A partial ellipsoidal approximation scheme for nonconvex homogeneous quadratic optimization with quadratic constraints

Zhuoyi Xu (), Linbin Li () and Yong Xia ()
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Zhuoyi Xu: Capital University of Economics and Business
Linbin Li: Beihang University
Yong Xia: Beihang University

Mathematical Methods of Operations Research, 2023, vol. 98, issue 1, No 6, 93-109

Abstract: Abstract An efficient partial ellipsoid approximation scheme is presented to find a $$\frac{1}{\lceil {\frac{m}{2}}\rceil }$$ 1 ⌈ m 2 ⌉ -approximation solution to the nonconvex homogeneous quadratic optimization with m convex quadratic constraints, where $$\lceil x \rceil $$ ⌈ x ⌉ is the smallest integer larger than or equal to x. If there is an additional nonconvex quadratic constraint beyond the m convex constraints, we can use the new scheme to find a $$\frac{1}{m}$$ 1 m -approximation solution.

Keywords: Quadratically constrained quadratic optimization; Ellipsoidal approximation; Approximation algorithm; 90C20; 90C26; 90C59 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s00186-023-00827-y

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