Class information for:
Level 1: NORMAL NECESSARY CONDITIONS//DISCRETE APPROXIMATIONS//MIXED CONSTRAINTS

Basic class information
Class id #P Avg. number of
references		 Database coverage
of references
19397 507 19.1 30%


Bar chart of Publication_year

Last years might be incomplete

Hierarchy of classes
The table includes all classes above and classes immediately below the current class.


Cluster id Level Cluster label #P
15 4 MATHEMATICS//MATHEMATICS, APPLIED//MATH 719832
244 3       MATHEMATICS, APPLIED//MATHEMATICS//BLOW UP 46988
2434 2             HAMILTON JACOBI EQUATION//MEAN FIELD GAMES//VISCOSITY SOLUTIONS 4110
19397 1                   NORMAL NECESSARY CONDITIONS//DISCRETE APPROXIMATIONS//MIXED CONSTRAINTS 507

Terms with highest relevance score


rank Term termType Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 NORMAL NECESSARY CONDITIONS authKW 361359 1% 100% 6
2 DISCRETE APPROXIMATIONS authKW 358537 3% 37% 16
3 MIXED CONSTRAINTS authKW 333549 2% 46% 12
4 EULER LAGRANGE CONDITION authKW 309734 1% 86% 6
5 PROPER RELAXATION PROCEDURES authKW 309734 1% 86% 6
6 LOCALLY ADJOINT MAPPINGS authKW 301132 1% 100% 5
7 NECESSARY CONDITIONS authKW 268879 5% 19% 24
8 NONSMOOTH ANALYSIS authKW 255585 8% 10% 41
9 STATE CONSTRAINTS authKW 242913 8% 10% 39
10 DISCRETE AND DIFFERENTIAL INCLUSIONS authKW 240906 1% 100% 4

Web of Science journal categories


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 Automation & Control Systems 11465 31% 0% 158
2 Mathematics, Applied 10749 57% 0% 291
3 Mathematics 2913 33% 0% 169
4 Operations Research & Management Science 1960 14% 0% 73
5 Computer Science, Cybernetics 699 4% 0% 18
6 COMPUTER APPLICATIONS & CYBERNETICS 361 1% 0% 4
7 Instruments & Instrumentation 247 8% 0% 39
8 Multidisciplinary Sciences 95 3% 0% 13
9 Computer Science, Theory & Methods 11 2% 0% 10
10 Mathematics, Interdisciplinary Applications 8 1% 0% 7

Address terms


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 SYSTEC ISR 180679 1% 100% 3
2 DIFFERENTIAL EQUAT FUNCT ANAL 96358 1% 40% 4
3 INRA INRIA MODEMIC TEAM 80301 0% 67% 2
4 CNRSIMJ PRGUMR 7586SORBONNE PARIS CITE 60226 0% 100% 1
5 COMMUN INFORMAT INNOVAT CIRIC 60226 0% 100% 1
6 DEEC ISR 60226 0% 100% 1
7 ENGN IND MECH 60226 0% 100% 1
8 INRIA RECH SACLAY ILE FRANCE 60226 0% 100% 1
9 INS SISTEMAS ROBOT 60226 0% 100% 1
10 MODEMIC 2 60226 0% 100% 1

Journals


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 SIAM JOURNAL ON CONTROL AND OPTIMIZATION 57575 12% 2% 59
2 AUTOMATION AND REMOTE CONTROL 23159 7% 1% 38
3 SET-VALUED AND VARIATIONAL ANALYSIS 15100 2% 3% 8
4 DIFFERENTIAL EQUATIONS 12627 6% 1% 28
5 JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 12151 6% 1% 32
6 JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS 11380 2% 2% 9
7 CONTROL AND CYBERNETICS 7653 2% 1% 9
8 PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS 6959 2% 1% 11
9 NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 4768 6% 0% 31
10 SET-VALUED ANALYSIS 4609 1% 2% 5

Author Key Words


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class		 LCSH search Wikipedia search
1 NORMAL NECESSARY CONDITIONS 361359 1% 100% 6 Search NORMAL+NECESSARY+CONDITIONS Search NORMAL+NECESSARY+CONDITIONS
2 DISCRETE APPROXIMATIONS 358537 3% 37% 16 Search DISCRETE+APPROXIMATIONS Search DISCRETE+APPROXIMATIONS
3 MIXED CONSTRAINTS 333549 2% 46% 12 Search MIXED+CONSTRAINTS Search MIXED+CONSTRAINTS
4 EULER LAGRANGE CONDITION 309734 1% 86% 6 Search EULER+LAGRANGE+CONDITION Search EULER+LAGRANGE+CONDITION
5 PROPER RELAXATION PROCEDURES 309734 1% 86% 6 Search PROPER+RELAXATION+PROCEDURES Search PROPER+RELAXATION+PROCEDURES
6 LOCALLY ADJOINT MAPPINGS 301132 1% 100% 5 Search LOCALLY+ADJOINT+MAPPINGS Search LOCALLY+ADJOINT+MAPPINGS
7 NECESSARY CONDITIONS 268879 5% 19% 24 Search NECESSARY+CONDITIONS Search NECESSARY+CONDITIONS
8 NONSMOOTH ANALYSIS 255585 8% 10% 41 Search NONSMOOTH+ANALYSIS Search NONSMOOTH+ANALYSIS
9 STATE CONSTRAINTS 242913 8% 10% 39 Search STATE+CONSTRAINTS Search STATE+CONSTRAINTS
10 DISCRETE AND DIFFERENTIAL INCLUSIONS 240906 1% 100% 4 Search DISCRETE+AND+DIFFERENTIAL+INCLUSIONS Search DISCRETE+AND+DIFFERENTIAL+INCLUSIONS

Core articles
The table includes core articles in the class. The following variables is taken into account for the relevance score of an article in a cluster c:
(1) Number of references referring to publications in the class.
(2) Share of total number of active references referring to publications in the class.
(3) Age of the article. New articles get higher score than old articles.
(4) Citation rate, normalized to year.


