SEMI-INFINITE PROGRAMMING DUALITY: HOW SPECIAL IS IT?

In this article we describe and compare some frameworks within which semi-infinite programming duality theory can be studied. The emphasis is on abstract duality and reduction theorems for infinite systems.

[1]  V. Klee The Critical Set of a Convex Body , 1953 .

[2]  W. Rogosinski Moments of non-negative mass , 1958, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[3]  M. Day,et al.  Normed Linear Spaces , 1960 .

[4]  K. S. Kretschmer,et al.  Programmes in Paired Spaces , 1961, Canadian Journal of Mathematics.

[5]  A. Charnes,et al.  Duality in Semi-Infinite Programs and some Works of Haar and Caratheodory , 1963 .

[6]  R. J. Duffin,et al.  An Infinite Linear Program with a Duality Gap , 1965 .

[7]  Abraham Charnes,et al.  ON REPRESENTATIONS OF SEMI-INFINITE PROGRAMS WHICH HAVE NO DUALITY GAPS. , 1965 .

[8]  Helly’s theorem and minima of convex functions , 1965 .

[9]  W. J. Studden,et al.  Tchebycheff Systems: With Applications in Analysis and Statistics. , 1967 .

[10]  N. Levinson,et al.  A class of continuous linear programming problems , 1966 .

[11]  G. McCormick Second Order Conditions for Constrained Minima , 1967 .

[12]  D. Luenberger Optimization by Vector Space Methods , 1968 .

[13]  Maretsugu Yamasaki Duality theorems in mathematical programmings and their applications. , 1968 .

[14]  Ky Fan,et al.  Asymptotic cones and duality of linear relations , 1969 .

[15]  M. Guignard Generalized Kuhn–Tucker Conditions for Mathematical Programming Problems in a Banach Space , 1969 .

[16]  G. Jameson Ordered Linear Spaces , 1970 .

[17]  B. N. Pshenichnyi Necessary Conditions for an Extremum , 1971 .

[18]  E. Prescott,et al.  A Note on Price Systems in Infinite Dimensional Space , 1972 .

[19]  Kenneth O. Kortanek,et al.  Numerical treatment of a class of semi‐infinite programming problems , 1973 .

[20]  Richard James Duffin Convex analysis treated by linear programming , 1973, Math. Program..

[21]  Charles E. Blair A note on infinite systems of linear inequalities in Rn , 1974 .

[22]  U. Eckhardt Theorems on the dimension of convex sets , 1975 .

[23]  F. Clarke Generalized gradients and applications , 1975 .

[24]  I. Ekeland,et al.  Convex analysis and variational problems , 1976 .

[25]  K. Kortanek Constructing a perfect duality in infinite programming , 1976 .

[26]  J. Borwein,et al.  Weak tangent cones and optimization in a Banach space | NOVA. The University of Newcastle's Digital Repository , 1978 .

[27]  G. A. Garreau,et al.  Mathematical Programming and Control Theory , 1979, Mathematical Gazette.

[28]  R. Rockafellar,et al.  The Optimal Recourse Problem in Discrete Time: $L^1 $-Multipliers for Inequality Constraints , 1978 .

[29]  J. Penot Calcul sous-differentiel et optimisation , 1978 .

[30]  Jochem Zowe Sandwich theorems for convex operators with values in an ordered vector space , 1978 .

[31]  J. Zowe,et al.  Second-order necessary and sufficient optimality conditions for infinite-dimensional programming problems , 1979 .

[32]  A. Ioffe Necessary and Sufficient Conditions for a Local Minimum. 3: Second Order Conditions and Augmented Duality , 1979 .

[33]  M. S. Bazaraa,et al.  Nonlinear Programming , 1979 .

[34]  Marc Teboulle,et al.  Second order necessary optimality conditions for semi-infinite programming problems , 1979 .

[35]  A. Ioffe Regular points of Lipschitz functions , 1979 .

[36]  M. Yamasaki,et al.  Sufficient conditions for duality theorems in infinite linear programming problems , 1979 .

[37]  A. Ioffe Necessary and Sufficient Conditions for a Local Minimum. 1: A Reduction Theorem and First Order Conditions , 1979 .

[38]  Klaus Glashoff Duality theory of semi-infinite programming , 1979 .

[39]  P. Lévine,et al.  Sufficient conditions for Kuhn-Tucker vectors in convex programming , 1979 .

[40]  Werner Krabs,et al.  Optimization and approximation , 1979 .

[41]  J. Borwein,et al.  Some Generalizations of Carathéodory′s Theorem Via Barycentres, with Application to Mathematical Programming , 1980, Canadian Mathematical Bulletin.

[42]  Jonathan M. Borwein,et al.  A note on perfect duality and limiting lagrangeans , 1980, Math. Program..

[43]  Robert G. Jeroslow,et al.  Lagrangean functions and affine minorants , 1981 .

[44]  Dennis F. Karney,et al.  Duality gaps in semi-infinite linear programming—an approximation problem , 1981, Math. Program..

[45]  J. Borwein The limiting Lagrangian as a consequence of Helly's theorem , 1981 .

[46]  J. M. Borwein,et al.  Direct theorems in semi-infinite convex programming , 1981, Math. Program..

[47]  Jonathan M. Borwein,et al.  A Lagrange multiplier theorem and a sandwich theorem for convex relations , 1981 .

[48]  R. Jeroslow A limiting Lagrangian for infinitely constrained convex optimization inRn , 1981 .

[49]  W. Ziemba,et al.  Generalized concavity in optimization and economics , 1981 .

[50]  J. Ponstein,et al.  On the use of purely finitely additive multipliers in mathematical programming , 1981 .

[51]  Charles E. Blair,et al.  A limiting infisup theorem , 1982 .

[52]  Robert G. Jeroslow,et al.  Duality in Semi-Infinite Linear Programming , 1983 .

[53]  Jonathan M. Borwein,et al.  Adjoint Process Duality , 1983, Math. Oper. Res..

[54]  A. D. Ioffe Second Order Conditions in Nonlinear Nonsmooth Problems of Semi-Infinite Programming , 1983 .

[55]  J. Flachs,et al.  Saddle-point theorems for rational approximation , 1984 .