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Mathematics Subject Classification – MSC2010

Calculus of variations and optimal control; optimization [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] 80171

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

Instructional exposition (textbooks, tutorial papers, etc.) 679

Research exposition (monographs, survey articles) 939

Historical (must also be assigned at least one classification number from Section 01) 202

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

Proceedings, conferences, collections, etc. 918

Existence theories 36118

Free problems in one independent variable 344

Free problems in two or more independent variables 1014

Optimal control problems involving ordinary differential equations 3782

Optimal control problems involving partial differential equations 5214

Optimal control problems involving relations other than differential equations 235

Problems in abstract spaces [See also 90C48, 93C25] 2102

Optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) 1205

Minimax problems 2051

Variational methods including variational inequalities [See also 47J20] 10375

Methods involving semicontinuity and convergence; relaxation 4989

Fréchet and Gateaux differentiability [See also 46G05, 58C20] 775

Nonsmooth analysis [See also 46G05, 58C50, 90C56] 4981

Set-valued and variational analysis [See also 28B20, 47H04, 54C60, 58C06] 2491

Problems involving randomness [See also 93E20] 998

None of the above, but in this section 1062

Optimality conditions 18259

Free problems in one independent variable 565

Free problems in two or more independent variables 720

Problems involving ordinary differential equations 4960

Problems involving partial differential equations 3918

Problems involving relations other than differential equations 401

Problems in abstract spaces [See also 90C48, 93C25] 1907

Optimal solutions belonging to restricted classes 1044

Minimax problems 1114

Sensitivity, stability, well-posedness [See also 90C31] 2451

Problems involving randomness [See also 93E20] 1136

None of the above, but in this section 1369

Hamilton-Jacobi theories, including dynamic programming 5957

Dynamic programming method 2970

Viscosity solutions 1840

None of the above, but in this section 1616

Numerical methods [See also 90Cxx, 65Kxx] 14420

Methods based on necessary conditions 1161

Newton-type methods 2724

Methods of relaxation type 520

Discrete approximations 2369

Decomposition methods 1027

Methods involving duality 745

Other methods 2938

Methods of nonlinear programming type [See also 90C30, 65Kxx] 2920

None of the above, but in this section 1130

Miscellaneous topics 13116

Linear optimal control problems [See also 93C05] 464

Linear-quadratic problems 2316

Duality theory 2254

Periodic optimization 130

Impulsive optimal control problems 392

Problems with incomplete information [See also 93C41] 154

Optimal feedback synthesis [See also 93B52] 806

Inverse problems 749

Regularity of solutions 1546

Differential games 1642

Pursuit and evasion games 1004

Applications of optimal control and differential games [See also 90C90, 93C95] 2932

None of the above, but in this section 292

Manifolds [See also 58Exx] 7166

Minimal surfaces [See also 53A10, 58E12] 1642

Optimization of shapes other than minimal surfaces [See also 90C90] 2010

Sensitivity analysis 276

Geometric measure and integration theory, integral and normal currents [See also 28A75, 32C30, 58A25, 58C35] 1181

Variational problems in a geometric measure-theoretic setting 2567

None of the above, but in this section 343

Variational methods for eigenvalues of operators [See also 47A75] 1264

Variational methods for eigenvalues of operators [See also 47A75] (should also be assigned at least one other classification number in Section 49) 290

None of the above, but in this section 3

Variational principles of physics 3277

Variational principles of physics (should also be assigned at least one other classification number in section 49) 3266

None of the above, but in this section 10

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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