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

We present DCA for globally minimizing quadratic forms on Euclidean balls and spheres. Since these problems admit at most one local-nonglobal minimizer, DCA converges in general to a solution for these problems. Numerical simulations show robustness, stability and efficiency of DCA with respect to r...

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Published in:	Operations research letters Vol. 19; no. 5; pp. 207 - 216
Main Authors:	Tao, Pham Dinh, An, Le Thi Hoai
Format:	Journal Article
Language:	English
Published:	Amsterdam Elsevier B.V 01.11.1996 Elsevier
Subjects:	Applied sciences Computer Science d.c. optimization d.c. optimization algorithms Exact sciences and technology Local and global optimality conditions Mathematical programming Nonconvex quadratic minimization Operational research and scientific management Operational research. Management science Optimization. Search problems d.c. optimization algorithms Local and global optimality conditions Nonconvex quadratic minimization d.c. optimization Non convex programming Algorithms Euclidean theory Optimality condition Spheres Quadratic programming Optimization
ISSN:	0167-6377, 1872-7468
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Abstract	We present DCA for globally minimizing quadratic forms on Euclidean balls and spheres. Since these problems admit at most one local-nonglobal minimizer, DCA converges in general to a solution for these problems. Numerical simulations show robustness, stability and efficiency of DCA with respect to related standard methods.
AbstractList	We present DCA for globally minimizing quadratic forms on Euclidean balls and spheres. Since these problems admit at most one local-nonglobal minimizer, DCA converges in general to a solution for these problems. Numerical simulations show robustness, stability and efficiency of DCA with respect to related standard methods.
Author	An, Le Thi Hoai Tao, Pham Dinh
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Keywords	d.c. optimization algorithms Local and global optimality conditions Nonconvex quadratic minimization d.c. optimization Non convex programming Algorithms Euclidean theory Optimality condition Spheres Quadratic programming Optimization
Language	English
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France – year: 1986 ident: 10.1016/S0167-6377(96)00036-3_BIB18 article-title: Algorithms for solving a class of non-convex optimization problems, Methods of subgradients – volume: 24 start-page: 523 year: 1990 ident: 10.1016/S0167-6377(96)00036-3_BIB24 article-title: Training multi-layered neural network with a Trust region based algorithm publication-title: Math. Modell. Numer. Anal. doi: 10.1051/m2an/1990240405231
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Snippet	We present DCA for globally minimizing quadratic forms on Euclidean balls and spheres. Since these problems admit at most one local-nonglobal minimizer, DCA...
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SubjectTerms	Applied sciences Computer Science d.c. optimization d.c. optimization algorithms Exact sciences and technology Local and global optimality conditions Mathematical programming Nonconvex quadratic minimization Operational research and scientific management Operational research. Management science Optimization. Search problems
Title	Difference of convex functions optimization algorithms (DCA) for globally minimizing nonconvex quadratic forms on Euclidean balls and spheres
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