This study proposes an iterative method to approximate an N-dimensional optimisation problem with a weighted L p and L 2 norm objective function by a sequence of N independent one-dimensional optimisation problems. Inspired by the existing weighted L 1 and L 2 norm separable surrogate functional (SSF) iterative shrinkage algorithm, there are N independent one-dimensional optimisation problems with weighted L p and L 2 norm objective functions. However, these optimisation problems are non-convex. Hence, they may have more than one locally optimal solutions and it is very difficult to find their globally optimal solutions. This paper proposes to partition the feasible set of each approximated problem into various regions such that the sign of the convexity of the objective function in each region remains unchanged. Here, there is no more than one stationary point in each region. By finding the stationary point in each region, the globally optimal solution of each approximated optimisation problem can be found. Besides, this study also shows that the sequence of the globally optimal solutions of the approximated problems converge to the globally optimal solution of the original optimisation problem. Computer numerical simulation results show that the proposed method outperforms the existing weighted L 1 and L 2 norm SSF iterative shrinkage algorithm.
This paper extends the existing 1 L norm separable surrogate functional (SSF) iterative shrinkage algorithm to approximate the objective function of a weighted p L norm and 2 L norm optimization problem by N one dimensional independent objective functions. However, as the weighted p L norm and 2 L norm optimization problem is nonconvex, there may be more than one locally optimal solution. Hence, it is difficult to find the globally optimal solution. To address this difficulty, this paper further characterizes the regions that the signs of the convexity of the objective function within the regions remain unchanged. Then, the optimal solution within each region and eventually the globally optimal solution of the original optimization problem are found.
The college-enterprise cooperation is an effective method to cultivate innovative and applied talents facing enterprises, achieving the transformation of student status to staff. In this model, the resources of college and enterprises could be exchanged more efficiently to maximize the mutual benefits, with meeting the demands of both, relying on the support of college and enterprises to explore the best approaches for teaching reform. As an application of this method, the practice of Wuyi University and the Fifth Research Institute of the Ministry of Industry and Information Technology of China have employed some new approaches: compensation of course credit and interest matching (software design or hardware design), and after a three-years' study, students will train in the enterprise at last year.
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