Journal ArticleDOI
Error Bounds Via Exact Penalization with Applications to Concave and Quadratic Systems
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The relationships between the error bound and the exact penalization are investigated and the new error bounds for inequality systems of concave functions and of nonconvex quadratic functions over polyhedral convex sets are established.Abstract:
In this paper, we deal with the error bounds for inequality systems and the exact penalization for constrained optimization problems. We firstly investigate the relationships between the error bound and the exact penalization. Then we establish the new error bounds for inequality systems of concave functions and of nonconvex quadratic functions over polyhedral convex sets.read more
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Journal ArticleDOI
DC programming and DCA: thirty years of developments
Hoai An Le Thi,Tao Pham Dinh +1 more
TL;DR: A short survey on thirty years of developments of DC (Difference of Convex functions) programming and DCA (DC Algorithms) which constitute the backbone of nonconvex programming and global optimization.
Journal ArticleDOI
DC programming and DCA for supply chain and production management: state-of-the-art models and methods
TL;DR: It is undoubtedly that mathematical modelling and optimisation play a key role in the supply chain and the production management (SCPM) and this paper provides a survey on DC.
Posted Content
Stochastic Difference-of-Convex Algorithms for Solving nonconvex optimization problems
TL;DR: The paper deals with stochastic difference-of-convex functions programs, that is, optimization problems whose cost function is a sum of a lower semicontinuous difference- of- Convex function and the expectation of a stochastically difference-Of-concex function with respect to a probability distribution.
Journal ArticleDOI
DC auxiliary principle methods for solving lexicographic equilibrium problems
Journal ArticleDOI
Open issues and recent advances in DC programming and DCA
Hoai An Le Thi,T.Pham Dinh +1 more
TL;DR: In this article , the authors present key open issues, recent advances and trends in the development of these tools to meet the growing need for nonconvex programming and global optimization.
References
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TL;DR: In this article, the authors present preliminary results on functional analysis and convex analysis in Locally Convex Spaces (LCS) and describe some applications of convex analyses in Normed Spaces.
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On approximate solutions of systems of linear inequalities
TL;DR: In this paper, it is shown that if (1) is consistent, one can infer that there is a solution x0 of (1)-close to x. The purpose of this report is to justify and formulate precisely this assertion.
Journal ArticleDOI
Error bounds in mathematical programming
TL;DR: This paper gives a comprehensive, state-of-the-art survey of the extensive theory and rich applications of error bounds for inequality and optimization systems and solution sets of equilibrium problems.
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Generalizations of the trust region problem
TL;DR: The main results are a characterization of the global minimizer of the generalized trust region problem, and the development of an algorithm that finds an approximateglobal minimizer in a finite number of iterations.
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