Simplex-Like Trajectories on Quasi-Polyhedral Sets

References

• Anderson E. J., Goberna M. A., López M. A. Locally polyhedral linear inequality systems. Linear Algebra Appl. (1998) 270:231–253Crossref, Google Scholar
• Anderson E. J., Lewis A. S. An extension of the simplex algorithm for semi-infinite linear programming. Math. Programming (1989) 44:247–269Crossref, Google Scholar
• Anderson E. J., Nash P.Linear Programming in Infinite Dimensional Spaces (1987) (Wiley, New York) Google Scholar
• Blum E., Oettli W.Mathematische Optimierung (1975) (Springer-Verlag, Berlin, Germany) Crossref, Google Scholar
• Carasso C.L'algorithme d'exchange en Optimisation Convexe, Thèse (1973) (Université de Grenoble, Grenoble, France) Google Scholar
• Gill P. E., Murray W. A numerically stable form of the simplex algorithm. Linear Algebra Appl. (1973) 7:99–138Crossref, Google Scholar
• Glashoff K., Gustafson S. A.Linear Optimization and Approximation (1983) (Springer-Verlag, Berlin, Germany) Crossref, Google Scholar
• Goberna M. A., López M. A. Optimality theory for semi-infinite linear programming. Numer. Funct. Anal. Optim. (1995) 16:669–700Crossref, Google Scholar
• Goberna M. A., López M. A.Linear Semi-Infinite Optimization (1998) (Wiley, New York) Google Scholar
• Hoffmann K. H., Klostermair A., Lorentz G. G. A semi-infinite linear programming procedure and applications to approximation problems in optimal control. Approximation Theory II (1976) (Academic Press, New York) 379–389Google Scholar
• Ito S., Kelley C. T., Sachs E. W. Inexact primal-dual interior point iteration for linear programs in function spaces. Comput. Optim. Appl. (1995) 4:189–202Crossref, Google Scholar
• Klee V. L. Some characterizations of convex polyhedra. Acta Math. (1959) 102:79–107Crossref, Google Scholar
• Osborne M. R.Finite Algorithms in Optimization and Data Analysis (1985) (Wiley, New York) Google Scholar
• Powell M. J. D. Karmarkar's algorithm: A view from nonlinear programming. IMA Bull. (1990) 26:165–181Google Scholar
• Rockafellar R. T.Convex Analysis (1970) (Princeton University Press, Princeton, NJ) Crossref, Google Scholar
• Schättler U. An interior-point method for semi-infinite programming problems. Ann. Oper. Res. (1996) 62:277–301Crossref, Google Scholar
• Todd M. J. Interior point algorithms for semi-infinite programming. Math. Programming (1994) 65:217–245Crossref, Google Scholar
• Tunçel L., Todd M. J. Asymptotic behavior of interior-points methods: A view from semi-infinite programming. Math. Oper. Res. (1996) 21:354–381Link, Google Scholar
• Vanderbei R. J. Affine scaling trajectories associated with a semi-infinite linear program. Math. Oper. Res. (1995) 20:163–174Link, Google Scholar
• Walkup D., Wets R. J. B. A Lipschitzian characterization of convex polyhedra. Proc. Amer. Math. Soc. (1969) 23:167–173Crossref, Google Scholar