Numerical treatment of a class of semi‐infinite programming problems
Tóm tắt
Many optimization problems occur in both theory and practice when one has to optimize an objective function while an infinite number of constraints must be satisfied. The aim of this paper in to describe methods of handling such problems numerically in an effective manner. We also indicate a number of applications.
Từ khóa
Tài liệu tham khảo
Bojanic R., 1966, On Polynomials of Best One‐Sided Approximation, L'Ensignement Math., 12, 139
Charnes A., 1961, Management models and industrial applications of linear programming
Cheney W. E., 1966, Introduction to approximation theory
Duffin R. J., 1956, Linear Inequalities and Related Systems, 157
Fan Ky, 1956, Linear Inequalities and Related Systems, 99
Gorr W. andK. O.Kortanek “Numerical Aspects of Pollution Abatement Problems: Constrained Generalized Moment Techniques ” IPP Report No. 12 School of Urban and Public Affairs Carnegie‐Mellon University (Oct.1970).
Gustafson S.‐Å. “Numerical Aspects of the Moment Problem ” Fildr. Thesis Institutionen for Informations Behandling Stockholms Universitet Stockholm Sweden (Apr.1970).
Gustafson S.‐Å., 1972, On the Computation of Slowly Convergent Fourier Integrals, Methoden und Verfahren der Mathematischen Physik, 6, 37
Gustafson S.‐Å., Models for Environmental Pollution Control
Gustafson S.‐Å.andW.Rom “Applications of Semi‐Infinite Programming to the Computa tional Solution of Approximation Problems ” Tech. Report No. 88 Dept. of Operations Ressearch Cornell University Ithaca N. Y. (Sept.1969).
Haar A., 1924, Über lineare ungleichungen, Acta. Math. (Szeged), 2, 1
John Fritz, 1948, Studies and essays. Courant Anniversary, 187
Kantorovich L. V., 1957, Concerning a Functional Space and Some Extremum Problems, Dokl. Akad. Nauk. SSSR, 115, 1058
Karlin S., 1966, Tchebycheff Systems: with Applications in Analysis and Statistics
Kretschmer K. S. “Linear Programming in Locally Convex Spaces and Its Use in Analysis.” Ph. D. Thesis Carnegie‐Mellon University Pittsburgh Pa. (1958).
Rosen J. B., 1970, Nonlinear programming
Ortega J. M., 1970, Iterative Solution of Nonlinear Equations in Several Pariables
Rubinshtein G. Sh. “Investigations on Dual Extremal Problems ” Doctoral Dissertation Inst. Matem. SO AN SSSR Novosibirsk (1965).
Shapiro H. S., 1961, On a Class of Extremal Problems for Polynomials in the Unit Circle., Portugaliae Math., 20, 67
Shohat J. A.andJ. D.Tamarkin “The Problem of Moments ” Mathematical Surveys. No. 1. Am. Math. Soc. New York (1943).
Todd J., 1962, A survey of numerical analysis
Vershik A. M., 1968, Some Questions Concerning the Approximation of the Optimal Value of Infinite‐Dimensional Problems in Linear Programming, Sibirskii Matematicheskii Zhurnal, 9, 591
Wilkinson J. H., 1963, Rounding Errors in Algebraic Processes
Wilkinson J. H., 1965, The Algebraic Eigenvalue Problem