Biquadratic Optimization Over Unit Spheres and Semidefinite Programming Relaxations
نویسندگان
چکیده
منابع مشابه
Biquadratic Optimization Over Unit Spheres and Semidefinite Programming Relaxations
This paper studies the so-called bi-quadratic optimization over unit spheres min x∈Rn,y∈Rm ∑ 1≤i,k≤n, 1≤j,l≤m bijklxiyjxkyl subject to ‖x‖ = 1, ‖y‖ = 1. We show that this problem is NP-hard and there is no polynomial time algorithm returning a positive relative approximation bound. After that, we present various approximation methods based on semidefinite programming (SDP) relaxations. Our theo...
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ژورنال
عنوان ژورنال: SIAM Journal on Optimization
سال: 2010
ISSN: 1052-6234,1095-7189
DOI: 10.1137/080729104