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Mathematics Subject Classification – MSC2020

History of calculus of variations and optimal control [Consider also classification numbers pertaining to Section 01-XX] 216

49-04

Software, source code, etc. for problems pertaining to calculus of variations and optimal control 116

49-06

Proceedings, conferences, collections, etc. pertaining to calculus of variations and optimal control 963

49-11

Research data for problems pertaining to calculus of variations and optimal control 0

49Jxx

Existence theories in calculus of variations and optimal control 38339

49J05

Existence theories for free problems in one independent variable 355

49J10

Existence theories for free problems in two or more independent variables 1043

49J15

Existence theories for optimal control problems involving ordinary differential equations 3959

49J20

Existence theories for optimal control problems involving partial differential equations 5657

49J21

Existence theories for optimal control problems involving relations other than differential equations 288

49J27

Existence theories for problems in abstract spaces [See also 90C48, 93C25] 2174

49J30

Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) 1300

49J35

Existence of solutions for minimax problems 2142

49J40

Variational inequalities [See also 47J20] 10990

49J45

Methods involving semicontinuity and convergence; relaxation 5274

49J50

Fréchet and Gateaux differentiability in optimization [See also 46G05, 58C20] 830

49J52

Nonsmooth analysis [See also 46G05, 58C50, 90C56] 5298

49J53

Set-valued and variational analysis [See also 28B20, 47H04, 54C60, 58C06] 2838

49J55

Existence of optimal solutions to problems involving randomness [See also 93E20] 1036

49J99

None of the above, but in this section 1071

49Kxx

Optimality conditions 19516

49K05

Optimality conditions for free problems in one independent variable 601

49K10

Optimality conditions for free problems in two or more independent variables 755

49K15

Optimality conditions for problems involving ordinary differential equations 5233

49K20

Optimality conditions for problems involving partial differential equations 4303

49K21

Optimality conditions for problems involving relations other than differential equations 507

49K27

Optimality conditions for problems in abstract spaces [See also 90C48, 93C25] 1960

49K30

Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) 1130

49K35

Optimality conditions for minimax problems 1174

49K40

Sensitivity, stability, well-posedness [See also 90C31] 2626

49K45

Optimality conditions for problems involving randomness [See also 93E20] 1237

49K99

None of the above, but in this section 1418

49Lxx

Hamilton-Jacobi theories [See also 70H20, 35F21] 6275

49L12

Hamilton-Jacobi equations in optimal control and differential games 0

49L20

Dynamic programming in optimal control and differential games 3143

49L25

Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games 2001

49L99

None of the above, but in this section 1628

49Mxx

Numerical methods in optimal control [See also 65Kxx, 90-08, 90Cxx] 15451

49M05

Numerical methods based on necessary conditions 1266

49M15

Newton-type methods [See also 90C53] 2916

49M20

Numerical methods of relaxation type 593

49M25

Discrete approximations in optimal control 2685

49M27

Decomposition methods 1093

49M29

Numerical methods involving duality 805

49M37

Numerical methods based on nonlinear programming [See also 65Kxx, 90C30] 3092

49M41

PDE constrained optimization (numerical aspects) 2

49M99

None of the above, but in this section 1150

49Nxx

Miscellaneous topics in calculus of variations and optimal control 14542

49N05

Linear optimal control problems [See also 93C05] 503

49N10

Linear-quadratic optimal control problems 2544

49N15

Duality theory (optimization) [See also 90C46] 2372

49N20

Periodic optimal control problems 136

49N25

Impulsive optimal control problems 444

49N30

Problems with incomplete information (optimization) [See also 93C41] 170

49N35

Optimal feedback synthesis [See also 93B52] 895

49N45

Inverse problems in optimal control 877

49N60

Regularity of solutions in optimal control 1715

49N70

Differential games and control [See also 91A23] 1756

49N75

Pursuit and evasion games [See also 91A24] 1036

49N80

Mean field games and control [See also 91A16] 15

49N90

Applications of optimal control and differential games [See also 90C90, 91A80, 93C95] 3438

49N99

None of the above, but in this section 315

49Qxx

Manifolds and measure-geometric topics [See also 58Exx] 7872

49Q05

Minimal surfaces and optimization [See also 53A10, 58E12] 1752

49Q10

Optimization of shapes other than minimal surfaces [See also 90C90] 2248

49Q12

Sensitivity analysis for optimization problems on manifolds 364

49Q15

Geometric measure and integration theory, integral and normal currents in optimization [See also 28A75, 32C30, 58A25, 58C35] 1266

49Q20

Variational problems in a geometric measure-theoretic setting 2799

49Q22

Optimal transportation [See also 90B06] 7

49Q99

None of the above, but in this section 359

49Rxx

Variational methods for eigenvalues of operators (should also be assigned at least one other classification number in Section 49-XX) [See also 47A75] 1324

49R05

Variational methods for eigenvalues of operators (should also be assigned at least one other classification number in Section 49-XX) [See also 47A75] 349

49R99

None of the above, but in this section 3

49Sxx

Variational principles of physics (should also be assigned at least one other classification number in Section 49-XX) 3438

49S05

Variational principles of physics (should also be assigned at least one other classification number in Section 49-XX) 3425

49S99

None of the above, but in this section 12

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Mathematics Subject Classification – MSC2020

Overview