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Exact solutions of some nonconvex quadratic optimization problems via SDP and SOCP relaxations

Title
Exact solutions of some nonconvex quadratic optimization problems via SDP and SOCP relaxations
Authors
Kim S.Kojima M.
Ewha Authors
김선영
SCOPUS Author ID
김선영scopus
Issue Date
2003
Journal Title
Computational Optimization and Applications
ISSN
0926-6003JCR Link
Citation
vol. 26, no. 2, pp. 143 - 154
Indexed
SCI; SCIE; SCOPUS WOS scopus
Abstract
We show that SDP (semidefinite programming) and SOCP (second order cone programming) relaxations provide exact optimal solutions for a class of nonconvex quadratic optimization problems. It is a generalization of the results by S. Zhang for a subclass of quadratic maximization problems that have nonnegative off-diagonal coefficient matrices of quadratic objective functions and diagonal coefficient matrices of quadratic constraint functions. A new SOCP relaxation is proposed for the class of nonconvex quadratic optimization problems by extracting valid quadratic inequalities for positive semidefinite cones. Its effectiveness to obtain optimal values is shown to be the same as the SDP relaxation theoretically. Numerical results are presented to demonstrate that the SOCP relaxation is much more efficient than the SDP relaxation.
DOI
10.1023/A:1025794313696
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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