In general normed spaces, we consider a multiobjective piecewise linear optimization problem with the ordering cone being convex and having a nonempty interior. We establish that the weak Pareto optimal solution set o...In general normed spaces, we consider a multiobjective piecewise linear optimization problem with the ordering cone being convex and having a nonempty interior. We establish that the weak Pareto optimal solution set of such a problem is the union of finitely many polyhedra and that this set is also arcwise connected under the cone convexity assumption of the objective function. Moreover, we provide necessary and sufficient conditions about the existence of weak (sharp) Pareto solutions.展开更多
In this paper, we study the ill posed Perona-Malik equation of image processing[14] and the regularized P-M model i.e. C-model proposed by Catte et al.[4]. The authors present the convex compound of these two models i...In this paper, we study the ill posed Perona-Malik equation of image processing[14] and the regularized P-M model i.e. C-model proposed by Catte et al.[4]. The authors present the convex compound of these two models in the form of the system of partial differential equations. The weak solution for the equations is proved in detail. The additive operator splitting （AOS） algorithm for the proposed model is also given. Finally, we show some numeric experimental results on images.展开更多
基金supported by the National Natural Science Foundation of China (Grant No. 10761012)theNatural Science Foundation of Yunnan Province,China (Grant No. 2003A002M) the Research GrantsCouncil of Hong Kong (Grant No. B-Q771)
文摘In general normed spaces, we consider a multiobjective piecewise linear optimization problem with the ordering cone being convex and having a nonempty interior. We establish that the weak Pareto optimal solution set of such a problem is the union of finitely many polyhedra and that this set is also arcwise connected under the cone convexity assumption of the objective function. Moreover, we provide necessary and sufficient conditions about the existence of weak (sharp) Pareto solutions.
基金Supported in part by the National Natural Science Foundation of China under Grant(No.11571325,No.11271126)Science Research Project of CUC under Grant No.3132016XNL1612
文摘In this paper, we study the ill posed Perona-Malik equation of image processing[14] and the regularized P-M model i.e. C-model proposed by Catte et al.[4]. The authors present the convex compound of these two models in the form of the system of partial differential equations. The weak solution for the equations is proved in detail. The additive operator splitting （AOS） algorithm for the proposed model is also given. Finally, we show some numeric experimental results on images.
