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Mathematics Subject Classification – MSC2010

Calculus of variations and optimal control; optimization [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] 81502

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

Instructional exposition (textbooks, tutorial papers, etc.) 685

Research exposition (monographs, survey articles) 947

Historical (must also be assigned at least one classification number from Section 01) 207

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

Proceedings, conferences, collections, etc. 931

Existence theories 36606

Free problems in one independent variable 345

Free problems in two or more independent variables 1017

Optimal control problems involving ordinary differential equations 3829

Optimal control problems involving partial differential equations 5302

Optimal control problems involving relations other than differential equations 246

Problems in abstract spaces [See also 90C48, 93C25] 2120

Optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) 1222

Minimax problems 2073

Variational methods including variational inequalities [See also 47J20] 10528

Methods involving semicontinuity and convergence; relaxation 5043

Fréchet and Gateaux differentiability [See also 46G05, 58C20] 785

Nonsmooth analysis [See also 46G05, 58C50, 90C56] 5051

Set-valued and variational analysis [See also 28B20, 47H04, 54C60, 58C06] 2565

Problems involving randomness [See also 93E20] 1007

None of the above, but in this section 1065

Optimality conditions 18549

Free problems in one independent variable 574

Free problems in two or more independent variables 729

Problems involving ordinary differential equations 5021

Problems involving partial differential equations 4015

Problems involving relations other than differential equations 419

Problems in abstract spaces [See also 90C48, 93C25] 1920

Optimal solutions belonging to restricted classes 1059

Minimax problems 1124

Sensitivity, stability, well-posedness [See also 90C31] 2490

Problems involving randomness [See also 93E20] 1163

None of the above, but in this section 1379

Hamilton-Jacobi theories, including dynamic programming 6042

Dynamic programming method 3027

Viscosity solutions 1870

None of the above, but in this section 1617

Numerical methods [See also 90Cxx, 65Kxx] 14661

Methods based on necessary conditions 1172

Newton-type methods 2780

Methods of relaxation type 533

Discrete approximations 2434

Decomposition methods 1042

Methods involving duality 756

Other methods 2986

Methods of nonlinear programming type [See also 90C30, 65Kxx] 2960

None of the above, but in this section 1137

Miscellaneous topics 13462

Linear optimal control problems [See also 93C05] 473

Linear-quadratic problems 2370

Duality theory 2279

Periodic optimization 130

Impulsive optimal control problems 406

Problems with incomplete information [See also 93C41] 163

Optimal feedback synthesis [See also 93B52] 821

Inverse problems 783

Regularity of solutions 1593

Differential games 1666

Pursuit and evasion games 1016

Applications of optimal control and differential games [See also 90C90, 93C95] 3054

None of the above, but in this section 298

Manifolds [See also 58Exx] 7295

Minimal surfaces [See also 53A10, 58E12] 1659

Optimization of shapes other than minimal surfaces [See also 90C90] 2063

Sensitivity analysis 294

Geometric measure and integration theory, integral and normal currents [See also 28A75, 32C30, 58A25, 58C35] 1194

Variational problems in a geometric measure-theoretic setting 2608

None of the above, but in this section 345

Variational methods for eigenvalues of operators [See also 47A75] 1276

Variational methods for eigenvalues of operators [See also 47A75] (should also be assigned at least one other classification number in Section 49) 301

None of the above, but in this section 3

Variational principles of physics 3312

Variational principles of physics (should also be assigned at least one other classification number in section 49) 3301

None of the above, but in this section 12

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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