Duality for optimization and best approximation over finite intersections

Numerical Functional Analysis and Optimization

Volumn 19, Issue 7-8, 1998, Pages 903-915

  Singer, Ivan ^a  

^a INSTITUTE OF MATHEMATICS   (Romania)

Author keywords

Convex optimization; Lagrangian dual problem; m Lagrangian dual problem; Nearest point; Strong conical hull intersection property

Indexed keywords

APPROXIMATION THEORY; FUNCTIONS; SET THEORY;

CONVEX OPTIMIZATION; LAGRANGIAN DUAL PROBLEMS;

OPTIMIZATION;

EID: 0032164745     PISSN: 01630563     EISSN: None     Source Type: Journal    
DOI: 10.1080/01630569808816864     Document Type: Article

References (9)

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2. F. Deutsch, W. Li and J. Swetits, Fenchel duality and the strong conical hull intersection property (to appear).
3. F. Deutsch, W. Li and J. Ward, A dual approach to constrained interpolation from a convex subset of Hubert space, J. Approx. Theory 90 (1997), 385-414.
4. I. Ekeland and R. Temam, Convex analysis and variational problems. North-Holland, Amsterdam, 1976.
5. N. Gaffke and R. Mathar, A cyclic projection algorithm via duality, Metrika 36 (1989), 29-54.
6. J. R. Giles, Convex analysis with application in differentiation of convex functions. Research Notes in Mathematics, vol. 58, Pitman, Boston, 1982.
7. J.-B. Hiriart-Urruty and C. Lemaréchal, Convex analysis and minimization algorithms. I, Springer-Verlag, Berlin, Heidelberg, 1993.
8. I. Singer, Generalizations of methods of best approximation to convex optimization in locally convex spaces. I: Extensions of continuous linear functionals and characterizations of solutions of continuous convex programs. Rev. roumaine math. pures appl. 19 (1974), 65-77.
9. I. Singer, Some new applications of the Fenchel-Rockafellar duality theorem: Lagrange multiplier theorems and hyperplane theorems for convex optimization and best approximation. Nonlinear Anal. Theory, Methods, Appl. 3 (1979), 239-248.