凸二次规划SDP松弛解的存在性证明

针对利用CVX软件求解半定规划问题的有效性依赖于该半定规划问题的原始-对偶性,提出利用半定规划问题的强对偶定理和Gershgorin圆盘定理证明在箱子约束及单位球形约束下的凸二次规划问题的半定规划松弛模型解的存在性。该证明方法为嵌入了SeDuMi和SDPT3这两种内点算法的CVX软件提供了有效求解半定规划松弛模型的理论依据;一旦利用该方法证明了半定规划问题解的存在,必然可利用CVX软件有效求解。

The Existence Proof of the Solution of SDP Relaxation for Convex Quadratic Program

International knowledge spillover effect is mainly realized by FDI channel and import trade channel and is regulated by technical absorption capacity. Based on the panel data of 20 Chinese industrial enterprises from 2009 to 2017, this paper empirically tests the influence of FDI knowledge spillover and import trade knowledge spillover on the innovation output of Chinese enterprises and the regulatory role of the absorption capacity of the enterprises, and the results find that from the perspective of all industries, capital and technology intensive industries, the knowledge spillover effect of FDI is significantly positive, however, the knowledge spillover of import trade has negative impact on the innovation output of the enterprises, the knowledge spillover effect of the two channels increases with the increasing of technical absorption capacity of the enterprises. From the perspective of resources and labor intensive industries, the international knowledge spillover effect of the two channels is not optimistic, furthermore, the knowledge spillover effect of import trade channel weakens with the increasing of technical absorption capacity of the enterprises. In the one hand, China should encourage and support Chinese enterprises to enlarge the input of R&D and new products development and to better make use of international knowledge spillover effect by boosting self technical absorption capacity. In the other hand, China should accelerate the transformation and upgrading of foreign openness, promote the FDI introduction for capital and technology intensive industries, create more opportunities and better environment for international knowledge spillover, and further effectively boost the improvement of technical level and high quality innovation output of Chinese enterprises.