Duality in Nonlinear Programming: A Simplified Applications-Oriented Development

The number of computational or theoretical applications of nonlinear duality theory is small compared to the number of theoretical papers on this subject over the last decade. This study attempts t...

[1]  Philip Wolfe,et al.  An algorithm for quadratic programming , 1956 .

[2]  G. Debreu,et al.  Theory of Value , 1959 .

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

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

[5]  Harvey J. Everett.  Generalized Lagrange Multiplier Method for Solving Problems of Optimum Allocation of Resources , 1963 .

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

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

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

[9]  Kanti Swarup,et al.  A Duality Theorem for Non-Linear Programming , 1965 .

[10]  Robert B. Wilson.  Computation of optimal controls , 1966 .

[11]  E. G. Golshtein,et al.  A General Approach to the Linear Programming of Block Structures , 1966 .

[12]  Decomposition programming and economic planning , 1967 .

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

[14]  M. Balinski,et al.  The Dual in Nonlinear Programming and its Economic Interpretation , 1968 .

[15]  Kenneth O. Kortanek,et al.  Asymptotic Lagrange Regularity for Pseudoconcave Programming with Weak Constraint Qualification , 1968, Oper. Res..

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

[17]  Leon S. Lasdon,et al.  Duality and Decomposition in Mathematical Programming , 1968, IEEE Trans. Syst. Sci. Cybern..

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

[19]  Arthur M. Geoffrion,et al.  Elements of large-scale mathematical programming , 1969 .

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

[21]  A. Charnes,et al.  On the theory of semi‐infinite programming and a generalization of the kuhn‐tucker saddle point theorem for arbitrary convex functions , 1969 .

[22]  Olvi L. Mangasarian,et al.  Nonlinear Programming , 1969 .

[23]  Arthur M. Geoffrion,et al.  Primal Resource-Directive Approaches for Optimizing Nonlinear Decomposable Systems , 1970, Oper. Res..