A continuous approach for the concave cost supply problem via DC programming and DCA
Discrete Applied Mathematics
Extending the geometric build-up algorithm for the molecular distance geometry problem
Information Processing Letters
Noisy Image Segmentation by a Robust Clustering Algorithm Based on DC Programming and DCA
ICDM '08 Proceedings of the 8th industrial conference on Advances in Data Mining: Medical Applications, E-Commerce, Marketing, and Theoretical Aspects
Optimization Methods & Software - Mathematical programming in data mining and machine learning
DC programming techniques for solving a class of nonlinear bilevel programs
Journal of Global Optimization
Locating Objects in the Plane Using Global Optimization Techniques
Mathematics of Operations Research
Journal of Global Optimization
Solving the Euclidean k-median problem by DCA
ACS'10 Proceedings of the 10th WSEAS international conference on Applied computer science
Properties of two DC algorithms in quadratic programming
Journal of Global Optimization
On the computation of protein backbones by using artificial backbones of hydrogens
Journal of Global Optimization
Combining DC-programming and steepest-descent to solve the single-vehicle inventory routing problem
Computers and Industrial Engineering
Hierarchical clustering based on mathematical optimization
PAKDD'06 Proceedings of the 10th Pacific-Asia conference on Advances in Knowledge Discovery and Data Mining
A DC programming approach for solving the symmetric Eigenvalue Complementarity Problem
Computational Optimization and Applications
Exact penalty and error bounds in DC programming
Journal of Global Optimization
The discretizable molecular distance geometry problem
Computational Optimization and Applications
Clustering data stream by a sub-window approach using DCA
MLDM'12 Proceedings of the 8th international conference on Machine Learning and Data Mining in Pattern Recognition
Journal of Combinatorial Optimization
International Journal of Intelligent Information and Database Systems
Binary classification via spherical separator by DC programming and DCA
Journal of Global Optimization
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A so-called DCA method based on a d.c.\ (difference of convex functions) optimization approach (algorithm) for solving large-scale distance geometry problems is developed. Different formulations of equivalent d.c.\ programs in the $l_{1}$-approach are stated via the Lagrangian duality without gap relative to d.c.\ programming, and new nonstandard nonsmooth reformulations in the $l_{\infty }$-approach (resp., the $l_{1}-l_{\infty }$-approach) are introduced. Substantial subdifferential calculations permit us to compute sequences of iterations in the DCA quite simply. The computations actually require matrix-vector products and only one Cholesky factorization (resp., with an additional solution of a convex program) in the $l_{1}$-approach (resp., the $l_{1}-l_{\infty }$-approach) and allow the exploitation of sparsity in the large-scale setting. Two techniques---respectively, using shortest paths between all pairs of atoms to generate the complete dissimilarity matrix and the spanning trees procedure---are investigated in order to compute a good starting point for the DCA. Finally, many numerical simulations of the molecular optimization problems with up to 12567 variables are reported, which prove the practical usefulness of the nonstandard nonsmooth reformulations, the globality of found solutions, and the robustness and efficiency of our algorithms.