-
1
-
-
4143144565
-
First order approximations for differential inclusions
-
Z. Artstein, "First order approximations for differential inclusions," Set-Valued Anal, 2, 7-17 (1994).
-
(1994)
Set-Valued Anal
, vol.2
, pp. 7-17
-
-
Artstein, Z.1
-
2
-
-
0031140636
-
Investigation of the degeneracy phenomenon of the maximum principle for optimal control problems with state constraints
-
A. V. Arutyunov and S. M. Aseev, "Investigation of the degeneracy phenomenon of the maximum principle for optimal control problems with state constraints," SIAM J. Control Optim., 35, 930-952 (1997).
-
(1997)
SIAM J. Control Optim.
, vol.35
, pp. 930-952
-
-
Arutyunov, A.V.1
Aseev, S.M.2
-
3
-
-
0042093958
-
A method of smooth approximations in the theory of necessary optimality conditions for differential inclusions
-
S. M. Aseev, "A method of smooth approximations in the theory of necessary optimality conditions for differential inclusions," Izv. Ross. Akad. Nauk, Ser. Mat., 61, 3-26 (1997);
-
(1997)
Izv. Ross. Akad. Nauk, Ser. Mat.
, vol.61
, pp. 3-26
-
-
Aseev, S.M.1
-
4
-
-
21744454217
-
-
English transl.
-
English transl.: Izvestiya: Mathematics, 61, 235-258 (1997).
-
(1997)
Izvestiya: Mathematics
, vol.61
, pp. 235-258
-
-
-
6
-
-
0016114904
-
Application of abstract variational theory to hereditary systems - A survey
-
H. T. Banks and A. Manitius, "Application of abstract variational theory to hereditary systems - a survey," IEEE Trans. Automat. Control, 19, 524-533 (1974).
-
(1974)
IEEE Trans. Automat. Control
, vol.19
, pp. 524-533
-
-
Banks, H.T.1
Manitius, A.2
-
7
-
-
5244283395
-
Maximum principle for differential inclusions
-
V. I. Blagodatskikh, "Maximum principle for differential inclusions," Trudy Mat. Inst. Akad. Nauk SSSR, 166, 23-43 (1984);
-
(1984)
Trudy Mat. Inst. Akad. Nauk SSSR
, vol.166
, pp. 23-43
-
-
Blagodatskikh, V.I.1
-
8
-
-
52849086674
-
-
English transl.
-
English transl.: Proc. Steklov Inst. Math., 166 (1986).
-
(1986)
Proc. Steklov Inst. Math.
, vol.166
-
-
-
9
-
-
34347176514
-
Sur quelques methodes nouvelles dans le calculus des variations
-
N. N. Bogolyubov, "Sur quelques methodes nouvelles dans le calculus des variations," Ann. Math. Pure Appl., 7, 249-271 (1930).
-
(1930)
Ann. Math. Pure Appl.
, vol.7
, pp. 249-271
-
-
Bogolyubov, N.N.1
-
10
-
-
12744266723
-
Local section method in the theory of optimal processes
-
V. G. Boltyanskii, "Local section method in the theory of optimal processes," Differents. Uravn., 4, 2166-2183 (1968);
-
(1968)
Differents. Uravn.
, vol.4
, pp. 2166-2183
-
-
Boltyanskii, V.G.1
-
11
-
-
52849093924
-
-
English transl.
-
English transl.: in Differential Equations, 4 (1968).
-
(1968)
Differential Equations
, vol.4
-
-
-
12
-
-
0016973122
-
Optimal solutions to differential inclusions
-
F. H. Clarke, "Optimal solutions to differential inclusions," J. Optim. Theory Appl., 19, 460-478 (1976).
-
(1976)
J. Optim. Theory Appl.
, vol.19
, pp. 460-478
-
-
Clarke, F.H.1
-
13
-
-
49449116515
-
Necessary conditions for a general control problem
-
(D. Russel, Ed.), Academic Press, New York
-
F. H. Clarke, "Necessary conditions for a general control problem," in: Calculus of Variations and Control Theory (D. Russel, Ed.), Academic Press, New York (1976), pp. 257-278.
