Algorithm 813: SPG—Software for Convex-Constrained Optimization
ACM Transactions on Mathematical Software (TOMS)
Solving a Class of Linearly Constrained Indefinite QuadraticProblems by D.C. Algorithms
Journal of Global Optimization
Journal of Global Optimization
DC Solutions of Postbuckling Problems
Journal of Global Optimization
Combined SVM-Based Feature Selection and Classification
Machine Learning
Discrete tomography by convex-concave regularization and D.C. programming
Discrete Applied Mathematics - Special issue: IWCIA 2003 - Ninth international workshop on combinatorial image analysis
A regularization framework for multiple-instance learning
ICML '06 Proceedings of the 23rd international conference on Machine learning
Sparse eigen methods by D.C. programming
Proceedings of the 24th international conference on Machine learning
Algorithm 873: LSTRS: MATLAB software for large-scale trust-region subproblems and regularization
ACM Transactions on Mathematical Software (TOMS)
A continuous approach for the concave cost supply problem via DC programming and DCA
Discrete Applied Mathematics
On image reconstruction algorithms for binary electromagnetic geotomography
Theoretical Computer Science
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
On Sparsity Maximization in Tomographic Particle Image Reconstruction
Proceedings of the 30th DAGM symposium on Pattern Recognition
Gene Selection for Cancer Classification Using DCA
ADMA '08 Proceedings of the 4th international conference on Advanced Data Mining and Applications
Catenary Support Vector Machines
ECML PKDD '08 Proceedings of the 2008 European Conference on Machine Learning and Knowledge Discovery in Databases - Part I
Optimization Methods & Software - Mathematical programming in data mining and machine learning
Low Order-Value Optimization and applications
Journal of Global Optimization
DC programming techniques for solving a class of nonlinear bilevel programs
Journal of Global Optimization
Maximum margin clustering made practical
IEEE Transactions on Neural Networks
Discrete tomography by convex-concave regularization and D.C. programming
Discrete Applied Mathematics - Special issue: IWCIA 2003 - Ninth international workshop on combinatorial image analysis
Recovering sparse signals with a certain family of nonconvex penalties and DC programming
IEEE Transactions on Signal Processing
Minimum sum-of-squares clustering by DC programming and DCA
ICIC'09 Proceedings of the Intelligent computing 5th international conference on Emerging intelligent computing technology and applications
A combined DCA: GA for constructing highly nonlinear balanced boolean functions in cryptography
Journal of Global Optimization
DC models for spherical separation
Journal of Global Optimization
Journal of Global Optimization
ACIIDS'10 Proceedings of the Second international conference on Intelligent information and database systems: Part II
Solving QoS routing problems by DCA
ACIIDS'10 Proceedings of the Second international conference on Intelligent information and database systems: Part II
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
Batch and online learning algorithms for nonconvex neyman-pearson classification
ACM Transactions on Intelligent Systems and Technology (TIST)
A robust approach for nonlinear UAV task assignment problem under uncertainty
Transactions on computational collective intelligence II
An efficient DCA for spherical separation
ACIIDS'11 Proceedings of the Third international conference on Intelligent information and database systems - Volume Part II
Solving an inventory routing problem in supply chain by DC programming and DCA
ACIIDS'11 Proceedings of the Third international conference on Intelligent information and database systems - Volume Part II
Multi-instance multi-label learning
Artificial Intelligence
Hierarchical clustering based on mathematical optimization
PAKDD'06 Proceedings of the 10th Pacific-Asia conference on Advances in Knowledge Discovery and Data Mining
Binary tomography by iterating linear programs from noisy projections
IWCIA'04 Proceedings of the 10th international conference on Combinatorial Image Analysis
Binary tomography with deblurring
IWCIA'06 Proceedings of the 11th international conference on Combinatorial Image Analysis
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
DC programming and DCA for large-scale two-dimensional packing problems
ACIIDS'12 Proceedings of the 4th Asian conference on Intelligent Information and Database Systems - Volume Part II
Gaussian kernel minimum sum-of-squares clustering and solution method based on DCA
ACIIDS'12 Proceedings of the 4th Asian conference on Intelligent Information and Database Systems - Volume Part II
Behavior of DCA sequences for solving the trust-region subproblem
Journal of Global Optimization
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
Margin maximization in spherical separation
Computational Optimization and Applications
Computational Optimization and Applications
DC programming and DCA based cross-layer optimization in multi-hop TDMA networks
ACIIDS'13 Proceedings of the 5th Asian conference on Intelligent Information and Database Systems - Volume Part II
Sparse high-dimensional fractional-norm support vector machine via DC programming
Computational Statistics & Data Analysis
Binary classification via spherical separator by DC programming and DCA
Journal of Global Optimization
Robust feature selection for SVMs under uncertain data
ICDM'13 Proceedings of the 13th international conference on Advances in Data Mining: applications and theoretical aspects
New and efficient DCA based algorithms for minimum sum-of-squares clustering
Pattern Recognition
Optimizing a multi-stage production/inventory system by DC programming based approaches
Computational Optimization and Applications
Stability for trust-region methods via generalized differentiation
Journal of Global Optimization
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This paper is devoted to difference of convex functions (d.c.) optimization: d. c. duality, local and global optimality conditions in d. c. programming, the d. c. algorithm (DCA), and its application to solving the trust-region problem. The DCA is an iterative method that is quite different from well-known related algorithms. Thanks to the particular structure of the trust-region problem, the DCA is very simple (requiring only matrix-vector products) and, in practice, converges to the global solution. The inexpensive implicitly restarted Lanczos method of Sorensen is used to check the optimality of solutions provided by the DCA. When a nonglobal solution is found, a simple numerical procedure is introduced both to find a feasible point having a smaller objective value and to restart the DCA at this point. It is shown that in the nonconvex case, the DCA converges to the global solution of the trust-region problem, using only matrix-vector products and requiring at most 2m+2 restarts, where m is the number of distinct negative eigenvalues of the coefficient matrix that defines the problem. Numerical simulations establish the robustness and efficiency of the DCA compared to standard related methods, especially for large-scale problems.