Constraint Nondegeneracy in Variational Analysis

References

  • Bonnans J. F., Shapiro A.Perturbation Analysis of Optimization Problems (2000) (Springer-Verlag, New York) Springer Series in Operations ResearchCrossrefGoogle Scholar
  • Cottle R. W., Pang J-S., Stone R. E.The Linear Complementarity Problem (1992) (Academic Press, Inc., Boston, MA) Google Scholar
  • Dantzig G. B.Linear Programming and Extensions (1963) (Princeton University Press, Princeton NJ) CrossrefGoogle Scholar
  • Dontchev A. L., Rockafellar R. T. Characterizations of strong regularity for variational inequalities over polyhedral convex sets. SIAM J. Optim. (1996) 6:1087–1105CrossrefGoogle Scholar
  • Dontchev A. L., Rockafellar R. T. Ample parametrization of variational inclusions. SIAM J. Optim. (2001) 12:170–187CrossrefGoogle Scholar
  • Facchinei F., Pang J-S.Finite-Dimensional Variational Inequalities and Complementarity Problems (2003) (Springer-Verlag, New York) Springer Series in Operations ResearchGoogle Scholar
  • Guddat J., Guerra Vasquez F., Jongen H. T.Parametric Optimization: Singularities, Pathfollowing and Jumps (1990) (John Wiley & Sons, Stuttgart and Chichester) . 1990CrossrefGoogle Scholar
  • Hestenes M. R.Optimization Theory (1975) (Wiley-Interscience, New York) Google Scholar
  • Levy A. B. Implicit multifunction theorems for the sensitivity analysis of variational conditions. Math. Programming (1996) 74(3):333–350CrossrefGoogle Scholar
  • Levy A. B. Stability of solutions to parameterized nonlinear complementarity problems. Math. Programming (1999) 85(2):397–406CrossrefGoogle Scholar
  • Levy A. B. Lipschitzian multifunctions and a Lipschitzian inverse mapping theorem. Math. Oper. Res. (2001 a) 26(1):105–118LinkGoogle Scholar
  • Levy A. B. Solution sensitivity from general principles. SIAM J. Control Optim. (2001b) 40(1):1–38CrossrefGoogle Scholar
  • Levy A. B., Rockafellar R. T. Sensitivity analysis of solutions to generalized equations. Trans. Amer. Math. Soc. (1994) 345:661–671CrossrefGoogle Scholar
  • Mangasarian O. L., Fromovitz S. The Fritz John necessary optimality conditions in the presence of equality and inequality constraints. J. Math. Anal. Appl. (1967) 17:37–47CrossrefGoogle Scholar
  • Nocedal J., Wright S. J.Numerical Optimization (1999) (Springer-Verlag, New York) Springer Series in Operations ResearchCrossrefGoogle Scholar
  • Ralph D. On branching numbers of normal manifolds. Nonlinear Anal.: Theory Methods, Appl. (1994) 22:1041–1050CrossrefGoogle Scholar
  • Robinson S. M. Stability theory for systems of inequalities, part I: Linear systems. SIAM J. Numer. Anal. (1975) 12:754–769CrossrefGoogle Scholar
  • Robinson S. M. Stability theory for systems of inequalities, part II: Differentiable nonlinear systems. SIAM J. Numer. Anal. (1976) 13:497–513CrossrefGoogle Scholar
  • Robinson S. M. Local structure of feasible sets in nonlinear programming, part II: Nondegeneracy. Math. Programming Stud. (1984) 22:217–230CrossrefGoogle Scholar
  • Robinson S. M. Normal maps induced by linear transformations. Math. Oper. Res. (1992) 17:691–714LinkGoogle Scholar
  • Robinson S. M. Newton's method for a class of nonsmooth functions. Set-Valued Anal. (1994) 2:291–305CrossrefGoogle Scholar
  • Robinson S. M., Giannessi F., Maugeri A. Sensitivity analysis of variational inequalities by normal-map techniques. Variational Inequalities and Network Equilibrium Problems (1995) (Plenum Press, New York) 257–269CrossrefGoogle Scholar
  • Rockafellar R. T.Convex Analysis (1970) (Princeton University Press, Princeton, NJ) CrossrefGoogle Scholar
  • Rockafellar R. T., Wets R. J.Variational Analysis (1998) (Springer-Verlag, Berlin, Germany) . Grundlehren der mathematischen Wissenschaften, Number 317CrossrefGoogle Scholar
  • Scholtes S. A proof of the branching number bound for normal manifolds. Linear Algebra and Its Appl (1996) 246:83–95CrossrefGoogle Scholar
  • Shapiro A. Sensitivity analysis of generalized equations. J. Math. Sci.ForthcomingGoogle Scholar
  • Spingarn J. E. Generic conditions for optimality in constrained minimization problems. (1977) . Ph.D. dissertation, Department of Mathematics, University of Washington, Seattle, WAGoogle Scholar
  • Stampacchia G. Variational inequalities. Proc. of a NATO Adv. Study Inst. (1969) June 17–30, 1968Venice, ItalyTheory and Applications of Monotone Operators. Edizioni Oderisi, Gubbio, ItalyGoogle Scholar
  • Struik D. J.Lectures on Classical Differential Geometry (1950) (Addison-Wesley, Reading, MA) Google Scholar
  • Vanderbei R. J.Linear Programming: Foundations and Extensions (1997) (Kluwer Academic Publishers, Boston, MA) International Series in Operations Research & Management ScienceGoogle Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.