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您的检索式：作者名="PENG Dingtao"
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| 1 | SOLVABILITY OF VECTOR KY FAN INEQUALITIES WITH APPLICATIONS显示文摘This paper aims to study the solvability of vector Ky Fan inequalities and the compactness of its solution sets.For vector-valued functions with the cone semicontinuity and the cone quasiconvexity in infinite dimensional spaces,the authors prove some existence results of the solutions and the compactness of the solution sets.Especially,some results for the vector Ky Fan inequalities on noncompact sets are built and the compactness of its solution sets are also discussed.As applications,some existence theorems of the solutions of vector variational inequalities are obtained. | YU Jian PENG Dingtao | 2013 | Journal of Systems Science & Complexity2013，26，6： | 2 |
| 2 | Global optimality condition and fixed point continuation algorithm for non-Lipschitz ?_p regularized matrix minimization显示文摘Regularized minimization problems with nonconvex, nonsmooth, even non-Lipschitz penalty functions have attracted much attention in recent years, owing to their wide applications in statistics, control,system identification and machine learning. In this paper, the non-Lipschitz ?_p(0 < p < 1) regularized matrix minimization problem is studied. A global necessary optimality condition for this non-Lipschitz optimization problem is firstly obtained, specifically, the global optimal solutions for the problem are fixed points of the so-called p-thresholding operator which is matrix-valued and set-valued. Then a fixed point iterative scheme for the non-Lipschitz model is proposed, and the convergence analysis is also addressed in detail. Moreover,some acceleration techniques are adopted to improve the performance of this algorithm. The effectiveness of the proposed p-thresholding fixed point continuation(p-FPC) algorithm is demonstrated by numerical experiments on randomly generated and real matrix completion problems. | Dingtao Peng Naihua Xiu Jian Yu | 2018 | Science China Mathematics2018，61，6： | 0 |
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