First order conditions for nonsmooth discretized constrained optimal control problems

SIAM Journal on Control and Optimization

Volumn 42, Issue 6, 2004, Pages 2004-2015

  Chen, Xiaojun ^a  

^a HIROSAKI UNIVERSITY   (Japan)

Author keywords

Discretization; First order condition; Nonsmooth; Optimal control

Indexed keywords

APPROXIMATION THEORY; FINITE ELEMENT METHOD; MAGNETOHYDRODYNAMICS; PROBLEM SOLVING; THEOREM PROVING;

DISCRETIZATION; FIRST ORDER CONDITION; NONSMOOTH CONSTRAINTS;

OPTIMAL CONTROL SYSTEMS;

EID: 10244235403     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012902414160     Document Type: Article

References (12)

1. A. K. AZIZ, A. B. STEPHENS, AND M. SURI, Numerical methods for reaction-diffusion problems with non-differentiable kinetics, Numer. Math., 51 (1988), pp. 1-11.
2. M. BERGOUNIOUX, K. ITO, AND K. KUNISCH, Primal-dual strategy for constrained optimal control problems, SIAM J. Control Optim., 37 (1999), pp. 1176-1194.
3. E. CASAS AND M. MATEOS, Second order optimality conditions for semilinear elliptic control problems with finitely many state constraints, SIAM J. Control Optim., 40 (2002), pp. 1431-1454.
4. X. CHEN, N. MATSUNAGA, AND T. YAMAMOTO, Smoothing Newton methods for nonsmooth Dirichlet problems, in Reformulation - Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods, M. Fukushima and L. Qi, eds., Kluwer Academic Publishers, Dordrecht, The Netherlands, 1999, pp. 65-79.
5. X. CHEN, Z. NASHED, AND L. QI, Smoothing methods and semismooth methods for nondifferentiable operator equations, SIAM J. Numer. Anal., 38 (2000), pp. 1200-1216.
6. F. H. CLARKE, Optimization and Nonsmooth Analysis, John Wiley & Sons, New York, 1983.
7. R. FLETCHER, Practical Methods of Optimization, 2nd ed., John Wiley & Sons, New York, 1987.
8. J. B. HIRIART-URRUTY AND C. LEMARÉCHAL, Convex Analysis and Minimization Algorithms, Springer-Verlag, Berlin, 1993.
9. F. KIKUCHI, K. NAKAZATO, AND T. USHIJIMA, Finite element approximation of a nonlinear eigenvalue problem related to MHD equilibria, Japan J. Appl. Math., 1 (1984), pp. 369-403.
10. J. M. ORTEGA AND W. C. RHEINBOLDT, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, 1970.
11. J. RAPPAZ, Approximation of a nondifferentiable nonlinear problem related to MHD equilibria, Numer. Math., 45 (1984), pp. 117-133.
12. M. ULBRICH, Nonmonotone trust-region methods for bound-constrained semismooth equations with applications to nonlinear mixed complementarity problems, SIAM J. Optim., 11 (2001), pp. 889-917.