Theory and Algorithm of Nonsmooth Matrix Optimization View Homepage


Ontology type: schema:MonetaryGrant     


Grant Info

YEARS

2014-2016

FUNDING AMOUNT

220000 CNY

ABSTRACT

In this project, we will study a class of optimization problems involving the matrix unknown variables and the nonsmooth objective function. Such kind of matrix optimization problems (MOPs) has recently been found to have many important applications in different fields such as electronic engineering, communication technology, financial management, applied statistics, machine Learning, data mining and control theory. However, for MOPs, there is not much work done on both theoretical part and the algorithm design. Therefore, in the theoretical part, we will focus on the perturbation analysis of the MOP. The systematical theoretical study of the MOP is not only of crucial important itself but also the foundation of the convergence and stability study of algorithms. For algorithms, by applying the obtained theoretical results, we will try to design a framework of solving the general MOP. Also, for some special MOPs, we will design the semismooth Newton based argument Lagrange method to solve the large scale problems. Overall, after this project, we will try to build up the theoretical foundation of MOPs and design the efficient algorithms for to solve the problems. More... »

URL

http://npd.nsfc.gov.cn/projectDetail.action?pid=11301515

Related SciGraph Publications

  • 2018-03. Spectral operators of matrices in MATHEMATICAL PROGRAMMING
  • 2017-07. Convex optimization learning of faithful Euclidean distance representations in nonlinear dimensionality reduction in MATHEMATICAL PROGRAMMING
  • 2017-06. Variational Analysis of the Ky Fan k-norm in SET-VALUED AND VARIATIONAL ANALYSIS
  • JSON-LD is the canonical representation for SciGraph data.

    TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

    [
      {
        "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
        "about": [
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/2201", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/2201", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "type": "DefinedTerm"
          }
        ], 
        "amount": {
          "currency": "CNY", 
          "type": "MonetaryAmount", 
          "value": "220000"
        }, 
        "description": "In this project, we will study a class of optimization problems involving the matrix unknown variables and the nonsmooth objective function. Such kind of matrix optimization problems (MOPs) has recently been found to have many important applications in different fields such as electronic engineering, communication technology, financial management, applied statistics, machine Learning, data mining and control theory. However, for MOPs, there is not much work done on both theoretical part and the algorithm design. Therefore, in the theoretical part, we will focus on the perturbation analysis of the MOP. The systematical theoretical study of the MOP is not only of crucial important itself but also the foundation of the convergence and stability study of algorithms. For algorithms, by applying the obtained theoretical results, we will try to design a framework of solving the general MOP. Also, for some special MOPs, we will design the semismooth Newton based argument Lagrange method to solve the large scale problems. Overall, after this project, we will try to build up the theoretical foundation of MOPs and design the efficient algorithms for to solve the problems.", 
        "endDate": "2016-12-31T00:00:00Z", 
        "funder": {
          "id": "https://www.grid.ac/institutes/grid.419696.5", 
          "type": "Organization"
        }, 
        "id": "sg:grant.7184049", 
        "identifier": [
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "7184049"
            ]
          }, 
          {
            "name": "nsfc_id", 
            "type": "PropertyValue", 
            "value": [
              "11301515"
            ]
          }
        ], 
        "inLanguage": [
          "zh"
        ], 
        "keywords": [
          "matrix", 
          "convergence", 
          "control theory", 
          "problem", 
          "foundation", 
          "data mining", 
          "general MOP", 
          "MOP", 
          "framework", 
          "nonsmooth objective function", 
          "class", 
          "communication technologies", 
          "optimization problem", 
          "algorithm", 
          "large scale problems", 
          "unknown variables", 
          "Nonsmooth Matrix Optimization", 
          "algorithm design", 
          "theoretical part", 
          "statistics", 
          "different fields", 
          "theoretical results", 
          "matrix optimization problems", 
          "semismooth Newton", 
          "stability studies", 
          "theory", 
          "financial management", 
          "algorithms", 
          "theoretical foundation", 
          "machine learning", 
          "such kind", 
          "argument Lagrange method", 
          "systematical theoretical study", 
          "electronic engineering", 
          "efficient algorithms", 
          "many important applications", 
          "special MOPs", 
          "project", 
          "perturbation analysis", 
          "much work"
        ], 
        "name": "Theory and Algorithm of Nonsmooth Matrix Optimization", 
        "recipient": [
          {
            "id": "https://www.grid.ac/institutes/grid.458463.8", 
            "type": "Organization"
          }, 
          {
            "affiliation": {
              "id": "https://www.grid.ac/institutes/grid.458463.8", 
              "name": "Academy of Mathematics and Systems Science, Chinese Academy of Sciences", 
              "type": "Organization"
            }, 
            "familyName": "Ding", 
            "givenName": "Chao", 
            "id": "sg:person.016072273611.19", 
            "type": "Person"
          }, 
          {
            "member": "sg:person.016072273611.19", 
            "roleName": "PI", 
            "type": "Role"
          }
        ], 
        "sameAs": [
          "https://app.dimensions.ai/details/grant/grant.7184049"
        ], 
        "sdDataset": "grants", 
        "sdDatePublished": "2019-03-07T12:45", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com.uberresearch.data.processor/core_data/20181219_192338/projects/base/nsfc_projects_7.xml.gz", 
        "startDate": "2014-01-01T00:00:00Z", 
        "type": "MonetaryGrant", 
        "url": "http://npd.nsfc.gov.cn/projectDetail.action?pid=11301515"
      }
    ]
     

