Convex nondifferentiable optimization: A survey focused on the analytic center cutting plane method

By Jean-Louis Goffin, Jean-Philippe Vial. 2002

217 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Numerical Analysis

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Citations in the corpus

Selected Topics in Column Generation (2002, methodology): “Among them are the bundle method (Hiriart-Urruty and Lemaréchal 1993) based on quadratic programming, and the analytic center cutting-plane method (Gofﬁn and Vial 2003), an interior point solution approach.”
A Primer in Column Generation (2005, background): “The Lagrangian functionL(π) is therefore the lower envelope of all lines and its topmost point corresponds to the valueL of the Lagrangian dual problem.”
A Convex Primal Formulation for Convex Hull Pricing (2016, unknown): “Algorithms such as sub-gradient methods, bundle methods [13], and cutting plane methods [14] have been proposed to solve the Lagrangian dual problem of mixedinteger programming problems.”
An interior-point Benders based branch-and-cut algorithm for mixed integer programs (2010, background): “ticular constraint to push the analytic center away from it. To balance the effect of the constraints, a weight equal to the number of constraints is associated with the bound constraint g T u ≤ γ to force the analytic center away from the upper bound ( Goffin and Vial 2002 ).”
Predicting abnormal returns from news using text classification (2008, methodology): “Text classification has also been used to directly predict volatility (see Mittermayer and Knolmayer ( 2006b ) for a survey of trading systems that use text).”
A Faster Cutting Plane Method and its Implications for Combinatorial and Convex Optimization (2015, unknown): “6 2.3 Submodular Function Minimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8”
Support vector machine classification with indefinite kernels (2007, background): “Other schemes are available with slightly different complexities: an O(n(2)/ǫ(2)) is achieved in [19] using (cheaper) approximate centers for example.”
Simultaneous routing and resource allocation via dual decomposition (2004, background): “For computational details and convergence analysis of ACCPM, see [21, 22, 8] and references therein.”
An Interior-Point Method for a Class of Saddle-Point Problems (2003, background): “Let us start with the following question: Given points x∈X and y∈Y , how does one determine whether this pair is or is not close to a saddle point? Recall the functions f and g defined in (4) and (10).”