Stability in the Discretization of a Parametric Semi-Infinite Convex Inequality System

References

• Beer G.Topologies on Closed and Closed Convex Sets (1993) (Kluwer Academic Publishers, Dordrecht, The Netherlands) Crossref, Google Scholar
• Brosowski B. Parametric semi-infinite linear programming I. Continuity of the feasible set and of the optimal value. Math. Programming Study (1984) 21:18–42Crossref, Google Scholar
• Cánovas M. J., López M. A., Parra J. Stability of linear inequality systems in a parametric setting. (2001) . Technical Report, Operations Research Center, Miguel Hernández University of Elche, Elche, SpainGoogle Scholar
• Cánovas M. J., López M. A., Parra J., Todorov M. I. Stability and well-posedness in linear semi-infinite programming. SIAM J. Optim. (1999) 10:82–98Crossref, Google Scholar
• Cánovas M. J., López M. A., Parra J., Todorov M. I. Solving strategies and well-posedness in linear semi-infinite programming. Ann. Oper. Res (2001) 101:171–190Crossref, Google Scholar
• Cánovas M. J., López M. A., Parra J., Todorov M. I. Stability of the Lagrangian dual of a parametric nonlinear programming problem. (2002) . Technical Report, Operations Research Center, Miguel Hernández University of Elche, Elche, SpainGoogle Scholar
• Fischer T., Brosowski B., Martensen E. Contributions to semi-infinite linear optimization. Approximation and Optimization in Mathematical Physics (1983) (Peter Lang, Frankfurt-am-Main) 175–199Google Scholar
• Goberna M. A., López M. A. Topological stability of linear semi-infinite inequality systems. J. Optim. Theory Appl. (1996) 89:227–236Crossref, Google Scholar
• Goberna M. A., López M. A.Linear Semi-Infinite Optimization (1998) (John Wiley & Sons, Chichester, UK) Google Scholar
• Goberna M. A., López M. A.Semi-Infinite Programming: Recent Advances (2001) (Kluwer, Dordrecht, The Netherlands) Crossref, Google Scholar
• Goberna M. A., López M. A. Stability theory for linear inequality systems. SIAM J. Matrix Anal. Appl. (1996) 17:730–743Crossref, Google Scholar
• Henrion R., Klatte D. Metric regularity of the feasible set mapping in semi-infinite optimization. Appl. Math. Optim. (1994) 30:103–109Crossref, Google Scholar
• Hettich R., Kortanek K. O. Semi-infinite programming: Theory, methods and applications. SIAM Rev. (1993) 35:380–429Crossref, Google Scholar
• Jiménez M. A., Rückmann J. J. On equivalent stability properties in semi-infinite optimization. Z. Oper. Res. (1995) 41:175–190Google Scholar
• Jongen H. Th., Rückmann J. J., Weber G. W. One-parametric semi-infinite optimization: On the stability of the feasible set. SIAM J. Optim. (1994) 4:637–648Crossref, Google Scholar
• Jongen H. Th., Twilt F., Weber G. W. Semi-infinite optimization: Structure and stability of the feasible set. J. Optim. Theory Appl. (1992) 72:529–552Crossref, Google Scholar
• Klatte D. Stable local minimizers in semi-infinite optimization: Regularity and second-order conditions. J. Comp. Appl. Math. (1994) 56:137–57Crossref, Google Scholar
• Li W., Nahak C., Singer I. Constraint qualifications for semi-infinite systems of convex inequalities. SIAM J. Optim. (2000) 11:31–52Crossref, Google Scholar
• López M. A., Vera de Serio V. N., Goberna M. A., López M. A. Stability of the feasible set mapping in convex semi-infinite programming. Semi-Infinite Programming: Recent Advances (2001) (Kluwer, Dordrecht, The Netherlands) 101–120Crossref, Google Scholar
• Reemtsen R., Floudas C. A., Pardalos P. M. Semi-infinite programming: Discretization methods. Encyclopedia of Optimization (2001) (Kluwer, Boston/London) 1–8Crossref, Google Scholar
• Reemtsen R., Rückmann J. J.Semi-Infinite Programming (1998) (Kluwer, Dordrecht, The Netherlands) Crossref, Google Scholar
• Robinson S. M. Stability theory for systems of inequalities. Part I: Linear systems. SIAM J. Numer. Anal. (1975) 12:754–769Crossref, Google Scholar
• Rockafellar R. T.Convex Analysis (1970) (Princeton University Press, Princeton, NJ) Crossref, Google Scholar
• Rockafellar R. T., Wets R. J.-B.Variational Analysis (1998) (Springer, Berlin) Crossref, Google Scholar
• Rückmann J. J. Topological stability of feasible sets in semi-infinite optimization: A tutorial. . Institut für Geometrie und Praktische Mathematik, Bericht Nr. 123, RWTH Aachen, Aachen, GermanyGoogle Scholar
• Schochetman I. E. Pointwise version of the maximum theorem with applications in optimization. Appl. Math. Lett. (1990) 3(1):89–92Crossref, Google Scholar
• Schochetman I. E., Smith R. L. Convergence of selections with applications in optimization. J. Math. Anal. Appl. (1991) 155:278–292Crossref, Google Scholar
• Zhu Y. J. Generalizations of some fundamental theorems on linear inequalities. Acta Math. Sinica (1966) 16:25–40Google Scholar
• Zlobec S. Stability in linear programming models: An index set approach. Ann. Oper. Res. (2001) 101:363–382Crossref, Google Scholar