Global Error Bounds for Convex Multifunctions and Applications
Published Online:1 May 1998https://doi.org/10.1287/moor.23.2.443
References
- Noncoercive optimization problems. Math. Oper. Res. (1996) 21:769–782Link, Google Scholar
- Global regularity theorems. Math. Oper. Res. (1988) 13:243–253Link, Google Scholar
- The distance to a polyhedron. Linear Alg. Appl. (1992) 169:111–129Crossref, Google Scholar
- Adjoint process duality. Math. Oper. Res. (1983) 8:403–434Link, Google Scholar
- A Gauss-Newton approach to solving generalized inequalities. Math. Oper. Res. (1996) 11:632–643Link, Google Scholar
- A unified analysis of Hoffman's bound via Fenchel duality. SIAM J. Optim. (1996) 6:265–282Crossref, Google Scholar
- Metric regularity, tangent sets, and second-order optimality conditions. Appl. Math. Optim. (1990) 21:265–287Crossref, Google Scholar
- On approximate solutions of systems of linear inequalities. J. Res. Natl. Bur. Standards (1952) 49:263–265Crossref, Google Scholar
- Approximations and metric regularity in mathematical programming in Banach space. Math. Oper. Res. (1993) 18:390–401Link, Google Scholar
- , Guddat J., Jongen H. Th., Nožička F., Twilt F., Still G. Lipschitz stability and Hoffman's error bounds for convex inequality systems. Parametric Optimization and Related Topics IV (1996) (Peter Lang Verlag, Frankfurt/M) 201–212Google Scholar
- Asymptotic constraint qualifications and global error bounds for convex inequalities. Math. Programming (1997) . (to appear)Google Scholar
- Error bounds for convex inequality systems. (1996) . Preprint, Department of Mathematical Sciences, The Johns Hopkins University, Baltimore, MD 21218Google Scholar
- Remarks on convergence of matrix splitting algorithm for the symmetric linear complementarity problem. SIAM J. Optim. (1993) 3:155–163Crossref, Google Scholar
- Linearly convergent descent methods for unconstrained minimization of a convex quadratic spline. J. Optim. Theory Appl. (1995) 86:145–172Crossref, Google Scholar
- Abadie's constraint qualification, metric regularity, and error bounds for differentiable convex inequalities. SIAM J. Optim. (1997) 7:966–978Crossref, Google Scholar
- An estimate of solution set perturbations for a system of linear inequalities. Optim. Methods and Software (1995) 6:1–24Crossref, Google Scholar
- Extension of Hoffman's error bound to polynomial systems. SIAM J. Optim. (1994) 4:383–392Crossref, Google Scholar
- On the convergence of a matrix splitting algorithm for the symmetric monotone linear complementarity problem. SIAM J. Control Optim. (1991) 29:1037–1060Crossref, Google Scholar
- Error bound and convergence analysis of matrix splitting algorithms for the affine variational inequality problem. SIAM J. Optim. (1992a) 2:43–54Crossref, Google Scholar
- On the linear convergence of descent methods for convex essentially smooth minimization. SIAM J. Control Optim. (1992b) 30:408–425Crossref, Google Scholar
- On a global error bound for a class of monotone affine variational inequality problems. Oper. Res. Let. (1992c) 11:159–165Crossref, Google Scholar
- Perturbation analysis of a condition number for linear systems. SIAM J. Matrix Anal. Appl. (1994) 15:636–660Crossref, Google Scholar
- Convergence of iterates of an inexact matrix splitting algorithm for the symmetric monotone linear complementarity problem. SIAM J. Optim. (1991) 1:114–122Crossref, Google Scholar
- Complete characterization of openness, metric regularity, and Lipschitzian properties of multifunctions. Trans. Amer. Math. Soc. (1993) 340:1–35Crossref, Google Scholar
- Error bounds in mathematical programming. (1996) . Plenary lecture at the 5th symposium on generalized convexity, Luminy-Marseille, June 1996Google Scholar
- On regularity conditions in mathematical programming. Math. Programming Stud. (1982) 19:167–199Crossref, Google Scholar
- Metric regularity, openness and Lipschitzian behavior of multifunctions. Nonlinear Anal., Theory, Methods, Appl. (1989) 13:629–643Crossref, Google Scholar
- Stability theory for systems of inequalities, Part I: Linear systems. SIAM J. Numer. Anal. (1973) 12:754–769Crossref, Google Scholar
- An application of error bounds for convex programming in a linear space. SIAM J. Control Optim. (1975) 13:271–273Crossref, Google Scholar
- Regularity and stability for convex multivalued functions. Math. Oper. Res. (1976) 1:130–143Link, Google Scholar
- Strongly regular generalized equations. Math. Oper. Res. (1980) 5:43–62Link, Google Scholar
- An implicit function theorem for a class of nonsmooth functions. Math. Oper. Res. (1991) 16:292–309Link, Google Scholar
- Multifunctions with closed convex graph. Czech. Math. J. (1975) 25:438–441Google Scholar
- Global error bounds for convex quadratic inequality systems. Optimization (1994) 31:1–12Crossref, Google Scholar
- A remark on a regularity assumption in mathematical programming. J. Optim. Theory Appl. (1978) 25:375–382Crossref, Google Scholar

