A simple constraint qualification in infinite dimensional programming
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A new, simple, constraint qualification for infinite dimensional programs with linear programming type constraints is used to derive the dual program; see Theorem 3.1. Applications include a proof of the explicit solution of the best interpolation problem presented in .
Key wordsInfinite dimensional linear programming semi-infinite programming constraint qualification optimality conditions dual program
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- A. Ben-Israel, “Linear equations and inequalities on finite dimensional, real or complex, vector spaces: A unified theory“,Journal of Mathematical Analysis and Applications 27 (1969) 367–389.Google Scholar
- A. Ben-Israel, A. Ben-Tal and S. Zlobec,Optimality in non-linear programming: A feasible directions approach (Wiley, New York, 1981).Google Scholar
- J.M. Borwein and H. Wolkowicz, “Characterizations of optimality for the abstract convex program with finite dimensional range“,Journal of the Australian Mathematical Society 30 (1981) 390–411.Google Scholar
- J.M. Borwein and H. Wolkowicz, “Characterizations of optimality without constraint qualification for the abstract convex program“,Mathematical Programming Study 19 (1982) 77–100.Google Scholar
- B.D. Craven and J.J. Koliha, “Generalizations of Farkas' theorem“,SIAM Journal on Mathematical Analysis 8 (1977) 938–997.Google Scholar
- R.B. Holmes,Geometric functional analysis and its applications (Springer-Verlag, Berlin, 1975).Google Scholar
- C. Kallina and A.C. Williams, “Linear programming in reflexive spaces“,SIAM Review 13 (1971) 350–376.Google Scholar
- C.A. Micchelli, P.W. Smith, J. Swetits, and J.D. Ward, “ConstrainedL p approximation“,Journal of Constructive Approximation 1 (1985) 93–102.Google Scholar
- H. Wolkowicz, “Some applications of optimization in matrix theory“,Linear Algebra and Its Applications 40 (1981) 101–118.Google Scholar