Abstract
The article examines the relationships of inverse nonlinear programming problems with n-person games, hierarchical games, and solution of operator equations. Numerical solution of inverse nonlinear programming problems is considered.
Similar content being viewed by others
References
A. S. Antipin, "A class of inverse optimization problems," in: Methods of Mathematical Programming and Computer Software [in Russian], abstracts of papers, Sverdlovsk (1989), pp. 6–7.
A. S. Antipin, "Inverse optimization problems and methods for their solution," in: System Modeling and Optimization, Proc. 14th IFIP Conf., Leipzig, 1989, Lect. Notes Contr. Inf. Sci., vol. 143, 544–553, Springer, Berlin (1990).
L. A. Istomin, "Solving some inverse problems of mathematical programming," Dokl. Akad. Nauk SSSR,214, No. 5, 1013–1015 (1974).
I. I. Eremin and V. V. Mazurov, Nonstationary Processes in Mathematical Programming [in Russian], Nauka, Moscow (1979).
V. M. Glushkov, "On system optimization," Kibernetika, No. 5, 89–90 (1980).
A. G. Zubrev, Inverse Optimization Problems in System Analysis and Automatic Control Theory [in Russian], abstract of dissertation, VNIISI, Moscow (1987).
L. A. Istomin, "Some models for parameter choosing in mathematical programming problems," in: Improper Optimization Methods [in Russian], UNTs AN SSSR, Sverdlovsk (1982), pp. 37–41.
E. B. Ershov, "On simple closed-loop models of optimal economic planning," in: Conf on Mathematical Optimal Programming [in Russian], abstracts of papers, Inst. Matem. SO AN SSSR, Novosibirsk (1965), p. 70.
E. B. Ershov and E. S. Levitin, "Closure of optimal planning models by exogenous parameters," in: Mathematical-Economic Models and Methods [in Russian], Voronezh. Univ., Voronezh (1989), pp. 68–83.
S. M. Shvartin, General Stability of Canonical Linear Programming Problems [in Russian], Preprint, VTs AN SSSR, Moscow (1989).
A. S. Antipin, "Flow control in local-area computer networks with bus topology," in: Topics in Cybernetics. Models and Methods of Large System Analysis [in Russian], Nauchnyi Sovet po Kompleksnoi Probleme "Kibernetika", AN SSSR, Moscow (1991), pp. 4–16.
E. N. Pavenko and V. M. Khomenko, "Interactive exchange of information when solving inverse mathematical programming problems," in: Mathematical Models of Information Representation and Data Processing Problems [in Russian], VTs SO AN SSSR, Novosibirsk (1986).
E. P. Lavrinenko, "A class of two-level multicriterion linear programming problems," in: Multicriterion Mathematical Programming Problems [in Russian], abstracts of papers, Kiev (1988), pp. 8–9.
M. A. Krasnosel'skii, G. M. Vainikko, P. P. Zabreiko, Ya. B. Rutitskii, and V. Ya. Stetsenko, Approximate Solution of Operator Equations [in Russian], Nauka, Moscow (1969).
J. Ortega and W. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables [Russian translation], Mir, Moscow (1975).
H. Nikaido and K. Isoda, "A note on coalitionless convex games," in: Infinite Nonzero-Sum Games [Russian translation], Fizmatgiz, Moscow (1963).
S. I. Zukhovitskii, R. A. Polyak, and M. E. Primak, "Convexn-person games (numerical methods)," Ekon. i Mat. Metody,7, No. 6, 888–900 (1971).
Yu. M. Ermol'ev and S. P. Uryas'ev, "Seeking Nash equilibrium inn-person games," Kibernetika, No. 3, 85–88 (1982).
A. S. Antipin, "Nongradient optimization methods for saddle-point functions," in: Topics in Cybernetics. Methods and Algorithms for Large System Analysis [in Russian], Nauchnyi Sovet po Kompleksnoi Probleme "Kibernetika", AN SSSR, Moscow (1987), pp. 4–13.
O. A. Malafeev, "Existence of equilibria inn-person differential coalitionless games," Vestnik LGU, No. 13, 40–43 (1982).
