Mathematics Subject Classification 1991

49-XX Calculus of variations and optimal control; optimization, See also {34H05, 65Kxx, 90Cxx, 93-XX} ( 0 Dok.)

• 49-00 General reference works (handbooks, dictionaries, bibliographies, etc.) ( 0 Dok.)
• 49-01 Instructional exposition (textbooks, tutorial papers, etc.) ( 0 Dok.)
• 49-02 Research exposition (monographs, survey articles) ( 0 Dok.)
• 49-03 Historical (must be assigned at least one classification number from Section 01) ( 0 Dok.)
• 49-04 Explicit machine computation and programs (not the theory of computation or programming) ( 0 Dok.)
• 49-06 Proceedings, conferences, collections, etc. ( 0 Dok.)
• 49Jxx Existence theory for optimal solutions ( 0 Dok. )
• 49J05 Free problems in one independent variable ( 0 Dok.)
• 49J10 Free problems in two or more independent variables ( 0 Dok.)
• 49J15 Optimal control problems involving ordinary differential equations ( 0 Dok.)
• 49J20 Optimal control problems involving partial differential equations ( 0 Dok.)
• 49J22 Optimal control problems involving integral equations ( 0 Dok.)
• 49J24 Optimal control problems involving differential inclusions ( 0 Dok.)
• 49J25 Optimal control problems involving equations with retarded arguments, See also {34K35} ( 0 Dok.)
• 49J27 Problems in abstract spaces [see 90C48] ( 0 Dok.)
• 49J30 Optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) ( 0 Dok.)
• 49J35 Minimax problems ( 0 Dok.)
• 49J40 Variational methods including variational inequalities ( 0 Dok.)
• 49J45 Problems involving semicontinuity and convergence ( 0 Dok.)
• 49J50 Frechet and Gateaux differentiability, See also {46G05, 58C20} ( 0 Dok.)
• 49J52 Nonsmooth analysis (other weak concepts of optimality), See also {58C20, 90C48} ( 0 Dok.)
• 49J55 Problems involving randomness, See also {93E20} ( 0 Dok.)
• 49J99 None of the above but in this section ( 0 Dok.)
• 49Kxx Necessary conditions and sufficient conditions for optimality ( 0 Dok. )
• 49K05 Free problems in one independent variable ( 0 Dok.)
• 49K10 Free problems in two or more independent variables ( 0 Dok.)
• 49K15 Problems involving ordinary differential equations ( 0 Dok.)
• 49K20 Problems involving partial differential equations ( 0 Dok.)
• 49K22 Problems involving integral equations ( 0 Dok.)
• 49K24 Problems involving differential inclusions ( 0 Dok.)
• 49K25 Problems involving equations with retarded arguments, See also {34K35} ( 0 Dok.)
• 49K27 Problems in abstract spaces [See 90C48, 93C25] ( 0 Dok.)
• 49K30 Optimal solutions belonging to restricted classes ( 0 Dok.)
• 49K35 Minimax problems ( 0 Dok.)
• 49K40 Sensitivity of optimal solutions in the presence of perturbations ( 0 Dok.)
• 49K45 Problems involving randomness, See also {93E20} ( 0 Dok.)
• 49K99 None of the above but in this section ( 0 Dok.)
• 49Lxx Caratheodory, Hamilton-Jacobi theories, including dynamic programming ( 0 Dok. )
• 49L05 Free problems and problems involving ordinary differential equations ( 0 Dok.)
• 49L10 Free problems and problems involving partial differential equations ( 0 Dok.)
• 49L15 Problems in abstract spaces or problems involving functional relations other than differential equations ( 0 Dok.)
• 49L20 Dynamic programming method ( 0 Dok.)
• 49L25 Viscosity solutions ( 0 Dok.)
• 49L99 None of the above but in this section ( 0 Dok.)
• 49Mxx Methods of successive approximations, {For discrete problems, See 90Cxx; See also 65Kxx} ( 0 Dok. )
• 49M05 Methods based on necessary conditions ( 0 Dok.)
• 49M07 Gradient methods ( 0 Dok.)
• 49M10 Methods of steepest descent type ( 0 Dok.)
• 49M15 Methods of Newton-Raphson, Galerkin and Ritz types ( 0 Dok.)
• 49M20 Methods of relaxation type ( 0 Dok.)
• 49M25 Finite difference methods ( 0 Dok.)
• 49M27 Decomposition methods ( 0 Dok.)
• 49M29 Multiplier methods ( 0 Dok.)
• 49M30 Other methods, not based on necessary conditions (penalty function, etc.) ( 0 Dok.)
• 49M35 Methods of linear programming type, See also {90C05} ( 0 Dok.)
• 49M37 Nonlinear programming, See also {90C30} ( 0 Dok.)
• 49M39 Semi-infinite programming, See also {90C34} ( 0 Dok.)
• 49M40 Methods of quadratic programming type, See also {90C20} ( 0 Dok.)
• 49M45 Methods of convex programming type, See also {90C25} ( 0 Dok.)
• 49M49 Geometric programming, See also {90C28} ( 0 Dok.)
• 49M99 None of the above but in this section ( 0 Dok.)
• 49Nxx Miscellaneous topics ( 0 Dok. )
• 49N05 Linear optimal control problems, See also {93C05} ( 0 Dok.)
• 49N10 Linear-quadratic problems ( 0 Dok.)
• 49N15 Duality theory ( 0 Dok.)
• 49N20 Periodic optimization ( 0 Dok.)
• 49N25 Impulsive optimal control problems, See also {93C57} ( 0 Dok.)
• 49N30 Problems with incomplete information, See also {93C41} ( 0 Dok.)
• 49N35 Closed-loop controls ( 0 Dok.)
• 49N40 Open-loop controls ( 0 Dok.)
• 49N45 Inverse problems in calculus of variations ( 0 Dok.)
• 49N50 Inverse problems in optimal control theory ( 0 Dok.)
• 49N55 Noneconomic applications of optimal control theory and differential games, See also {90D25} ( 0 Dok.)
• 49N60 Regularity of solutions in the calculus of variations ( 0 Dok.)
• 49N65 Applications of measurable selections to control theory, See also {28B20, 26E25} ( 0 Dok.)
• 49N99 None of the above but in this section ( 0 Dok.)
• 49Qxx Manifolds, See also {58Fxx} ( 0 Dok. )
• 49Q05 Minimal surfaces, See also {53A10, 58E12} ( 0 Dok.)
• 49Q10 Optimization of the shape other than minimal surfaces, See also {73K40, 90C90} ( 0 Dok.)
• 49Q12 Sensitivity analysis ( 0 Dok.)
• 49Q15 Geometric measure and integration theory, integral and normal currents, See also {28A75, 32C30, 58A25, 58C35} ( 0 Dok.)
• 49Q20 Variational problems in a geometric measure-theoretic setting ( 0 Dok.)
• 49Q25 Surface area ( 0 Dok.)
• 49Q99 None of the above but in this section ( 0 Dok.)
• 49Rxx Variational methods, {For eigenvalues of operators, See 47A75} ( 0 Dok. )
• 49R05 Variational approach to eigenvalues ( 0 Dok.)
• 49R10 Rayleigh-Ritz methods ( 0 Dok.)
• 49R15 Weinstein and Aronszajn methods, intermediate problems ( 0 Dok.)
• 49R20 Linear operators in Hilbert spaces ( 0 Dok.)
• 49R99 None of the above but in this section ( 0 Dok.)
• 49S05 Variational principles of physics ( 0 Dok.)