-
(1976)
Calculus of Variations and Control Theory
, pp. 257-278
-
-
Clarke, F.H.1
-
16
-
-
0001563557
-
Necessary conditions, controllability and the value function for differential-difference inclusons
-
F. H. Clarke and G. G. Watkins, "Necessary conditions, controllability and the value function for differential-difference inclusons," Nonlinear Anal., Theory, Meth., Appl., 10, 1155-1179 (1986).
-
(1986)
Nonlinear Anal., Theory, Meth., Appl.
, vol.10
, pp. 1155-1179
-
-
Clarke, F.H.1
Watkins, G.G.2
-
17
-
-
0030182214
-
Necessary conditions for functional differential inclusions
-
F. H. Clarke and P. R. Wolenski, "Necessary conditions for functional differential inclusions," Appl. Math. Optim., 34, 51-78 (1996).
-
(1996)
Appl. Math. Optim.
, vol.34
, pp. 51-78
-
-
Clarke, F.H.1
Wolenski, P.R.2
-
19
-
-
0026876816
-
Difference methods for differential inclusions: A survey
-
A. D. Dontchev and F. Lempio, "Difference methods for differential inclusions: a survey," SIAM Rev., 34, 263-294 (1992).
-
(1992)
SIAM Rev.
, vol.34
, pp. 263-294
-
-
Dontchev, A.D.1
Lempio, F.2
-
21
-
-
12744256969
-
Maximum principle for differential inclusions (necessity)
-
R. P. Fedorenko, "Maximum principle for differential inclusions (necessity)," Zh. Vychsl. Mat. Mat. Fiz., 11, 885-893 (1971);
-
(1971)
Zh. Vychsl. Mat. Mat. Fiz.
, vol.11
, pp. 885-893
-
-
Fedorenko, R.P.1
-
23
-
-
0023090297
-
The maximum principle for an optimal solution to differential inclusions with endpoint constraints
-
H. Frankowska, "The maximum principle for an optimal solution to differential inclusions with endpoint constraints," SIAM J. Control Optim., 25, 147-157 (1987).
-
(1987)
SIAM J. Control Optim.
, vol.25
, pp. 147-157
-
-
Frankowska, H.1
-
25
-
-
0002365232
-
The maximum principle in optimal control of systems governed by semilinear equations
-
(B.S. Mordukhovich and H. J. Sussmann, Eds.), Springer-Verlag, New York
-
B. Ginsburg and A. Ioffe, "The maximum principle in optimal control of systems governed by semilinear equations," in: Nonsmooth Analysis and Geometric Methods in Deterministic Optimal Control (B.S. Mordukhovich and H. J. Sussmann, Eds.), Springer-Verlag, New York (1996), pp. 153-202.
-
(1996)
Nonsmooth Analysis and Geometric Methods in Deterministic Optimal Control
, pp. 153-202
-
-
Ginsburg, B.1
Ioffe, A.2
-
26
-
-
84967717450
-
Approximate subdifferentials and applications, I: The finite dimensional theory
-
A. D. Ioffe, "Approximate subdifferentials and applications, I: the finite dimensional theory," Trans. Amer. Math. Soc., 281, 289-316 (1984).
-
(1984)
Trans. Amer. Math. Soc.
, vol.281
, pp. 289-316
-
-
Ioffe, A.D.1
-
27
-
-
21744456348
-
Euler-Lagrange and Hamiltonian formalisms in dynamic optimization
-
A. D. Ioffe, "Euler-Lagrange and Hamiltonian formalisms in dynamic optimization," Trans. Amer. Math. Soc., 349, 2871-2900 (1997).
-
(1997)
Trans. Amer. Math. Soc.
, vol.349
, pp. 2871-2900
-
-
Ioffe, A.D.1
-
28
-
-
0001812895
-
The Euler and Weierstrass conditions for nonsmooth variational problems
-
A. D. Ioffe and R. T. Rockafellar, "The Euler and Weierstrass conditions for nonsmooth variational problems," Calc. Var. Partial Diff. Eq., 4, 59-87 (1996).
-
(1996)
Calc. Var. Partial Diff. Eq.
