From our results it follows that any dcA sequence for solving the trust-region subproblem (see Pham Dinh and Le Thi, in SIAM J Optim 8:476-505, 1998) is convergent provided that the basic matrix of the problem is nons...
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From our results it follows that any dcA sequence for solving the trust-region subproblem (see Pham Dinh and Le Thi, in SIAM J Optim 8:476-505, 1998) is convergent provided that the basic matrix of the problem is nonsingular and it does not have multiple negative eigenvalues. Besides, under this additional assumption, there exists such an open set containing the global minimizers and the unique local-nonglobal minimizer (if such exists) that any dcA sequence with the initial point from is contained in the set and converges to a global minimizer or the local-nonglobal minimizer. Various examples are given to illustrate the limiting behavior and stability of the dcA sequences. Structure of the KKT point set of the trust-region subproblem is also analyzed.
We describe and evaluate two algorithms for Neyman-Pearson (NP) classification problem which has been recently shown to be of a particular importance for bipartite ranking problems. NP classification is a nonconvex pr...
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We describe and evaluate two algorithms for Neyman-Pearson (NP) classification problem which has been recently shown to be of a particular importance for bipartite ranking problems. NP classification is a nonconvex problem involving a constraint on false negatives rate. We investigated batch algorithm based on dc programming and stochastic gradient method well suited for large-scale datasets. Empirical evidences illustrate the potential of the proposed methods.
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