The Historical Development of Parametric Programming

The well known tremendous and explosive development of Linear Programming and Operations Research (LP and OR for short, resp.) in general in the 50ties has been connected with the names like CHARNESS, COOPER, GALE, HOFFMAN, KANTOROWICZ, KUHN, TUCKER, WOLFE, to mention only a few of the coryphaei.

[1]  A. M. Geoffrion.  Strictly Concave Parametric Programming, Part I: Basic Theory , 1966 .

[2]  J. Tolle,et al.  Differential Stability in Nonlinear Programming , 1977 .

[3]  W. C. House.  CASE STUDY NO.4 ∗ Sensitivity Analysis — A Case Study of the Pipeline Industry , 1967 .

[4]  Arthur M. Geoffrion,et al.  Strictly Concave Parametric Programming, Part II: Additional Theory and Computational Considerations , 1967 .

[5]  C. O. Fong,et al.  Parametric studies in transportation‐type problems , 1975 .

[6]  R. E. Marsten,et al.  Parametric Integer Programming: The Right-Hand-Side Case , 2018 .

[7]  A. Fiacco,et al.  Nonlinear Programming Sensitivity Analysis Results Using Strong Second Order Assumptions. , 1978 .

[8]  A. Fiacco,et al.  Second-Order Parametric Sensitivity Analysis in NLP and Estimates by Penalty Function Methods, , 1975 .

[9]  F. Nožička.  Theorie der linearen parametrischen Optimierung , 1974 .

[10]  Thomas L. Saaty,et al.  Parametric Objective Function (Part 1) , 1954, Oper. Res..

[11]  John Glen,et al.  A Parametric Programming Method for Beef Cattle Ration Formulation , 1980 .

[12]  Richard D. McBride,et al.  Finding All Solutions for a Class of Parametric Quadratic Integer Programming Problems , 1980 .

[13]  Jati K. Sengupta,et al.  Sensitivity analysis methods for a crop-mix problem in linear programming , 1970, Unternehmensforschung.

[14]  H. Noltemeier.  Sensitivitätsanalyse bei diskreten linearen Optimierungsproblemen , 1970 .

[15]  Werner Dinkelbach,et al.  Sensitivitätsanalysen und parametrische Programmierung , 1969 .

[16]  Floyd J. Gould,et al.  Stability in Nonlinear Programming , 1970, Oper. Res..

[17]  Ikuyo Kaneko.  A Maximization Problem Related to Parametric Linear Complementarity , 1978 .

[18]  Anthony V. Fiacco,et al.  Sensitivity analysis for nonlinear programming using penalty methods , 1976, Math. Program..

[19]  Arthur M. Geoffrion,et al.  Exceptional Paper—Parametric and Postoptimality Analysis in Integer Linear Programming , 1977 .

[20]  K. Lommatzsch.  Anwendungen der linearen parametrischen Optimierung , 1979 .

[21]  S. Holm,et al.  Integer Programming Post-Optimal Analysis with Cutting Planes , 1979 .

[22]  D. Klatte.  ON THE LOWER SEMICONTINUITY OF OPTIMAL SETS IN CONVEX PARAMETRIC OPTIMIZATION , 1979 .

[23]  P. Yu,et al.  The set of all nondominated solutions in linear cases and a multicriteria simplex method , 1975 .

[24]  H. Kunzi,et al.  Lectu re Notes in Economics and Mathematical Systems , 1975 .

[25]  Thomas L. Saaty,et al.  Parametric Objective Function (Part 2) - Generalization , 1955, Oper. Res..

[26]  Anthony V. Fiacco,et al.  Nonlinear programming;: Sequential unconstrained minimization techniques , 1968 .

[27]  G. Dantzig,et al.  On the continuity of the minimum set of a continuous function , 1967 .

[28]  Gunter Lorenzeh.  Parametrische optimierung und einige anwendungen , 1974 .

[29]  T. Gal.  On Efficient Sets in Vector Maximum Problems — A Brief Survey , 1986 .

[30]  William Orchard-Hays,et al.  Advanced Linear-Programming Computing Techniques , 1968 .

[31]  Gerald L. Thompson,et al.  An operator theory of parametric programming for the generalized transportation problem: I. Basic theory , 1975 .

[32]  A. Dontchev.  Perturbations, Approximations, and Sensitivity Analysis of Optimal Control Systems , 1983 .

[33]  Jong-Shi Pang,et al.  A Parametric Linear Complementarity Technique for Optimal Portfolio Selection with a Risk-Free Asset , 1980, Oper. Res..

[34]  Bruno Brosowski,et al.  Parametric semi-infinite optimization , 1982 .

[35]  Über eine elasse von linearen einparametrischen optimierungsprowemen , 1972 .