, vol.4
, pp. 59-87
-
-
Ioffe, A.D.1
Rockafellar, R.T.2
-
30
-
-
0022012587
-
A maximum principle for generalized control systems
-
B. Kaśkosz and S. Lojasiewicz, Jr., "A maximum principle for generalized control systems," Nonlinear Anal. Theory, Meth. Appl., 9, 109-130 (1985).
-
(1985)
Nonlinear Anal. Theory, Meth. Appl.
, vol.9
, pp. 109-130
-
-
Kaśkosz, B.1
Lojasiewicz Jr., S.2
-
31
-
-
0026925456
-
Lagrange-type extremal trajectories in differential inclusions
-
B. Kaśkosz and S. Lojasiewicz, Jr., "Lagrange-type extremal trajectories in differential inclusions," Syst. Contr. Lett., 19, 241-247 (1992).
-
(1992)
Syst. Contr. Lett.
, vol.19
, pp. 241-247
-
-
Kaśkosz, B.1
Lojasiewicz Jr., S.2
-
32
-
-
0038992398
-
Maximum principle in the theory of optimal time-delayed processes
-
G. L. Kharatishvili, "Maximum principle in the theory of optimal time-delayed processes," Dokl. Akad. Nauk SSSR, 136, 39-42 (1961);
-
(1961)
Dokl. Akad. Nauk SSSR
, vol.136
, pp. 39-42
-
-
Kharatishvili, G.L.1
-
33
-
-
52849140078
-
-
English transl.
-
English transl.: Sov. Math. Dokl. (1961).
-
(1961)
Sov. Math. Dokl.
-
-
-
34
-
-
0000966105
-
Discrete approximations of differential inclusions
-
F. Lempio and V. Veliov, "Discrete approximations of differential inclusions," Bayrether Math. Schrif., 54, 149-232 (1998).
-
(1998)
Bayrether Math. Schrif.
, vol.54
, pp. 149-232
-
-
Lempio, F.1
Veliov, V.2
-
36
-
-
0028396661
-
Optimal control of unbounded differential inclusions
-
P. D. Loewen and R. T. Rockafellar, "Optimal control of unbounded differential inclusions," SIAM J. Control Optim., 32, 442-470 (1994).
-
(1994)
SIAM J. Control Optim.
, vol.32
, pp. 442-470
-
-
Loewen, P.D.1
Rockafellar, R.T.2
-
37
-
-
0030243608
-
New necessary conditions for the generalized problem of Bolza
-
P. D. Loewen and R. T. Rockafellar, "New necessary conditions for the generalized problem of Bolza," SIAM J. Control Optim., 34, 1496-1511 (1996).
-
(1996)
SIAM J. Control Optim.
, vol.34
, pp. 1496-1511
-
-
Loewen, P.D.1
Rockafellar, R.T.2
-
38
-
-
0031268176
-
Bolza problems with general time constraints
-
P. D. Loewen and R. T. Rockafellar, "Bolza problems with general time constraints," SIAM J. Control Optim., 35, 2050-2069 (1997).
-
(1997)
SIAM J. Control Optim.
, vol.35
, pp. 2050-2069
-
-
Loewen, P.D.1
Rockafellar, R.T.2
-
40
-
-
0033078383
-
Necessary optimality conditions for differential-difference inclusions
-
L. I. Minchenko, "Necessary optimality conditions for differential-difference inclusions," Nonlinear Anal., Theory Meth. Appl., 35, 307-322 (1999).
-
(1999)
Nonlinear Anal., Theory Meth. Appl.
, vol.35
, pp. 307-322
-
-
Minchenko, L.I.1
-
41
-
-
0008830845
-
Maximum principle in problems of time optimal control with nonsmooth constraints
-
B. S. Mordukhovich, "Maximum principle in problems of time optimal control with nonsmooth constraints," Prikl. Mat. Mekh., 40, 1014-1023 (1976);
-
(1976)
Prikl. Mat. Mekh.
, vol.40
, pp. 1014-1023
-
-
Mordukhovich, B.S.1
-
42
-
-
33646940121
-
-
English transl.
-
English transl.: J. Appl. Math. Mech., 40, 960-969 (1976).
