Semidefinite Programming Relaxations and Algebraic Optimization in Control
نویسندگان
چکیده
منابع مشابه
Semidefinite Programming Relaxations and Algebraic Optimization in Control
We present an overview of the essential elements of semidefinite programming as a computational tool for the analysis of systems and control problems. We make particular emphasis on general duality properties as providing suboptimality or infeasibility certificates. Our focus is on the exciting developments occurred in the last few years, including robust optimization, combinatorial optimizatio...
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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: European Journal of Control
سال: 2003
ISSN: 0947-3580
DOI: 10.3166/ejc.9.307-321