Finding the Point of a Polyhedron Closest to the Origin

By B. F. Mitchell, V. F. Dem'yanov, V. N. Malozemov. 1974

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In Algorithms & Complexity

Citations in the corpus

Minding the Gaps for Block Frank-Wolfe Optimization of Structured SVMs (2016, methodology): “Caching the results of the max oracle implements this idea by reusing the previous calls of the max oracle to store potentially promising corners.”
On the Global Linear Convergence of Frank-Wolfe Optimization Variants (2015, methodology): “[25], called the MDM algorithm, originally invented for the polytope distance problem.”
A novel Frank-Wolfe algorithm. Analysis and applications to large-scale SVM training (2013, methodology): “The Gilbert and MDM Algorithms Two classic iterative methods used to solve MNPs are the Gilbert algorithm [26] and the Mitchell-DemnyanovMalozemov (MDM) algorithm [42].”
Finding the nearest point in A polytope (1976, methodology): “, [2, 9]) are convergent, non-terminating methods, and cannot be properly compared with the present scheme.”
Continuous Subdifferential Approximations and Their Applications (2003, methodology): “Several effective methods for solving such problems are known (see, e.g., [17, 21, 43 , 60]).”
Linearly Convergent Frank-Wolfe with Backtracking Line-Search. (2018, methodology): “It generalizes the algorithm of Mitchell et al. (1974) used in geometry and SMO (Platt, 1998) for training SVMs.”
Advances in Large Margin Classifiers (2000, methodology): “, 1974] and [Keerthi comparison to [Michell et al., 1974] et al.”
A fast iterative nearest point algorithm for support vector machine classifier design (2000, methodology): “All these discussions point to the important fact that (15) can be used to effectively terminate a numerical algorithm for solving NPP. V. ITERATIVE ALGORITHMS FOR NPP NPP has been well studied in the literature, and a number of good algorithms have been given for it [10], [18], [29], [2], [15].”