-
(1976)
J. Appl. Math. Mech.
, vol.40
, pp. 960-969
-
-
-
43
-
-
0008821338
-
Metric approximations and necessary optimality conditions for general classes of nonsmooth extremal problems
-
B. S. Mordukhovich, "Metric approximations and necessary optimality conditions for general classes of nonsmooth extremal problems," Dokl. Akad. Nauk SSSR, 254, 1072-1976 (1980);
-
(1980)
Dokl. Akad. Nauk SSSR
, vol.254
, pp. 1072-1976
-
-
Mordukhovich, B.S.1
-
44
-
-
0001254208
-
-
English transl.
-
English transl.: Sov. Math. Dokl., 22, 526-530 (1980).
-
(1980)
Sov. Math. Dokl.
, vol.22
, pp. 526-530
-
-
-
45
-
-
5244350789
-
Optimization and approximation of differential inclusions
-
B. S. Mordukhovich, "Optimization and approximation of differential inclusions," Kibernetika, No. 6, 83-89 (1988);
-
(1988)
Kibernetika
, Issue.6
, pp. 83-89
-
-
Mordukhovich, B.S.1
-
46
-
-
4243164141
-
-
English transl.
-
English transl.: Cybernetics, 24, 781-787 (1988).
-
(1988)
Cybernetics
, vol.24
, pp. 781-787
-
-
-
47
-
-
52849095140
-
Approximate maximum principle for finite-difference control systems
-
B. S. Mordukhovich, "Approximate maximum principle for finite-difference control systems," Zh. Vychsl. Mat. Mat. Fiz., 28, 163-177 (1988);
-
(1988)
Zh. Vychsl. Mat. Mat. Fiz.
, vol.28
, pp. 163-177
-
-
Mordukhovich, B.S.1
-
48
-
-
38249032546
-
-
English transl.
-
English transl.: USSR Comput. Math. Math. Phys., 28, 106-114 (1988).
-
(1988)
USSR Comput. Math. Math. Phys.
, vol.28
, pp. 106-114
-
-
-
50
-
-
0001530657
-
On variational analysis of differential inclusions
-
(A. Ioffe et al., Eds.), Longman, Harlow
-
B. S. Mordukhovich, "On variational analysis of differential inclusions," in: Optimization and Nonlinear Analysis (A. Ioffe et al., Eds.), Longman, Harlow (1992), pp. 199-213.
-
(1992)
Optimization and Nonlinear Analysis
, pp. 199-213
-
-
Mordukhovich, B.S.1
-
51
-
-
84966250815
-
Complete characterization of openness, metric regularity, and Lipschitzian properties of multifunctions
-
B. S. Mordukhovich, "Complete characterization of openness, metric regularity, and Lipschitzian properties of multifunctions," Trans. Amer. Math. Soc., 340, 1-35 (1993).
-
(1993)
Trans. Amer. Math. Soc.
, vol.340
, pp. 1-35
-
-
Mordukhovich, B.S.1
-
52
-
-
0029307052
-
Discrete approximations and refined Euler-Lagrange conditions for nonconvex differential inclusions
-
B. S. Mordukhovich, "Discrete approximations and refined Euler-Lagrange conditions for nonconvex differential inclusions," SIAM J. Control Optim., 33, 882-915 (1995).
-
(1995)
SIAM J. Control Optim.
, vol.33
, pp. 882-915
-
-
Mordukhovich, B.S.1
-
53
-
-
0000551562
-
Generalized differential calculus for nonsmooth and set-valued mappings
-
B. S. Mordukhovich, "Generalized differential calculus for nonsmooth and set-valued mappings," J. Math. Anal. Appl., 183, 250-288 (1994).
-
(1994)
J. Math. Anal. Appl.
, vol.183
, pp. 250-288
-
-
Mordukhovich, B.S.1
-
54
-
-
84966206068
-
Stability theory for parametric generalized equations and variational inequalities via nonsmooth analysis
-
B. S. Mordukhovich, "Stability theory for parametric generalized equations and variational inequalities via nonsmooth analysis," Trans. Amer. Math. Soc., 343, 609-658 (1994).
-
(1994)
Trans. Amer. Math. Soc.
