Class information for:
Level 1: HADAMARD MANIFOLD//RIEMANNIAN OPTIMIZATION//MONOTONE VECTOR FIELDS

Basic class information
Class id #P Avg. number of
references		 Database coverage
of references
23850 333 27.6 42%


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
446 3       MATHEMATICS, APPLIED//JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS//GLOBAL CONVERGENCE 26149
114 2             MATHEMATICS, APPLIED//JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS//GLOBAL CONVERGENCE 25008
23850 1                   HADAMARD MANIFOLD//RIEMANNIAN OPTIMIZATION//MONOTONE VECTOR FIELDS 333

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 HADAMARD MANIFOLD authKW 2215770 13% 58% 42
2 RIEMANNIAN OPTIMIZATION authKW 793521 5% 58% 15
3 MONOTONE VECTOR FIELDS authKW 652067 2% 89% 8
4 PSEUDOMONOTONE VECTOR FIELD authKW 458486 2% 100% 5
5 L AVERAGE LIPSCHITZ CONDITION authKW 366789 1% 100% 4
6 MONOTONE VECTOR FIELD authKW 366789 1% 100% 4
7 RIEMANNIAN MANIFOLDS authKW 282429 9% 11% 29
8 STIEFEL MANIFOLD authKW 276019 5% 18% 17
9 MAXIMAL MONOTONE VECTOR FIELD authKW 275092 1% 100% 3
10 OPTIMIZATION ON MANIFOLDS authKW 264295 2% 41% 7

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 Mathematics, Applied 7749 60% 0% 200
2 Operations Research & Management Science 2188 19% 0% 62
3 Mathematics 1987 34% 0% 113
4 Computer Science, Artificial Intelligence 352 9% 0% 30
5 Automation & Control Systems 153 5% 0% 16
6 Computer Science, Software Engineering 73 4% 0% 13
7 Computer Science, Theory & Methods 65 5% 0% 15
8 Engineering, Electrical & Electronic 44 9% 0% 31
9 Multidisciplinary Sciences 28 2% 0% 6
10 Mathematics, Interdisciplinary Applications 11 2% 0% 6

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 UNIV NACL CALLAO 122262 1% 67% 2
2 ANLISIS MATEMAT 91697 0% 100% 1
3 CHAIR NUMER ALGORITHMS HPC 91697 0% 100% 1
4 DIPARTIMENTO ELETTRON INTELLIGENA ARTIFICIALE T 91697 0% 100% 1
5 DIPARTIMENTO INGN INFORMAZI 91697 0% 100% 1
6 GEN EDUC KUMAMOTO ASO 91697 0% 100% 1
7 KINSLEY ENGN 91697 0% 100% 1
8 ORATOIRE MATH LAMA 91697 0% 100% 1
9 POLO DIDATT SCI TERNANO 91697 0% 100% 1
10 RUA PEDRO NUNES 91697 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 OPTIMIZATION 7345 4% 1% 12
2 JOURNAL OF GLOBAL OPTIMIZATION 5951 4% 1% 12
3 BALKAN JOURNAL OF GEOMETRY AND ITS APPLICATIONS 5884 1% 2% 4
4 JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 5848 5% 0% 18
5 IMA JOURNAL OF NUMERICAL ANALYSIS 4045 2% 1% 8
6 FOUNDATIONS OF COMPUTATIONAL MATHEMATICS 3725 1% 1% 4
7 OPTIMIZATION LETTERS 3448 2% 1% 6
8 JOURNAL OF MACHINE LEARNING RESEARCH 2855 2% 0% 7
9 JOURNAL OF COMPLEXITY 2848 2% 1% 5
10 OPTIMIZATION 2792 1% 1% 3

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 HADAMARD MANIFOLD 2215770 13% 58% 42 Search HADAMARD+MANIFOLD Search HADAMARD+MANIFOLD
2 RIEMANNIAN OPTIMIZATION 793521 5% 58% 15 Search RIEMANNIAN+OPTIMIZATION Search RIEMANNIAN+OPTIMIZATION
3 MONOTONE VECTOR FIELDS 652067 2% 89% 8 Search MONOTONE+VECTOR+FIELDS Search MONOTONE+VECTOR+FIELDS
4 PSEUDOMONOTONE VECTOR FIELD 458486 2% 100% 5 Search PSEUDOMONOTONE+VECTOR+FIELD Search PSEUDOMONOTONE+VECTOR+FIELD
5 L AVERAGE LIPSCHITZ CONDITION 366789 1% 100% 4 Search L+AVERAGE+LIPSCHITZ+CONDITION Search L+AVERAGE+LIPSCHITZ+CONDITION
6 MONOTONE VECTOR FIELD 366789 1% 100% 4 Search MONOTONE+VECTOR+FIELD Search MONOTONE+VECTOR+FIELD
7 RIEMANNIAN MANIFOLDS 282429 9% 11% 29 Search RIEMANNIAN+MANIFOLDS Search RIEMANNIAN+MANIFOLDS
8 STIEFEL MANIFOLD 276019 5% 18% 17 Search STIEFEL+MANIFOLD Search STIEFEL+MANIFOLD
9 MAXIMAL MONOTONE VECTOR FIELD 275092 1% 100% 3 Search MAXIMAL+MONOTONE+VECTOR+FIELD Search MAXIMAL+MONOTONE+VECTOR+FIELD
10 OPTIMIZATION ON MANIFOLDS 264295 2% 41% 7 Search OPTIMIZATION+ON+MANIFOLDS Search OPTIMIZATION+ON+MANIFOLDS

