论文信息 - The Dual Normal CHIP and Linear Regularity for Infinite Systems of Convex Sets in Banach Spaces

The Dual Normal CHIP and Linear Regularity for Infinite Systems of Convex Sets in Banach Spaces

For an indexed collection of convex sets in a Banach space with index set $I$ of cardinality $|I|$ of $I$, which may be finite or infinite, we investigate the interrelationship between various qualification notions including the linear regularity, the normal property, the dual normal conical hull intersection property, and Jameson's property $(G)$, together with their quantitative versions, and thereby we extend the well-known results of Bakan, Deutsch, and Li [Trans. Amer. Math. Soc., 357 (2005), pp. 3831--3863], and Bauschke, Borwein, and Li [Math. Program. Ser. A, 86 (1999), pp. 135--160] from the finite case to the more general case that allows $|I|$ to be infinite.

Chong Li | Kung Fu Ng | K. Ng | Chong Li

[1] H. H. Schaefer,et al. Topological Vector Spaces , 1967 .

[2] Heinz H. Bauschke,et al. On Projection Algorithms for Solving Convex Feasibility Problems , 1996, SIAM Rev..

[3] Wu Li,et al. Best Approximation from the Intersection of a Closed Convex Set and a Polyhedron in Hilbert Space, Weak Slater Conditions, and the Strong Conical Hull Intersection Property , 1999, SIAM J. Optim..

[4] Heinz H. Bauschke,et al. Projection algorithms and monotone operators , 1996 .

[5] P. L. Combettes. The foundations of set theoretic estimation , 1993 .

[6] Yair Censor,et al. Cyclic subgradient projections , 1982, Math. Program..

[7] Frank Deutsch,et al. A Dual Approach to Constrained Interpolationfrom a Convex Subset of Hilbert Space , 1997 .