, vol.343
, pp. 609-658
-
-
Mordukhovich, B.S.1
-
55
-
-
0028738704
-
Necessary optimality and controllability conditions for nonsmooth control systems
-
Lake Buena Vista, FL
-
B.S. Mordukhovich, "Necessary optimality and controllability conditions for nonsmooth control systems," in: Proc 33rd Conf. Decision Control, Lake Buena Vista, FL (1994), pp. 3992-3997.
-
(1994)
Proc 33rd Conf. Decision Control
, pp. 3992-3997
-
-
Mordukhovich, B.S.1
-
56
-
-
52549095612
-
Optimization and finite-difference approximations of differential inclusions with free time
-
(B. S. Mordukhovich and H. J. Sussmann, Eds.), Springer-Verlag, New York
-
B. S. Mordukhovich, "Optimization and finite-difference approximations of differential inclusions with free time," in: Nonsmooth Analysis and Geometric Methods in Deterministic Optimal Control (B. S. Mordukhovich and H. J. Sussmann, Eds.), Springer-Verlag, New York (1996), pp. 153-202.
-
(1996)
Nonsmooth Analysis and Geometric Methods in Deterministic Optimal Control
, pp. 153-202
-
-
Mordukhovich, B.S.1
-
58
-
-
0007633319
-
Prox-regular functions in variational analysis
-
R. A. Poliquin and R. T. Rockafellar, "Prox-regular functions in variational analysis," Trans. Amer. Math. Soc., 348, 1805-1838 (1996).
-
(1996)
Trans. Amer. Math. Soc.
, vol.348
, pp. 1805-1838
-
-
Poliquin, R.A.1
Rockafellar, R.T.2
-
59
-
-
0001081608
-
An approach to differentiation of multifunctions and necessary optimality conditions for differential inclusions
-
E. S. Polovinkin and G. V. Smirnov, "An approach to differentiation of multifunctions and necessary optimality conditions for differential inclusions," Differents. Uravn., 22, 944-954 (1986);
-
(1986)
Differents. Uravn.
, vol.22
, pp. 944-954
-
-
Polovinkin, E.S.1
Smirnov, G.V.2
-
60
-
-
0010810191
-
-
English transl.
-
English transl.: Differential Equations, 22, 660-668 (1986).
-
(1986)
Differential Equations
, vol.22
, pp. 660-668
-
-
-
62
-
-
0003716451
-
-
Fizmatgiz, Moscow English transl.: Wiley-Interscience, New York
-
L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, The Mathematical Theory of Optimal Processes [in Russian], Fizmatgiz, Moscow (1961); English transl.: Wiley-Interscience, New York (1962).
-
(1961)
The Mathematical Theory of Optimal Processes [in Russian]
-
-
Pontryagin, L.S.1
Boltyanskii, V.G.2
Gamkrelidze, R.V.3
Mishchenko, E.F.4
-
63
-
-
0014863723
-
Conjugate convex functions in optimal control and the calculus of variations
-
R. T. Rockafellar, "Conjugate convex functions in optimal control and the calculus of variations," J. Math. Anal. Appl., 32, 174-222 (1970).
-
(1970)
J. Math. Anal. Appl.
, vol.32
, pp. 174-222
-
-
Rockafellar, R.T.1
-
64
-
-
84966203576
-
Existence and duality theorems for convex problems of Bolza
-
R. T. Rockafellar, "Existence and duality theorems for convex problems of Bolza," Trans. Amer. Math. Soc., 159, 1-40 (1971).
-
(1971)
Trans. Amer. Math. Soc.
, vol.159
, pp. 1-40
-
-
Rockafellar, R.T.1
-
65
-
-
84966234425
-
Maximal monotone relations and the second derivatives of nonsmooth functions
-
R. T. Rockafellar, "Maximal monotone relations and the second derivatives of nonsmooth functions," Ann. Inst. H. Poincaré. Anal. Non Linéair, 2, 167-184 (1985).
-
(1985)
Ann. Inst. H. Poincaré. Anal. Non Linéair
, vol.2
, pp. 167-184
-
-
Rockafellar, R.T.1
-
66
-
-
0008315455
-
Dualization of subgradient conditions for optimality
-
R. T. Rockafellar, "Dualization of subgradient conditions for optimality," Nonlinear Anal. Theory, Meth. Appl., 20, 627-646 (1993).