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 BENTO, GC , FERREIRA, OP , OLIVEIRA, PR , (2015) PROXIMAL POINT METHOD FOR A SPECIAL CLASS OF NONCONVEX FUNCTIONS ON HADAMARD MANIFOLDS.OPTIMIZATION. VOL. 64. ISSUE 2. P. 289 -319 35 88% 5
2 BENTO, GC , NETO, JXC , (2014) FINITE TERMINATION OF THE PROXIMAL POINT METHOD FOR CONVEX FUNCTIONS ON HADAMARD MANIFOLDS.OPTIMIZATION. VOL. 63. ISSUE 9. P. 1281 -1288 22 92% 5
3 BENTO, GC , FERREIRA, OP , OLIVEIRA, PR , (2012) UNCONSTRAINED STEEPEST DESCENT METHOD FOR MULTICRITERIA OPTIMIZATION ON RIEMANNIAN MANIFOLDS.JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS. VOL. 154. ISSUE 1. P. 88 -107 26 81% 7
4 BENTO, GC , NETO, JXC , (2013) A SUBGRADIENT METHOD FOR MULTIOBJECTIVE OPTIMIZATION ON RIEMANNIAN MANIFOLDS.JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS. VOL. 159. ISSUE 1. P. 125-137 27 75% 3
5 LI, C , YAO, JC , (2012) VARIATIONAL INEQUALITIES FOR SET-VALUED VECTOR FIELDS ON RIEMANNIAN MANIFOLDS: CONVEXITY OF THE SOLUTION SET AND THE PROXIMAL POINT ALGORITHM.SIAM JOURNAL ON CONTROL AND OPTIMIZATION. VOL. 50. ISSUE 4. P. 2486 -2514 22 88% 18
6 BATISTA, EEA , BENTO, GD , FERREIRA, OP , (2016) ENLARGEMENT OF MONOTONE VECTOR FIELDS AND AN INEXACT PROXIMAL POINT METHOD FOR VARIATIONAL INEQUALITIES IN HADAMARD MANIFOLDS.JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS. VOL. 170. ISSUE 3. P. 916 -931 21 84% 0
7 TANG, GJ , WANG, X , LIU, HW , (2015) A PROJECTION-TYPE METHOD FOR VARIATIONAL INEQUALITIES ON HADAMARD MANIFOLDS AND VERIFICATION OF SOLUTION EXISTENCE.OPTIMIZATION. VOL. 64. ISSUE 5. P. 1081 -1096 22 76% 3
8 WANG, JH , (2011) CONVERGENCE OF NEWTON'S METHOD FOR SECTIONS ON RIEMANNIAN MANIFOLDS.JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS. VOL. 148. ISSUE 1. P. 125 -145 20 91% 12
9 TANG, GJ , HUANG, NJ , (2013) AN INEXACT PROXIMAL POINT ALGORITHM FOR MAXIMAL MONOTONE VECTOR FIELDS ON HADAMARD MANIFOLDS.OPERATIONS RESEARCH LETTERS. VOL. 41. ISSUE 6. P. 586-591 22 79% 2
10 WANG, JH , LI, C , LOPEZ, G , YAO, JC , (2016) PROXIMAL POINT ALGORITHMS ON HADAMARD MANIFOLDS: LINEAR CONVERGENCE AND FINITE TERMINATION.SIAM JOURNAL ON OPTIMIZATION. VOL. 26. ISSUE 4. P. 2696 -2729 27 59% 0

Classes with closest relation at Level 1


Rank Class id link
1 22378 HEAVY BALL WITH FRICTION//KURDYKA LOJASIEWICZ INEQUALITY//DISSIPATIVE DYNAMICAL SYSTEM
2 26953 LIE QUADRATIC//RIEMANNIAN CUBIC//COMP SCI GRP COMP SCI
3 5803 ORDER OF CONVERGENCE//SEMILOCAL CONVERGENCE//NONLINEAR EQUATIONS
4 11762 DIRECTIONAL DATA//CIRCULAR DATA//VON MISES DISTRIBUTION
5 31537 MULTITIME MAXIMUM PRINCIPLE//MATH INFORMAT 1//BALKAN JOURNAL OF GEOMETRY AND ITS APPLICATIONS
6 6938 SYMMETRIC DUALITY//DUALITY THEOREMS//GENERALIZED CONVEXITY
7 8093 CANDECOMP//TENSOR DECOMPOSITION//NONNEGATIVE TENSOR
8 24116 MULTIVARIATE EIGENVALUE PROBLEM//CANONICAL CORRELATION ANALYSIS//MAXBET
9 36676 CONVERGENCE IN THE SENSE OF RESOLVENT//DISCRETE HYPERBOLIC SYSTEM//ELLIPTIC LIKE REGULARIZATION
10 24581 MINIMAL DISPLACEMENT//MORSE SARD THEOREM//C 1 SMOOTH FUNCTION

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