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Mathematics Subject Classification – MSC2010

Calculus of variations and optimal control; optimization [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] 80753

General reference works (handbooks, dictionaries, bibliographies, etc.) 38

Instructional exposition (textbooks, tutorial papers, etc.) 682

Research exposition (monographs, survey articles) 944

Historical (must also be assigned at least one classification number from Section 01) 205

Explicit machine computation and programs (not the theory of computation or programming) 111

Proceedings, conferences, collections, etc. 924

Existence theories 36348

Free problems in one independent variable 344

Free problems in two or more independent variables 1016

Optimal control problems involving ordinary differential equations 3805

Optimal control problems involving partial differential equations 5256

Optimal control problems involving relations other than differential equations 237

Problems in abstract spaces [See also 90C48, 93C25] 2111

Optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) 1217

Minimax problems 2062

Variational methods including variational inequalities [See also 47J20] 10452

Methods involving semicontinuity and convergence; relaxation 5020

Fréchet and Gateaux differentiability [See also 46G05, 58C20] 780

Nonsmooth analysis [See also 46G05, 58C50, 90C56] 5010

Set-valued and variational analysis [See also 28B20, 47H04, 54C60, 58C06] 2528

Problems involving randomness [See also 93E20] 1002

None of the above, but in this section 1063

Optimality conditions 18385

Free problems in one independent variable 572

Free problems in two or more independent variables 724

Problems involving ordinary differential equations 4978

Problems involving partial differential equations 3963

Problems involving relations other than differential equations 409

Problems in abstract spaces [See also 90C48, 93C25] 1911

Optimal solutions belonging to restricted classes 1054

Minimax problems 1119

Sensitivity, stability, well-posedness [See also 90C31] 2469

Problems involving randomness [See also 93E20] 1142

None of the above, but in this section 1376

Hamilton-Jacobi theories, including dynamic programming 5990

Dynamic programming method 2993

Viscosity solutions 1849

None of the above, but in this section 1617

Numerical methods [See also 90Cxx, 65Kxx] 14519

Methods based on necessary conditions 1169

Newton-type methods 2749

Methods of relaxation type 527

Discrete approximations 2388

Decomposition methods 1035

Methods involving duality 750

Other methods 2951

Methods of nonlinear programming type [See also 90C30, 65Kxx] 2940

None of the above, but in this section 1133

Miscellaneous topics 13237

Linear optimal control problems [See also 93C05] 467

Linear-quadratic problems 2335

Duality theory 2267

Periodic optimization 131

Impulsive optimal control problems 397

Problems with incomplete information [See also 93C41] 155

Optimal feedback synthesis [See also 93B52] 814

Inverse problems 759

Regularity of solutions 1563

Differential games 1654

Pursuit and evasion games 1009

Applications of optimal control and differential games [See also 90C90, 93C95] 2967

None of the above, but in this section 294

Manifolds [See also 58Exx] 7225

Minimal surfaces [See also 53A10, 58E12] 1652

Optimization of shapes other than minimal surfaces [See also 90C90] 2038

Sensitivity analysis 284

Geometric measure and integration theory, integral and normal currents [See also 28A75, 32C30, 58A25, 58C35] 1190

Variational problems in a geometric measure-theoretic setting 2581

None of the above, but in this section 343

Variational methods for eigenvalues of operators [See also 47A75] 1267

Variational methods for eigenvalues of operators [See also 47A75] (should also be assigned at least one other classification number in Section 49) 294

None of the above, but in this section 3

Variational principles of physics 3292

Variational principles of physics (should also be assigned at least one other classification number in section 49) 3282

None of the above, but in this section 11

Overview

00

General mathematics

01

History and biography

03

Mathematical logic and foundations

05

Combinatorics

06

Order, lattices, ordered algebraic structures

08

General algebraic systems

11

Number theory

12

Field theory and polynomials

13

Commutative algebra

14

Algebraic geometry

15

Linear and multilinear algebra; matrix theory

16

Associative rings and algebras

17

Nonassociative rings and algebras

18

Category theory, homological algebra

19

$K$-theory

20

Group theory and generalizations

22

Topological groups, Lie groups

26

Real functions

28

Measure and integration

30

Functions of a complex variable

31

Potential theory

32

Several complex variables and analytic spaces

33

Special functions

34

Ordinary differential equations

35

Partial differential equations

37

Dynamical systems and ergodic theory

39

Difference and functional equations

40

Sequences, series, summability

41

Approximation and expansions

42

Harmonic analysis on Euclidean spaces

43

Abstract harmonic analysis

44

Integral transforms, operational calculus

45

Integral equations

46

Functional analysis

47

Operator theory

49

Calculus of variations and optimal control; optimization

51

Geometry

52

Convex and discrete geometry

53

Differential geometry

54

General topology

55

Algebraic topology

57

Manifolds and cell complexes

58

Global analysis, analysis on manifolds

60

Probability theory and stochastic processes

62

Statistics

65

Numerical analysis

68

Computer science

70

Mechanics of particles and systems

74

Mechanics of deformable solids

76

Fluid mechanics

78

Optics, electromagnetic theory

80

Classical thermodynamics, heat transfer

81

Quantum Theory

82

Statistical mechanics, structure of matter

83

Relativity and gravitational theory

85

Astronomy and astrophysics

86

Geophysics

90

Operations research, mathematical programming

91

Game theory, economics, social and behavioral sciences

92

Biology and other natural sciences

93

Systems theory; control

94

Information and communication, circuits

97

Mathematics education

W3C

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