-
(1993)
Nonlinear Anal. Theory, Meth. Appl.
, vol.20
, pp. 627-646
-
-
Rockafellar, R.T.1
-
67
-
-
0030191882
-
Equivalent subgradient versions of Hamiltonian and Euler-Lagrange equations in variational analysis
-
R. T. Rockafellar, "Equivalent subgradient versions of Hamiltonian and Euler-Lagrange equations in variational analysis," SIAM J. Control Optim., 34, 1300-1314 (1996).
-
(1996)
SIAM J. Control Optim.
, vol.34
, pp. 1300-1314
-
-
Rockafellar, R.T.1
-
69
-
-
0025927009
-
Discrete approximations and optimal solutions of differential inclusions
-
G. V. Smirnov, "Discrete approximations and optimal solutions of differential inclusions," Kibernetika, No. 1, 76-79 (1991);
-
(1991)
Kibernetika
, Issue.1
, pp. 76-79
-
-
Smirnov, G.V.1
-
70
-
-
0043028111
-
-
English transl.
-
English transl.: Cybernetics, 27, 101-107 (1991).
-
(1991)
Cybernetics
, vol.27
, pp. 101-107
-
-
-
71
-
-
0002671270
-
Geometry and optimal control
-
(J. B. Baillieul and J. C. Willems, Eds.), Springer-Verlag, New York
-
H. J. Sussmann, "Geometry and optimal control," in: Mathematical Control Theory (J. B. Baillieul and J. C. Willems, Eds.), Springer-Verlag, New York (1998).
-
(1998)
Mathematical Control Theory
-
-
Sussmann, H.J.1
-
72
-
-
21844524480
-
Controllability and extremality in nonconvex differential inclusions
-
H. D. Tuan, "Controllability and extremality in nonconvex differential inclusions," J. Optim. Theory Appl., 85, 435-472 (1995).
-
(1995)
J. Optim. Theory Appl.
, vol.85
, pp. 435-472
-
-
Tuan, H.D.1
-
73
-
-
0030815471
-
The extended Euler-Lagrange condition for nonconvex variational problems
-
R. B. Vinter and H. Zheng, "The extended Euler-Lagrange condition for nonconvex variational problems," SIAM J. Control Optim., 35, 56-77 (1997).
-
(1997)
SIAM J. Control Optim.
, vol.35
, pp. 56-77
-
-
Vinter, R.B.1
Zheng, H.2
-
74
-
-
21944450668
-
Necessary conditions for optimal control problems with state constraints
-
R. B. Vinter and H. Zheng, "Necessary conditions for optimal control problems with state constraints," Trans. Amer. Math. Soc., 350, 1181-1204 (1998).
-
(1998)
Trans. Amer. Math. Soc.
, vol.350
, pp. 1181-1204
-
-
Vinter, R.B.1
Zheng, H.2
-
76
-
-
0018006591
-
Controllability of nondifferentiable hereditary processes
-
J. Warga, "Controllability of nondifferentiable hereditary processes," SIAM J. Control Optim., 16, 813-831 (1978).
-
(1978)
SIAM J. Control Optim.
, vol.16
, pp. 813-831
-
-
Warga, J.1
-
77
-
-
0020813628
-
Controllability, extremality, and abnormality in nonsmooth optimal control
-
J. Warga, "Controllability, extremality, and abnormality in nonsmooth optimal control," J. Optim. Theory Appl., 41, 239-260 (1983).
-
(1983)
J. Optim. Theory Appl.
, vol.41
, pp. 239-260
-
-
Warga, J.1
-
78
-
-
0029715234
-
Necessary optimality conditions for nonconvex differential inclusions with endpoint constraints
-
Q. J. Zhu, "Necessary optimality conditions for nonconvex differential inclusions with endpoint constraints," J. Diff. Equat., 124, 186-204 (1996).
-
(1996)
J. Diff. Equat.
, vol.124
, pp. 186-204
-
-
Zhu, Q.J.1
|