Solving a Class of Linearly Constrained Indefinite QuadraticProblems by D.C. Algorithms

Authors:
Le Thi Hoai An;Pham Dinh Tao
Affiliations:
Mathematical Modelling and Applied Optimization Group, LMI, INSA Rouen, CNRS, URA 1378 BP 8, F 76 131 Mont Saint Aignan Cedex, France. $^*$ ;Mathematical Modelling and Applied Optimization Group, LMI, INSA Rouen, CNRS, URA 1378 BP 8, F 76 131 Mont Saint Aignan Cedex, France. $^*$
Venue:
Journal of Global Optimization
Year:
1997

Citing 7
Cited 39

Global minimization of large-scale constrained concave quadratic problems by separable programming

Mathematical Programming: Series A and B
An algorithm for global minimization of linearly constrained concave quadratic functions

Mathematics of Operations Research
Global minimization of indefinite quadratic problems

Computing
Iterative behaviour, fixed point of a class of monotone operators. Application to nonsymmetric threshold function

Discrete Mathematics
A parallel algorithm for constrained concave quadratic global minimization

Mathematical Programming: Series A and B
A D. C. Optimization Algorithm for Solving the Trust-Region Subproblem

SIAM Journal on Optimization
Difference of convex functions optimization algorithms (DCA) for globally minimizing nonconvex quadratic forms on Euclidean balls and spheres

Operations Research Letters

A Branch and Bound Method via d.c. Optimization Algorithms andEllipsoidal Technique for Box Constrained Nonconvex Quadratic Problems

Journal of Global Optimization
Dual Bounds and Optimality Cuts for All-Quadratic Programs with Convex Constraints

Journal of Global Optimization
Branch-and-bound approaches to standard quadratic optimization problems

Journal of Global Optimization
D.C. programming approach for multicommodity network optimization problems with step increasing cost functions

Journal of Global Optimization
Undominated d.c. Decompositions of Quadratic Functions and Applications to Branch-and-Bound Approaches

Computational Optimization and Applications
Decomposition Methods for Solving Nonconvex Quadratic Programs via Branch and Bound*

Journal of Global Optimization
A continuous approach for the concave cost supply problem via DC programming and DCA

Discrete Applied Mathematics
Combining DCA (DC Algorithms) and interior point techniques for large-scale nonconvex quadratic programming

Optimization Methods & Software - Mathematical programming in data mining and machine learning
Several multi-criteria programming methods for classification

Computers and Operations Research
Select Objective Functions for Multiple Criteria Programming Classification

WI-IAT '08 Proceedings of the 2008 IEEE/WIC/ACM International Conference on Web Intelligence and Intelligent Agent Technology - Volume 03
DC programming techniques for solving a class of nonlinear bilevel programs

Journal of Global Optimization
Multiple Criteria Quadratic Programming for Financial Distress Prediction of the Listed Manufacturing Companies

ICCS 2009 Proceedings of the 9th International Conference on Computational Science
A branch and reduce approach for solving a class of low rank d.c. programs

Journal of Computational and Applied Mathematics
Pattern classification with class probability output network

IEEE Transactions on Neural Networks
Multiple criteria programming models for VIP E-Mail behavior analysis

Web Intelligence and Agent Systems
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
An efficient combined DCA and B&B using DC/SDP relaxation for globally solving binary quadratic programs

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
An efficient DCA for spherical separation

ACIIDS'11 Proceedings of the Third international conference on Intelligent information and database systems - Volume Part II
Nonconvex quadratically constrained quadratic programming: best D.C. decompositions and their SDP representations

Journal of Global Optimization
Large Margin Hierarchical Classification with Mutually Exclusive Class Membership

The Journal of Machine Learning Research
Hierarchical clustering based on mathematical optimization

PAKDD'06 Proceedings of the 10th Pacific-Asia conference on Advances in Knowledge Discovery and Data Mining
Exact penalty and error bounds in DC programming

Journal of Global Optimization
Shakedown analysis with multidimensional loading spaces

Computational Mechanics
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
Variable selection in high-dimensional varying-coefficient models with global optimality

The Journal of Machine Learning Research
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
Solving the minimum M-dominating set problem by a continuous optimization approach based on DC programming and DCA

Journal of Combinatorial Optimization
Scheduling of lifting vehicle and quay crane in automated port container terminals

International Journal of Intelligent Information and Database Systems
Single straddle carrier routing problem in port container terminals: mathematical model and solving approaches

International Journal of Intelligent Information and Database Systems
Binary classification via spherical separator by DC programming and DCA

Journal of Global Optimization
Block clustering based on difference of convex functions dc programming and dc algorithms

Neural Computation
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
DCA based algorithms for feature selection in semi-supervised support vector machines

MLDM'13 Proceedings of the 9th international conference on Machine Learning and Data Mining in Pattern Recognition
New and efficient DCA based algorithms for minimum sum-of-squares clustering

Pattern Recognition
Cluster analysis: unsupervised learning via supervised learning with a non-convex penalty

The Journal of Machine Learning Research

Quantified Score

Hi-index	0.00

Visualization

Abstract

Linearly constrained indefinite quadratic problems play an important role inglobal optimization. In this paper we study d.c. theory and its local approachto such problems. The new algorithm, CDA, efficiently produces local optima andsometimes produces global optima. We also propose a decomposition branch andbound method for globally solving these problems. Finally many numericalsimulations are reported.