论文标题
在一类强大的非convex二次优化问题上
On a class of robust nonconvex quadratic optimization problems
论文作者
论文摘要
让我们考虑以下可靠的nonconvex二次优化问题：\ begin {equination*} \ begin {split} \ min＆〜\ dfrac {1} {2} {2} x^\ top ax+a^\ top a^\ top x \\ top x \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ \ \ \ \ \ \ \\ s.t. s.t.} （b_1+μb_2）x+（b_1+Δb_2）^\ top x \leqβ，〜\ forall〜μ \在[μ_1，μ_2]中对称矩阵，$μ_1，μ_2，δ_1，δ_2，α$，$β\ in \ mathbb {r} $满足$μ_1\ leqμ_2$，$Δ_1\ leqleqΔ_2$和$Δ_2$和$α<β$。我们建立了强大的替代结果；对于上述非凸问题，可靠的S-周期和可靠的最优性。
Let us consider the following robust nonconvex quadratic optimization problem: \begin{equation*} \begin{split} \min &~ \dfrac{1}{2} x^\top Ax+a^\top x \\ \text{s.t.}~ & α\leq\dfrac{1}{2}x^\top (B_1+μB_2)x+(b_1+δb_2)^\top x \leqβ,~ \forall~ μ\in [μ_1,μ_2],\forall~δ\in[δ_1,δ_2], \end{split} \end{equation*} where $A$, $B_1$, $B_2$ are real symmetric matrices, $μ_1,μ_2,δ_1,δ_2,α$, $β\in\mathbb{R}$ satisfying $μ_1\leq μ_2$, $δ_1\leqδ_2$ and $α<β$. We establish the robust alternative result; the robust S-lemma and the robust optimality for the above nonconvex problem.
