A sharp Lagrange multiplier rule for nonsmooth mathematical programming problems involving equality constraints

SIAM Journal on Optimization

Volumn 10, Issue 4, 2000, Pages 1136-1148

  Wang, X ^a   Jeyakumar, V ^a  

^a UNIVERSITY OF NEW SOUTH WALES   (Australia)

Author keywords

Equality constraints; Generalized Jacobians; Minimax problems; Nonsmooth analysis; Sharp Lagrange mutipliers

Indexed keywords

EID: 0034345422     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1052623499354540     Document Type: Article

References (22)

1. F. H. CLARKE, Optimization and Nonsmooth Analysis, 2nd ed., Classics in Applied Mathematics 5, SIAM, Philadelphia, 1990.
2. V. F. DEMYANOV AND V. JEYAKUMAR, Hunting for a smaller convex subdifferential, J. Global Optim., 10 (1997), pp. 305-326.
3. V. F. DEMYANOV AND A. M. RUBINOV, Constructive Nonsmooth Analysis, Verlag Peter Lang, 1995.
4. J.-B. HIRIART-URRUTY, On necessary optimality conditions in nondifferentiable programming, Math. Programming, 14 (1978), pp. 73-86.
5. J.-B. HIRIART-URRUTY, Tangent cones, generalized gradients and mathematical programming in Banach spaces, Math. Oper. Res., 4 (1979), pp. 79-97.
6. J.-B. HIRIART-URRUTY, Refinements of necessary optimality conditions in nondifferentiable programming, Appl. Math. Optim., 5 (1979), pp. 63-82.
7. A. D. IOFFE, Nonsmooth analysis: Differential calculus of non-differentiate mappings, Trans. Amer. Math. Soc., 266 (1981), pp. 1-56.
8. A. D. IOFFE, Necessary conditions in nonsmooth optimization, Math. Oper. Res., 9 (1984), pp. 159-189.
9. A. D. IOFFE, Approximate subdifferentials and applications 1, The finite dimensional theory, Trans. Amer. Math. Soc., 281 (1984), pp. 289-316.
10. A. D. IOFFE, A Lagrange multiplier rule with small convex-valued subdifferentials for nonsmooth problems of mathematical programming involving equality and nonfunctional constraints, Math. Programming, 58 (1993), pp. 137-145.
11. V. JEYAKUMAR, On optimality conditions in nonsmooth inequality constrained minimization, Numer. Funct. Anal. Optim., 9 (1987), pp. 535-546.
12. V. JEYAKUMAR, Simple Characterizations of Superlinear Convergence for Semismooth Equations via Approximate Jacobians, Applied Mathematical Report AMR98/28, University of New South Wales, Sydney, Australia, 1998.
13. 1-Optimization, SIAM J. Control Optim., 36 (1998), pp. 1815-1832.
14. V. JEYAKUMAR AND D. T. LUC, Nonsmooth calculus, minimality and monotonicity of convexificators, J. Optim. Theory Appl., 101 (1999), pp. 599-621.
15. V. JEYAKUMAR, D. T. LUC, AND S. SCHAIBLE, Characterizations of generalized monotone nonsmooth continuous maps using approximate Jacobians, J. Convex Anal., 5 (1998), pp. 119-132.
16. 1-data, J. Austral. Math. Soc. Ser. B, 40 (1999), pp. 403-420.
17. P. MICHEL AND J. P. PENOT, A generalized derivative for calm and stable functions, Differential Integral Equations, 5 (1992), pp. 433-454.
18. B. S. MORDUKHOVICH, Generalized differential calculus for nonsmooth and set-valued mappings, J. Math. Anal. Appl., 183 (1994), pp. 250-288.
19. B. S. MORDUKHOVICH AND Y. SHAO, On nonconvex subdifferential calculus in Banach spaces, J. Convex Anal., 2 (1995), pp. 211-228.
20. M. STUDNIARSKI AND V. JEYAKUMAR, A generalized mean-value theorem and optimality conditions in composite nonsmooth minimization, Nonlinear Anal., 24 (1995), pp. 883-894.
21. J. S. TREIMAN, Shrinking generalized gradients, Nonlinear Anal., 12 (1988), pp. 1429-1449.
22. J. S. TREIMAN, The linear nonconvex generalized gradient and Lagrange multipliers, SIAM J. Optim., 5 (1995), pp. 670-680.