DC programming and DCA: thirty years of developments

HA Le Thi, T Pham Dinh - Mathematical Programming, 2018 - Springer
The year 2015 marks the 30th birthday of DC (Difference of Convex functions) programming
and DCA (DC Algorithms) which constitute the backbone of nonconvex programming and …

On the cone eigenvalue complementarity problem for higher-order tensors

C Ling, H He, L Qi - Computational Optimization and Applications, 2016 - Springer
In this paper, we consider the tensor generalized eigenvalue complementarity problem
(TGEiCP), which is an interesting generalization of matrix eigenvalue complementarity …

[HTML][HTML] Complementary eigenvalues of graphs

R Fernandes, J Judice, V Trevisan - Linear Algebra and its Applications, 2017 - Elsevier
In this paper, we study the Eigenvalue Complementarity Problem (EiCP) when its matrix A
belongs to the class S (G)={A=[aij]: aij= aji≠ 0 iff ij∈ E}, where G=(V, E) is a connected …

Tensor eigenvalue complementarity problems

J Fan, J Nie, A Zhou - Mathematical Programming, 2018 - Springer
This paper studies tensor eigenvalue complementarity problems. Basic properties of
standard and complementarity tensor eigenvalues are discussed. We formulate tensor …

A DC programming approach for solving the symmetric eigenvalue complementarity problem

HA Le Thi, M Moeini, T Pham Dinh, J Judice - Computational Optimization …, 2012 - Springer
In this paper, we investigate a DC (Difference of Convex functions) programming technique
for solving large scale Eigenvalue Complementarity Problems (EiCP) with real symmetric …

A new method for solving Pareto eigenvalue complementarity problems

S Adly, H Rammal - Computational Optimization and Applications, 2013 - Springer
In this paper, we introduce a new method, called the Lattice Projection Method (LPM), for
solving eigenvalue complementarity problems. The original problem is reformulated to find …

Efficient DC programming approaches for the asymmetric eigenvalue complementarity problem

YS Niu, T Pham Dinh, HA Le Thi… - … Methods and Software, 2013 - Taylor & Francis
In this paper, we propose nonlinear programming (NLP) formulations and difference of
convex functions (DC) programming approaches for the asymmetric eigenvalue …

A new method for solving second-order cone eigenvalue complementarity problems

S Adly, H Rammal - Journal of Optimization Theory and Applications, 2015 - Springer
In this paper, we study numerical methods for solving eigenvalue complementarity problems
involving the product of second-order cones (or Lorentz cones). We reformulate such …

Higher-degree eigenvalue complementarity problems for tensors

C Ling, H He, L Qi - Computational Optimization and Applications, 2016 - Springer
In this paper, we introduce a unified framework of Tensor Higher-Degree Eigenvalue
Complementarity Problem (THDEiCP), which goes beyond the framework of the typical …

Copositivity and constrained fractional quadratic problems

P Amaral, IM Bomze, J Júdice - Mathematical Programming, 2014 - Springer
Abstract We provide Completely Positive and Copositive Optimization formulations for the
Constrained Fractional Quadratic Problem (CFQP) and Standard Fractional Quadratic …