Variational analysis of evolution inclusions

SIAM Journal on Optimization

Volumn 18, Issue 3, 2007, Pages 752-777

  Mordukhovich, Boris ^a  

^a WAYNE STATE UNIVERSITY   (United States)

Author keywords

Banach and Asplund spaces; Discrete finite difference approximations; Dynamic optimization and optimal control; Evolution and differential inclusions; Generalized differentiation; Nondifferentiable programming; Variational analysis

Indexed keywords

BANACH AND ASPLUND SPACES; DIFFERENTIAL INCLUSIONS; DISCRETE APPROXIMATIONS; DISCRETE/FINITE-DIFFERENCE APPROXIMATIONS; DYNAMIC OPTIMIZATION AND OPTIMAL CONTROL; EVOLUTION AND DIFFERENTIAL INCLUSIONS; EVOLUTION INCLUSIONS; GENERALIZED DIFFERENTIATION; LIPSCHITZIAN; NON-SMOOTH FUNCTIONS; NONCONVEX; NONDIFFERENTIABLE PROGRAMMING; OPTIMIZ ATION PROBLEMS; VARIATIONAL ANALYSIS;

BANACH SPACES; DIFFERENTIAL EQUATIONS; OPTIMAL CONTROL SYSTEMS; TOPOLOGY;

DIFFERENTIATION (CALCULUS);

EID: 49449088538     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/060652889     Document Type: Conference Paper

References (20)

1. J. M. BORWEIN AND Q. J. ZHU, Techniques of Variational Analysis, CMS Books Math., Springer, New York, 2005.
2. F. H. CLARKE, Necessary conditions for a general control problem, in Calculus of Variations and Control Theory, D. L. Russel, ed., Academic Press, New York, 1976, pp. 257-278.
3. F. H. CLARKE, Necessary conditions in dynamic optimization, Mem. Amer. Math. Soc., 173 (2005), no. 816.
4. J. DIESTEL AND J. J. UHL, JR., Vector Measures, AMS, Providence, RI, 1977.
5. F. S. DE BLASI, G. PIANIGIANI, AND A. A. TOLSTONOGOV, A Bogolyubov-type theorem with a nonconvex constraint in Banach spaces, SIAM J. Control Optim., 43 (2004), pp. 466-476.
6. K. DEIMLING, Multivalued Differential Equations, De Gruyter, Berlin, 1992.
7. H. O. FATTORINI, Infinite Dimensional Optimization and Control Theory, Cambridge University Press, Cambridge, UK, 1999.
8. A. D. IOFFE, Euler-Lagrange and Hamiltonian formalisms in dynamic optimization, Trans. Amer. Math. Soc., 349 (1997), pp. 2871-2900.
9. A. D. IOFFE AND R. T. ROCKAFELLAR, The Euler and Weierstrass conditions for nonsmooth variational problems, Calc. Var. Partial Differential Equations, 4 (1996), pp. 59-87.
10. X. LI AND J. YONG, Optimal Control Theory for Infinite-Dimensional Systems, Birkhäuser, Boston, 1995.
11. B. S. MORDUKHOVICH, Maximum principle in problems of time optimal control with nonsmooth constraints, J. Appl. Math. Mech., 40 (1976), pp. 960-969.
12. B. S. MORDUKHOVICH, Discrete approximations and refined Euler-Lagrange conditions for nonconvex differential inclusions, SIAM J. Control Optim., 33 (1995), pp. 882-915.
13. B. S. MORDUKHOVICH, Variational Analysis and Generalized Differentiation, I: Basic Theory, Grundlehren Math. Wiss. 330, Springer, Berlin, 2006.
14. B. S. MORDUKHOVICH, Variational Analysis and Generalized Differentiation, II: Applications, Grundlehren Math. Wiss. 331, Springer, Berlin, 2006.
15. B. S. MORDUKHOVICH AND D. WANG, Optimal control of semilinear evolution inclusions via discrete approximations, Control Cybernet., 34 (2005), pp. 849-870.
16. R. T. ROCKAFELLAR AND R. J.-B. WETS, Variational Analysis, Grundlehren Math. Wiss. 317, Springer, Berlin, 1998.
17. G. V. SMIRNOV, Introduction to the Theory of Differential Inclusions, AMS, Providence, RI, 2001.
18. A. A. TOLSTONOGOV, Differential Inclusions in a Banach Space, Kluwer, Dordrecht, The Netherlands, 2000.
19. R. B. VINTER, Optimal Control, Birkhäuser, Boston, 2000.
20. R. B. VINTER AND P. D. WOODFORD, On the occurrence of intermediate local minimizers that are not strong local minimizers, Systems Control Lett., 31 (1997), pp. 235-242.