Coderivatives in parametric optimization

Mathematical Programming

Volumn 99, Issue 2, 2004, Pages 311-327

  Levy, Adam B ^a   Mordukhovich, Boris S ^b  

^a BOWDOIN COLLEGE   (United States)

^b WAYNE STATE UNIVERSITY   (United States)

Author keywords

Coderivatives; Generalized differentiation; Lipschitzian stability; Parametric optimization; Sensitivity; Variational analysis

Indexed keywords

CODERIVATIVES; GENERALIZED DIFFERENTIATION; LIPSCHITZIAN STABILITY; PARAMETERIC OPTIMIZATION; SENSITIVITY; VARIATIONAL ANALYSIS;

COSTS; DIFFERENTIATION (CALCULUS); FUNCTIONS; MATHEMATICAL MODELS; MATRIX ALGEBRA; PROBLEM SOLVING; VECTORS;

MATHEMATICAL PROGRAMMING;

EID: 21044440287     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-003-0452-0     Document Type: Article

References (19)

1. Aubin, J.-P.: Lipschitz behavior of solutions to convex minimization problems. Math. Oper. Res. 9, 87-111 (1984)
2. Bonnans, J.F., Shapiro, A.: Perturbation Analysis of Optimization Problems. Springer-Verlag, New York, 2000
3. Burke, J.V., Overton, M.L.: Variational analysis of non-Lipschitz spectral functions. Math. Program. 90, 317-351 (2001)
4. Dontchev, A.L., Rockafellar, R.T.: Characterizations of strong regularity for variational inequalities over polyhedral convex sets. SIAM J. Optim. 7, 1087-1105 (1996)
5. Henrion, R., Römisch, W.: Metric regularity and quantitative stability in stochastic programming with probabilistic constraints. Math. Prog. 84, 55-88 (1999)
6. Klatte, D., Kummer, B.: Nonsmooth Equations in Optimization. Kluwer Academic Publishers, Boston, 2002
7. Lewis, A.S.: Nonsmooth analysis of eigenvalues. Math. Prog. 84, 1-24 (1999)
8. Lucet, Y, Ye, J.J.: Sensitivity analysis of the value function for optimization problems with variational inequality constraints. SLAM J. Control Optim. 40, 699-723 (2001)
9. Luo, Z.-Q., Pang, J.-S., Ralph, D.: Mathematical Programs with Equilibrium Constraints. Cambridge. University Press, Cambridge, U.K., 1996
10. Levy, A.B., Poliquin, R., Rockafellar, R.T.: Stability of locally optimal solutions. SIAM J. Optim. 10, 580-604 (2000)
11. Levy, A.B., Rockafellar, R.T.: Variational conditions and the proto-differentiation of partial subgradient mappings. Nonlinear Analysis, Theory, Methods and Applications 26, 1951-1964 (1996)
12. Mordukhovich, B.S.: Complete characterization of openness, metric regularity, and Lipschitzian properties of multifunctions. Trans. Am. Math. Soc. 340, 1-35 (1993)
13. Mordukhovich, B.S.: Generalized differential calculus for nonsmooth and set-valued mappings. J. Math. Anal. Appl. 183, 250-288 (1994)
14. Mordukhovich, B.S.: Stability theory for parametric generalized equations and variational inequalities via nonsmooth analysis. Trans. Am. Math. Soc. 343, 609-658 (1994)
15. Mordukhovich, B.S., Outrata, J.V.: On second-order subdifferentials and their applications. SIAM J. Optim. 12, 139-169 (2001)
16. Outrata, J.V.: A generalized mathematical program with equilibrium constraints. SIAM J. Control Optim. 38, 1623-1638 (2000)
17. Poliquin, R., Rockafellar, R.T.: Tilt stability of a local minimum. SIAM J. Optim. 8, 287-299 (1998)
18. Robinson, S.M.: Generalized equations and their solutions, part I: basic theory. Math. Prog. Study 10, 128-141 (1979)
19. Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Springer-Verlag, Berlin, 1998