convex procedure (OCCC) [34] that is guaranteed to converge.”
Parameter Learning and Convergent Inference for Dense Random Fields (2013, methodology): “We use the concave-convex procedure (CCCP) to minimize the KL divergence (Yuille & Rangarajan, 2001).”