Nondegeneracy Concepts for Zeros of Piecewise Smooth Functions

References

• Burke J. V., Moré J. J. On the identification of active constraints. SIAM J. Numerical Anal. (1988) 15:1197–1211Crossref, Google Scholar
• Burke J. V., Moré J. J. Exposing constraints. SIAM J. Optim. (1994) 4:573–595Crossref, Google Scholar
• Cottle R. W., Pang J.-S., Stone R. E.The Linear Complementarity Problem (1992) (Academic Press, Boston) Google Scholar
• Dunn J. C. On the convergence of projected gradient process to singular critical points. J. Optim. Theory Appl. (1987) 55:203–216Crossref, Google Scholar
• Eaves B. C., Rothblum U. G. Relationships of properties of piecewise affine maps over ordered fields. Linear Algebra Appl. (1990) 132:1–63Crossref, Google Scholar
• Eaves B. C., Scarf H. The solution of systems of piecewise linear equations. Math. Oper. Res. (1976) 1:1–27Link, Google Scholar
• Ferris M. C., Mangasarian O. L. Minimum principle sufficiency. Math. Programming (1992) 57:1–14Crossref, Google Scholar
• Ferris M. C., Pang J.-S. Nondegenerate solutions and related concepts in affine variational inequalities. SIAM J. Control Optim. (1996) 34:244–263Crossref, Google Scholar
• Fiacco A. V., Liu J. Degeneracy in NLP and the development of results motivated by its presence. Ann. Oper. Res. (1993) 46:61–80Crossref, Google Scholar
• Gal T.Degeneracy in Optimization Problems. Annals of Operations Research (1993) 46/47(J. C. Baltzer AG, Basel, Switzerland) Google Scholar
• Goldman A. J., Tucker A. W., Kuhn H. W., Tucker A. W. Theory of linear programming. Linear Inequalities and Related Systems (1956) (Princeton University Press, Princeton) 53–97Google Scholar
• Gowda M. S. Applications of degree theory to linear complementarity problems. Math. Oper. Res. (1993) 18:868–879Link, Google Scholar
• Gowda M. S., Pang J.-S. Stability analysis of variational inequalities and nonlinear complementarity problems, via the mixed linear complementarity problem and degree theory. Math. Oper. Res. (1994a) 19:831–879Link, Google Scholar
• Gowda M. S., Pang J.-S. On the boundedness and stability of solutions to the affine variational inequality problem. SIAM J. Control Optim. (1994b) 32:421–441Crossref, Google Scholar
• Gowda M. S., Sznajder R. The generalized order linear complementarity problem. SIAM J. Matrix Anal. Appl. (1994) 15:779–795Crossref, Google Scholar
• Güler O., Ye Y. Convergence behavior of interior-point algorithms. Math. Programming (1993) 60:215–228Crossref, Google Scholar
• Ha C. D. Stability of the linear complementarity problem. Math. Programming (1985) 31:327–338Crossref, Google Scholar
• Hoffman A. J. On approximate solutions of systems of linear inequalities. J. Res. Natl. Bureau of Standards (1952) 49:263–265Crossref, Google Scholar
• Jansen M. J. M., Tijs S. H. Robustness and nondegenerateness for linear complementarity problem. Math. Programming (1987) 37:293–308Crossref, Google Scholar
• Lloyd N. G.Degree Theory (1978) (Cambridge University Press, Cambridge) Google Scholar
• Mangasarian O. L.Nonlinear Programming (1969) (McGraw-Hill Book Company, New York) Google Scholar
• Mangasarian O. L. Error bounds for nondegenerate monotone linear complementarity problems. Math. Programming (1990) 48:437–445Series BCrossref, Google Scholar
• Milnor J. W.Topology from the Differentiable Viewpoint (1965) (University of Virginia Press, Charlottesville) Google Scholar
• Monteiro R. D. C., Wright S. J. Local convergence of interior-point algorithms for degenerate LCP. Comp. Optim. Appl. (1994) 3:131–155Crossref, Google Scholar
• Murty K. G. On the number of solutions to the complementarity problem and spanning properties of complementary cones. Linear Algebra and Its Appl. (1972) 5:65–108Crossref, Google Scholar
• Ortega J. M., Rheinboldt W. C.Iterative Solution of Nonlinear Equations in Several Variables (1970) (Academic Press, New York) Google Scholar
• Pang J.-S. Newton's method for B-differentiable equations. Math. Oper. Res. (1990) 15:311–341Link, Google Scholar
• Robinson S. M. Local structure of feasible sets in nonlinear programming, Part II: Nondegeneracy. Math. Programming Stud. (1984) 22:217–230Crossref, Google Scholar
• Robinson S. M. Local structure of feasible sets in nonlinear programming, Part III: Stability and Sensitivity. Math. Programming Stud. (1987) 30:45–66Crossref, Google Scholar
• Robinson S. M. Normal maps induced by linear transformations. Math. Oper. Res. (1992) 17:691–714Link, Google Scholar
• Rockafellar R. T.Convex Analysis (1970) (Princeton University Press, Princeton, New Jersey) Crossref, Google Scholar
• Scholtes S.Introduction to piecewise differentiable equations (1994) . Preprint No. 53/1994, Institut für Statistik und Mathematische Wirtschaftstheorie, Universität Karlsruhe, MayGoogle Scholar
• Szanc B. P. The generalized complementarity problem. (1989) . Ph.D. thesis, Rensselaer Polytechnic Institute, Troy, New YorkGoogle Scholar
• Sznajder R. Degree-theoretic analysis of the vertical and horizontal linear complementarity problem. (1994) . Ph.D. thesis, University of Maryland Baltimore County, Baltimore, MarylandGoogle Scholar
• Sznajder R., Gowda M. S. Generalizations of P0 and P-properties; Extended vertical and horizontal LCP's. Linear Algebra and Its Appl. (1995) 223/224:695–715Crossref, Google Scholar
• Tucker A. W., KuhnA H. W., Tucker A. W. Dual systems of homogeneous relations. Linear Inequalities and Related Systems (1956) (Princeton University Press, Princeton) 3–18Google Scholar
• Zhang Y. On the convergence of a class of infeasible interior-point methods for the horizontal linear complementarity problem. SIAM J. Optim. (1994) 4:208–227Crossref, Google Scholar