Optimization Letters Best Paper Award for 2015
Optimization Letters Best Paper Award for 2015
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DOI：
10.1007/s11590-016-1099-0
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发表时间：
2016-12
影响因子：
1.6
通讯作者：
P. Krokhmal;O. Prokopyev
中科院分区：
文献类型：
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作者：
P. Krokhmal;O. Prokopyev
研究了一类凸多项式优化问题在数据不确定性下的鲁棒解和半定线性规划（SDP）松弛。鲁棒SOS-凸多项式优化问题包括鲁棒二次约束凸优化问题和鲁棒可分凸多项式优化问题。它建立了平方和多项式表示表征各种常用的不确定性集下的鲁棒SOS凸多项式优化问题的鲁棒解和精确的SDP松弛。特别是，结果表明，多面体和椭球的不确定性集，允许二阶锥重新制定的强大的二次约束优化问题，继续允许精确的SDP松弛的广泛的一类强大的SOS凸多项式优化问题。
This paper studies robust solutions and semidefinite linear programming (SDP) relaxations of a class of convex polynomial optimization problems in the face of data uncertainty. The class of convex optimization problems, called robust SOS-convex polynomial optimization problems, includes robust quadratically constrained convex optimization problems and robust separable convex polynomial optimization problems. It establishes sums-of-squares polynomial representations characterizing robust solutions and exact SDP-relaxations of robust SOS-convex polynomial optimization problems under various commonly used uncertainty sets. In particular, the results show that the polytopic and ellipsoidal uncertainty sets, that allow second-order cone re-formulations of robust quadratically constrained optimization problems, continue to permit exact SDP-relaxations for a broad class of robust SOS-convex polynomial optimization problems.