Rank Reference # ref.
in cl.		 Shr. of ref. in
cl.		 Citations
1 KARAMZIN, DY , DE OLIVEIRA, VA , PEREIRA, FL , SILVA, GN , (2015) ON THE PROPERNESS OF AN IMPULSIVE CONTROL EXTENSION OF DYNAMIC OPTIMIZATION PROBLEMS.ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS. VOL. 21. ISSUE 3. P. 857 -875 20 100% 0
2 ARUTYUNOV, AV , KARAMZIN, DY , PEREIRA, FL , (2015) STATE CONSTRAINTS IN IMPULSIVE CONTROL PROBLEMS: GAMKRELIDZE-LIKE CONDITIONS OF OPTIMALITY.JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS. VOL. 166. ISSUE 2. P. 440 -459 17 100% 1
3 KARAMZIN, DY , DE OLIVEIRA, VA , PEREIRA, FL , SILVA, GN , (2014) ON SOME EXTENSION OF OPTIMAL CONTROL THEORY.EUROPEAN JOURNAL OF CONTROL. VOL. 20. ISSUE 6. P. 284 -291 14 100% 1
4 BISWAS, MHA , DE PINHO, MD , (2015) A MAXIMUM PRINCIPLE FOR OPTIMAL CONTROL PROBLEMS WITH STATE AND MIXED CONSTRAINTS.ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS. VOL. 21. ISSUE 4. P. 939 -957 15 88% 1
5 KARAMZIN, D , DE OLIVEIRA, V , PEREIRA, F , SILVA, G , (2016) MINIMAX OPTIMAL CONTROL PROBLEM WITH STATE CONSTRAINTS.EUROPEAN JOURNAL OF CONTROL. VOL. 32. ISSUE . P. 24 -31 14 93% 0
6 LOPES, SO , FONTES, FACC , DE PINHO, MD , (2013) AN INTEGRAL-TYPE CONSTRAINT QUALIFICATION TO GUARANTEE NONDEGENERACY OF THE MAXIMUM PRINCIPLE FOR OPTIMAL CONTROL PROBLEMS WITH STATE CONSTRAINTS.SYSTEMS & CONTROL LETTERS. VOL. 62. ISSUE 8. P. 686-692 17 77% 5
7 MAHMUDOV, EN , (2015) MATHEMATICAL PROGRAMMING AND POLYHEDRAL OPTIMIZATION OF SECOND ORDER DISCRETE AND DIFFERENTIAL INCLUSIONS.PACIFIC JOURNAL OF OPTIMIZATION. VOL. 11. ISSUE 3. P. 511 -525 14 88% 0
8 FONTES, FACC , FRANKOWSKA, H , (2015) NORMALITY AND NONDEGENERACY FOR OPTIMAL CONTROL PROBLEMS WITH STATE CONSTRAINTS.JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS. VOL. 166. ISSUE 1. P. 115 -136 15 79% 0
9 JOURANI, A , (2012) CONTROLLABILITY AND STRONG CONTROLLABILITY OF DIFFERENTIAL INCLUSIONS.NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS. VOL. 75. ISSUE 3. P. 1374 -1384 14 88% 0
10 SAMSONYUK, ON , (2015) INVARIANT SETS FOR THE NONLINEAR IMPULSIVE CONTROL SYSTEMS.AUTOMATION AND REMOTE CONTROL. VOL. 76. ISSUE 3. P. 405 -418 11 100% 0

Classes with closest relation at Level 1


Rank Class id link
1 31974 P REGULARITY//ABNORMAL POINT//P FACTOR OPERATOR
2 26505 SET OF TRAJECTORIES//ATTRACTION SET//INTEGRAL CONSTRAINT
3 5572 HAMILTON JACOBI EQUATION//VISCOSITY SOLUTIONS//VISCOSITY SOLUTION
4 20476 OCCUPATIONAL MEASURES//CONTROL SETS//DIFFERENTIAL INCLUSIONS
5 3266 METRIC REGULARITY//CODERIVATIVE//SUBDIFFERENTIAL
6 36216 MELENTIEV ENERGY SYST//MELENTEV POWER ENGN SYST//POWER ENGN SYST
7 14605 SWEEPING PROCESS//DIFFERENTIAL INCLUSIONS//CONTINUOUS SELECTOR
8 26009 REGULAR SYNTHESIS//SINGULAR CHARACTERISTICS//FOLD AND SIMPLE CUSP SINGULARITIES
9 37534 METHOD OF ORIENTING CURVES//DENSE WINDING//COINCIDENCE AND NON COINCIDENCE SET
10 37155 LOCATION OF THE ZEROS//ANNULAR BOUND//LOCATION OF ZEROS OF POLYNOMIALS

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