×

On a class of nonsmooth optimal control problems. (English) Zbl 0524.49021


MSC:

49M30 Other numerical methods in calculus of variations (MSC2010)
49M37 Numerical methods based on nonlinear programming
90C30 Nonlinear programming
90C90 Applications of mathematical programming
26A24 Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems
26B05 Continuity and differentiation questions
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Aubin JP (1978) Gradients généralisés de Clarke. Ann Sc Math Québec II:197-252 · Zbl 0411.49001
[2] Bertsekas DP, Mitter, SK (1973) Steepest descent for optimization problems with nondifferentiable cost functionals. In: Proceedings of the 5th Annual Princeton Conference on Information Sciences and Systems, pp 347-351
[3] Clarke FH (1976) A new approach to Lagrange multipliers. Math Oper Res 1:165-174 · Zbl 0404.90100
[4] Dem’yanov VF and Vasil’ev LV (1981) Nondifferentiable optimization. (in Russian) Nauka, Moscow
[5] Ioffe AD (1979) Necessary and sufficient conditions for a local minimum. 1: A reduction theorem and first order conditions. SIAM J Control Optim 17:245-250 · Zbl 0417.49027
[6] Ioffe AD (1979a) Necessary and sufficient conditions for a local minimum. 2: Conditions of Levitin-Miljutin-Osmolovskii type. SIAM J Control Optim 17:251-265 · Zbl 0417.49028
[7] Lemaréchal C, Strodiot JJ, and Bihain A (1980) On a bundle algorithm for nonsmooth optimization. NPS4, Madison · Zbl 0533.49023
[8] Mifflin R (1977) An algorithm for constrained optimization with semismooth functions. Math Operations Research 2:191-207 · Zbl 0395.90069
[9] Mifflin R (1977a) Semismooth and semiconvex functions in constrained optimization. SIAM J Control and Optimization 15:959-972 · Zbl 0376.90081
[10] Outrata, JV (1979) On the differentiability in dual optimal control problems. Math Operationsforsch Statist, Ser Optim 10:529-542 · Zbl 0435.49036
[11] Outrata JV (To appear) Minimization of nonsmooth nonregular functions: Application to discrete-time optimal control problems.
[12] Pschenichnyi BN (1971) Necessary conditions for an extremum. Marcel Dekker Inc, New York
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.