[36]  Thomas W. Knowles,et al.  Decomposition of Water Distribution Networks , 1976 .

[37]  Gary R. Wells.  A sensitivity analysis of simulated River Basin planning for capital budgeting decisions , 1975, Comput. Oper. Res..

[38]  Gerhard Tintner,et al.  Base duality theorem for stochastic and parametric linear programming , 1964, Unternehmensforschung.

[39]  S. M. Robinson.  Stability Theory for Systems of Inequalities. Part I: Linear Systems , 1975 .

[40]  Richard W. Cottle.  Monotone solutions of the parametric linear complementarity problem , 1972, Math. Program..

[41]  T. Gal,et al.  A Note on the History of Parametric Programming , 1983 .

[42]  H. Bialy,et al.  W. Dinkelbach, Sensitivitätsanalysen und parametrische Programmierung. (Ökonometrie und Unternehmensforschung, Band XII). XI + 190 S. Berlin/Heidelberg/New York 1969. Springer-Verlag. Preis geb. DM 48, - . , 1970 .

[43]  David M. Himmelblau,et al.  Modeling and Sensitivity Analysis for Planning Decisions in Water Resources Expansion , 1972 .

[44]  Bruno Brosowski,et al.  Methoden und Verfahren der mathematischen Physik , 1975 .

[45]  H. Maurer,et al.  Differential stability in infinite-dimensional nonlinear programming , 1980 .

[46]  Curtis H. Jones.  Parametric Production Planning , 1967 .

[47]  Gerald L. Thompson,et al.  An operator theory of parametric programming for the generalized transportation problem—IV—global operators , 1975 .

[48]  Harvey J. Greenberg,et al.  Extensions of the Evans-Gould Stability Theorems for Mathematical Programs , 1972, Oper. Res..

[49]  Alan S. Manne,et al.  Scheduling of Petroleum Refinery Operations , 1956 .

[50]  Bruno Brosowski.  On Parametric Linear Optimization , 1978 .

[51]  W. Jacobs,et al.  Smooth Patterns of Production , 1954 .

[52]  Tomas Gal,et al.  A “Historiogramme” of Parametric Programming , 1980 .

[53]  L. S. Srinath.  Parametric Linear Programming , 1982 .

[54]  George B. Dantzig,et al.  Linear programming and extensions , 1965 .

[55]  Note-An Objective Function Perturbation with Economic Interpretations , 1981 .

[56]  P. Kokotovic,et al.  D-Stability and Multi-Parameter Singular Perturbation , 1979 .

[57]  Diethard Klatte,et al.  On Procedures for Analysing Parametric Optimization Problems , 1982 .

[58]  W. Krabs.  Zur stetigen Abhängigkeit des Extremalwertes eines konvexen Optimierungsproblems von einer stetigen Änderung des Problems , 1972, Juli 1972.

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

[60]  A. L. Soyster,et al.  On equating the difference between optimal and marginal values of general convex programs , 1981 .

[61]  T. L. Saaty,et al.  The computational algorithm for the parametric objective function , 1955 .

[62]  Hisatoshi Suzuki.  A generalized knapsack problem with variable coefficients , 1978, Math. Program..

[63]  R. R. Hocking,et al.  Technical Note - Parametric Solution of a Class of Nonconvex Programs , 1971, Oper. Res..

[64]  T. Gal.  A general method for determining the set of all efficient solutions to a linear vectormaximum problem , 1977 .

[65]  E. Levitin.  Differentiability with respect to a parameter of the optimal value in parametric problems of mathematical programming , 1976, Cybernetics.

[66]  C. Panne,et al.  Minimum-Cost Cattle Feed Under Probabilistic Protein Constraints , 1963 .

[67]  S. M. Robinson.  Stability Theory for Systems of Inequalities, Part II: Differentiable Nonlinear Systems , 1976 .

[68]  Elmor L. Peterson,et al.  The Duality between Suboptimization and Parameter Deletion , 1977, Math. Oper. Res..

[69]  Tomas Gal,et al.  Betriebliche Entscheidungsprobleme, Sensitivitätsanalyse und parametrische Programmierung , 1973 .

[70]  J. Zowe,et al.  Regularity and stability for the mathematical programming problem in Banach spaces , 1979 .

[71]  Heiner Müller-Merbach.  Sensibilitätsanalyse der Losgrößenbestimmung , 1962, Unternehmensforschung.

[72]  Anthony V. Fiacco,et al.  Computational experience in sensitivity analysis for nonlinear programming , 1974, Math. Program..

[73]  Gerald L. Thompson,et al.  An operator theory of parametric programming for the generalized transportation problem: II Rim, cost and bound operators† , 1975 .