S. P. Uryas'ev, Adaptive Algorithms for Stochastic Optimization and Game Theory [in Russian], Nauka, Moscow (1990).
V. V. Fedorov, Numerical Maxmin Methods [in Russian], Nauka, Moscow (1979).
P. D. Krut'ko, "Inverse problems in controlled system dynamics," in: Linear Models [in Russian], Nauka, Moscow (1987).
A. S. Antipin, "Continuous and iterative processes with projection and projection type operators," in: Topics in Cybernetics. Computational Topics in Large System Analysis [in Russian], Nauchnyi Sovet po Kompleksnoi Probleme "Kibernetika", AN SSSR, Moscow (1989), pp. 5–43.
A. S. Antipin, "Feedback in optimization," in: Optimization Models and Methods [in Russian], Collection of papers, No. 11, VNIISI, Moscow (1990).
A. S. Antipin, "Optimization problems with several participants," IFAC/IFORS/IMASS Symp. on Large Scale Systems: Theory and Applications, LSS Preprints, Chinese Association of Automation, Beijing (1992), pp. 53–58.
A. S. Antipin, "Gradient and proximal controlled problems," Topics in Cybernetics. Large System Analysis [in Russian], Nauchnyi Sovet po Kompleksnoi Probleme "Kibernetika", RAN, Moscow (1992), pp. 5–38.
M. Bazaraa and C. M. Shetty, Nonlinear Programming: Theory and Algorithms [Russian translation], Mir, Moscow (1982).
J. S. Pang, "Methods for quadratic programming: A survey," Computers and Chemical Engineering,7, No. 5, 583–594 (1983).
Ya. M. Bershchanskii and M. V. Meerov, "Theory and methods of solution of complementarity problems," Avtomat. Telemekh., No. 3, 5–31 (1983).
A. S. Antipin, "Methods of solution of systems of convex programming problems," Zh. Vychisl. Matem. i Mat. Fiz.,27, No. 3, 368–376 (1987).
A. I. Golikov and G. G. Kotkin, "Characterization of the set of optimal values of multicriterion optimization problem," Zh. Vychisl. Matem. i Mat. Fiz.,28, No. 10, 1461–1470 (1988).
A. S. Antipin, "Optimization problems with several participants," in: Numerical Methods and Optimization [in Russian], Valgus, Tallin (1988), pp. 10–14.
A. S. Antipin, "An equilibrium problem and its solution methods," Avtomat. Telemekh., No. 9, 75–82 (1986).
A. S. Antipin, "Linear wholesale market: models and methods," in: Optimization Models and Methods [in Russian], Collected papers, No. 11, VNIISI, Moscow (1987), pp. 101–110.
P. Samuelson, Economics [Russian translation], Progress, Moscow (1964).
S. Karlin, Mathematical Methods in Theory of Games, Programming and Economics [Russian translation], Mir, Moscow (1964).
S. A. Ashmanov, An Introduction to Mathematical Economics [in Russian], Nauka, Moscow (1984).
V. A. Gorelik and A. F. Kononeko, Game-Theoretical Decision Models in Environmental-Economic Systems [in Russian], Radio i Svyaz’, Moscow (1982).
P. S. Krasnoshchekov and A. A. Petrov, Modeling Principles [in Russian], Izd. MGU, Moscow (1983).
E. R. Smol'yakov, Equilibrium Models with Divergent Agent Interests [in Russian], Nauka, Moscow (1986).
A. S. Antipin, "Interaction models for producer enterprises, consumer enterprises, and transportation system," Avtomat. Telemekh., No. 10, 105–113 (1989).
A. S. Antipin, "Extrapolation methods for computing the saddle point of the Lagrange function and their application to problems with block-separable structure," Zh. Vychisl. Matem. i Mat. Fiz.,26, No. 1, 150–151 (1986).
A. S. Antipin, "Predictor type optimization methods with application to problems with block-separable structure," in: Optimization Models and Methods [in Russian], Collected papers, No. 19, VNIISI, Moscow (1986), pp. 82–92.
Additional information
Translated from Nelineinye Dinamicheskie Sistemy: Kachestvennyi Analiz i Upravlenie—Sbornik Trudov, No. 2, pp. 5–32, 1993.
Rights and permissions
About this article
Cite this article
Antipin, A.S. Inverse problems of nonlinear programming. Comput Math Model 7, 263–287 (1996). https://doi.org/10.1007/BF01128160
Issue Date:
DOI: https://doi.org/10.1007/BF01128160