Stability and Duality in Convex Minimization Problems.

Abstract : The general relations between the stability of a convex minimiation problem and duality are studied. Several problems are considered, including spline function problems and approximation problems. (Author)

[1]  W. Fenchel On Conjugate Convex Functions , 1949, Canadian Journal of Mathematics.

[2]  W. Fenchel Convex cones, sets, and functions , 1953 .

[3]  P. Wolfe A duality theorem for non-linear programming , 1961 .

[4]  P. Huard,et al.  Dual programs , 1962 .

[5]  O. Mangasarian Duality in nonlinear programming , 1962 .

[6]  R. Cottle Symmetric dual quadratic programs , 1963 .

[7]  Josef Stoer,et al.  Duality in nonlinear programming and the minimax theorem , 1963 .

[8]  穂鷹 良介 Non-Linear Programming の計算法について , 1963 .

[9]  J. Stoer,et al.  Über einen Dualitätssatz der nichtlinearen programmierung , 1964 .

[10]  R. Rockafellar Duality theorems for convex functions , 1964 .

[11]  G. Dantzig,et al.  Symmetric dual nonlinear programs. , 1965 .

[12]  Olvi L. Mangasarian,et al.  Minmax and duality in nonlinear programming , 1965 .

[13]  R. Rockafellar,et al.  Duality and stability in extremum problems involving convex functions. , 1967 .

[14]  J. E. Falk Lagrange multipliers and nonlinear programming , 1967 .

[15]  Douglas Gale A Geometric Duality Theorem with Economic Applications , 1967 .

[16]  Marc Atteia Fonctions ≪ spline ≫ definies sur un ensemble convexe , 1968 .

[17]  R. Wets,et al.  A duality theory for abstract mathematical programs with applications to optimal control theory , 1968 .

[18]  P. Laurent Charakterisierung und Konstruktion Einer Besten Approximation in einer Konvexen Teilmenge eines Normierten Raumes , 1969 .

[19]  R. Rockafellar Convex Functions and Duality in Optimization Problems and Dynamics , 1969 .

[20]  R. Rockafellar Some Convex Programs Whose Duals Are Linearly Constrained , 1970 .

[21]  R. Rockafellar,et al.  Conjugate convex functions in optimal control and the calculus of variations , 1970 .

[22]  R. Rockafellar,et al.  Generalized Hamiltonian equations for convex problems of Lagrange. , 1970 .