Автор |
Nazareth, J.L. |
Дата выпуска |
1995 |
dc.description |
An approach to interior methods for linear programming premised on the optimality condition and two fundamental optimization principles (homotopy and symmetry) is described. It provides a concise, yet general introduction to the new area of optimization research germinated by Karmarkar, and a useful alternative to the current logarithmic Barrier-based perspective on the subject |
Формат |
application.pdf |
Издатель |
Gordon and Breach Science Publishers |
Копирайт |
Copyright Taylor and Francis Group, LLC |
Название |
A framework for interior methods of linear programming |
Тип |
research-article |
DOI |
10.1080/10556789508805612 |
Electronic ISSN |
1029-4937 |
Print ISSN |
1055-6788 |
Журнал |
Optimization Methods and Software |
Том |
5 |
Первая страница |
227 |
Последняя страница |
234 |
Аффилиация |
Nazareth, J.L.; Department of Pure and Applied Mathematics, Washington State University; Department of Applied Mathematics, University of Washington |
Выпуск |
3 |
Библиографическая ссылка |
Allgower, E.L. and Georg, K. 1990. “Numerical Continuation Methods: An Introduction”. In Series in Computational Mathematics, Vol. 13, Heidelberg: Springer-Verlag. |
Библиографическая ссылка |
Garcia, C.B. and Zangwill, W.I. 1981. “Pathways to Solutions”. In Fixed Point and Equilibria, Englewood Cliffs, NJ: Prentice-Hall. |
Библиографическая ссылка |
Gill, P.E., Murray, W., Ponceleón, D.B. and Saunders, M.A. 1991. “Primal-dual methods for linear programming”. In Systems Optimization Laboratary, Stanford, CA: Stanford University. Technical Report 91-3 |
Библиографическая ссылка |
Gonzaga, C.G. 1992. Path-following methods for linear programming. SIAM Review, 34: 167–224. |
Библиографическая ссылка |
Hirsch, M.W. and Smale, S. 1979. On algorithms for solving F(x) = 0. Comm. Pure Appl. Math, 32: 281–312. |
Библиографическая ссылка |
Karmarkar, N. 1984. A new polynomial-time algorithm for linear programming. Combinatorica, 4: 373–395. |
Библиографическая ссылка |
Keller, H.B. 1987. Lectures on Numerical Methods in Bifurcation Problems, Heidelberg: Springer-Verlag. |
Библиографическая ссылка |
Lustig, I.J., Marsten, R.E. and Shanno, D. 1992. On implementing Mehrotra's predictor-corrector interior point method for linear programming. SIAM J. Optimization, 2: 435–449. |
Библиографическая ссылка |
Lustig, I.J., Marsten, R.E. and Shanno, D. 1994. Interior point methods for linear programming: computational state of the art. ORSA J. on Computing, 6: 1–14. with commentaries by R. Bixby, M. Saunders, M. Todd and R. Vanderbei, 15-34, and a rejoinder, 35-36 |
Библиографическая ссылка |
Marsten, R., Subramanain, R., Saltzman, M., Lustig, I.J. and Shanno, D. 1990. Interior point methods for linear programming: Just call Newton, Lagrange, and Fiacco and McCormick!. Interfaces, 20: 105–116. |
Библиографическая ссылка |
Nazareth, J.L. 1986. Homotopy techniques in linear programming. Algorithmica, 1: 529–535. |
Библиографическая ссылка |
Nazareth, J.L. The homotopy principle and algorithms for linear programming. Presented at IIAS A Workshop on Nonstandard Optimization Methods and Related Topics. August1–41989, Laxenburg. Austria: Vienna. appears in SIAMJ. Optimization, 1, 316-332 (1991 |
Библиографическая ссылка |
Nazareth, J.L. 1994. “Deriving potential functions via a symmetry principle for nonlinear equations”. In Department of Pure and Applied Mathematics, Pullman, WA: Washington State University. Technical Report 94—2 |
Библиографическая ссылка |
Nesterov, Y.E. and Nemirovskii, A. 1994. “Interior-Point Polynomial Algorithms in Convex Programming”. In SIAM Studies in Applied Mathematics, Vol. 13, Philadelphia: SIAM. |
Библиографическая ссылка |
Ortega, J.M. and Rheinboldt, W.C. 1970. Iterative Solution of Nonlinear Equations in Several Variables, N.Y: Academic Press. |
Библиографическая ссылка |
Polak, E. 1971. Computational Methods in Optimization: A Unified Approach, Academic Press. |
Библиографическая ссылка |
Renegar, J. 1993. “Linear programming, complexity theory and elementary functional analysis”. In Department of OR&IE, Ithaca, NY: Cornell University. preprint, revised Summer, 1994 |
Библиографическая ссылка |
Renegar, J. and Shub, M. 1988. “Simplified complexity analysis for Newton LP methods”. In School of Operations Research and Industrial Engineering, Ithaca, NY: Cornell University. Report No. 807 |
Библиографическая ссылка |
Smale, S. 1976. A convergent process of price adjustment and globalNewtonmethods. J Math Econom, 3: 1–14. |
Библиографическая ссылка |
Strang, G. 1986. Introduction to Applied Mathematics, Cambridge, MA: Wellesley-Cambridge Press. |
Библиографическая ссылка |
Tapia, R. and Zhang, Y. 1992. On the quadratic convergence of the singular Newton's method. SIAG/OPT Views-and-News, 1 Fall: 6–8. 1992 |