An interior point algorithm for global optimal solutions and KKT points

Optimization Methods and Software

Volumn 15, Issue 3-4, 2001, Pages 225-256

  Pacelli, Graziella ^a   Recchioni, Maria Cristina ^a  

^a UNIVERSITÀ POLITECNICA DELLE MARCHE   (Italy)

Author keywords

Global optimization; Interior point methods; Karush Kuhn Tucker points

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; FINITE ELEMENT METHOD; NONLINEAR PROGRAMMING;

EUCLIDEAN NORMS;

GLOBAL OPTIMIZATION;

EID: 0036459440     PISSN: 10556788     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (23)

1. N. Karmarkar (1984). A new polynomial time algorithm in linear programming. Combinatorica, 4, 373-395.
2. N. Hooker (1986). Karmarkar's linear programming algorithm. Interfaces, 16, 75-90.
3. D.A. Bayer and J.C. Lagarias (1989). The nonlinear geometry of linear programming I. Trans. Amer. Math. Soc. 314, 499-526.
4. S. Herzel, M.C. Recchioni and F. Zirilli (1991). A quadratically convergent method of linear programming. Linear Algebra and its Appl., 152, 255-289.
5. F. Zirilli (1982). The use of ordinary differential equations in the solution of nonlinear systems of equations. In: M.J.D. Powell, (Ed.), Nonlinear Optimization 1981, pp. 39-47, Academic Press, New York.
6. G. Pacelli and M.C. Recchioni (2000). A monotonic variable - metric algorithm for linearly constrained nonlinear programming. JOTA 104, 255-279.
7. N. Megiddo (Ed.) (1989). Progress in Mathematical Programming-Interior Point and Related Methods. Springer-Verlag, New York.
8. J.C. Lagarias and M.J. Todd (Eds.) (1990). Mathematical developments arising from linear programming. In: Contemporary Mathematics, 114, American Mathematical Society, Providence, Rhode Island.
9. Y. Ye and E. Tse (1989). An extension of Karmarkar's projective algorithm for convex quadratic programming. Mathematical Programming, 44, 157-179.
10. A. Cambini, L. Martein and S. Schaible (1989). On maximizing a sum of ratios. J. Information & Optimization Sciences, 10, 65-79.
11. H. Konno and Y. Yajima (1992). Minimizing and maximizing the product of linear fractional functions. In: C.A. Floudas and P.M. Pardalos (Eds.), Recent Advances in Global Optimization, pp. 259-273, Princeton University Press, Princeton.
12. R.D.C. Monteiro and I. Adler (1989). Interior path following primal-dual algorithms. Part II: Convex Quadratic programming. Mathematical Programming, 44, 43-66.
13. T. Terlaky (Ed.) (1996). Interior Point Methods of Mathematical Programming. Kluwer Academic Publishers.
14. J. La Salle and S. Lefschetz (1961). Stability by Liapunov's direct method. Academic Press, New York.
15. O.L. Mangasarian (1969). Nonlinear programming. McGraw Hill Book Company, New York.
16. K. Swarup (1965). Linear fractional functional programming. Operations Research, 13, 1029-1036.
17. P. Wolfe (1972). On the convergence of gradient methods under constraints. IBM Journal of Research and Development, 16, 407-411.
18. J.P. Dussault and G. Fournier (1993). On the convergence of the projected gradient method. JOTA, 77, 197-208.
19. J.E. Falk and S.W. Polacsay (1992). Optimizing the sum of linear fractional functions. In: C.A. Floudas and P.M. Pardalos (Eds.), Recent Advances in Global Optimization, pp. 221-258, Princeton University Press, Princeton,
20. Y. Almogy and O. Levin (1971). A class of fractional programming problems. Operations Research, 19, 57-67.
21. K. Schittkowski (1987). More test examples for Nonlinear Programming codes. In: Lecture Notes in Economics and Mathematical Systems, 282, Springer-Verlag, Berlin, Heidelberg.
22. D.A. Pierre (1969). Optimization Theory and Applications. John Wiley & Sons, Inc., New York.
23. D.M. Gay (1985). Electronic mail distribution of linear programming test problems. Committee on Algorithms Newsletter, Math. Programming Soc., 13.