    Download the RDF metadata as:  json-ld nt turtle xml License info

    HOW TO GET THIS DATA PROGRAMMATICALLY:

    JSON-LD is a popular format for linked data which is fully compatible with JSON.

    curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/grant.7184049'

    N-Triples is a line-based linked data format ideal for batch operations.

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/grant.7184049'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/grant.7184049'

    RDF/XML is a standard XML format for linked data.

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/grant.7184049'


     

    This table displays all metadata directly associated to this object as RDF triples.

    84 TRIPLES      19 PREDICATES      62 URIs      54 LITERALS      5 BLANK NODES

    Subject Predicate Object
    1 sg:grant.7184049 schema:about anzsrc-for:2201
    2 schema:amount Nd6a57a01b35044d6aa49052a84c6d89c
    3 schema:description In this project, we will study a class of optimization problems involving the matrix unknown variables and the nonsmooth objective function. Such kind of matrix optimization problems (MOPs) has recently been found to have many important applications in different fields such as electronic engineering, communication technology, financial management, applied statistics, machine Learning, data mining and control theory. However, for MOPs, there is not much work done on both theoretical part and the algorithm design. Therefore, in the theoretical part, we will focus on the perturbation analysis of the MOP. The systematical theoretical study of the MOP is not only of crucial important itself but also the foundation of the convergence and stability study of algorithms. For algorithms, by applying the obtained theoretical results, we will try to design a framework of solving the general MOP. Also, for some special MOPs, we will design the semismooth Newton based argument Lagrange method to solve the large scale problems. Overall, after this project, we will try to build up the theoretical foundation of MOPs and design the efficient algorithms for to solve the problems.
    4 schema:endDate 2016-12-31T00:00:00Z
    5 schema:funder https://www.grid.ac/institutes/grid.419696.5
    6 schema:identifier N6558a5210d6b46bb950d954ba161f25b
    7 Nac27a74e6c0c4ebaae0be8bd0c45e5d9
    8 schema:inLanguage zh
    9 schema:keywords MOP
    10 Nonsmooth Matrix Optimization
    11 algorithm
    12 algorithm design
    13 algorithms
    14 argument Lagrange method
    15 class
    16 communication technologies
    17 control theory
    18 convergence
    19 data mining
    20 different fields
    21 efficient algorithms
    22 electronic engineering
    23 financial management
    24 foundation
    25 framework
    26 general MOP
    27 large scale problems
    28 machine learning
    29 many important applications
    30 matrix
    31 matrix optimization problems
    32 much work
    33 nonsmooth objective function
    34 optimization problem
    35 perturbation analysis
    36 problem
    37 project
    38 semismooth Newton
    39 special MOPs
    40 stability studies
    41 statistics
    42 such kind
    43 systematical theoretical study
    44 theoretical foundation
    45 theoretical part
    46 theoretical results
    47 theory
    48 unknown variables
    49 schema:name Theory and Algorithm of Nonsmooth Matrix Optimization
    50 schema:recipient N9ce1c7049ae64813b4e13bece18ffb03
    51 sg:person.016072273611.19
    52 https://www.grid.ac/institutes/grid.458463.8
    53 schema:sameAs https://app.dimensions.ai/details/grant/grant.7184049
    54 schema:sdDatePublished 2019-03-07T12:45
    55 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    56 schema:sdPublisher N2519d28f25fb41e3959d393e29eafff6
    57 schema:startDate 2014-01-01T00:00:00Z
    58 schema:url http://npd.nsfc.gov.cn/projectDetail.action?pid=11301515
    59 sgo:license sg:explorer/license/
    60 sgo:sdDataset grants
    61 rdf:type schema:MonetaryGrant
    62 N2519d28f25fb41e3959d393e29eafff6 schema:name Springer Nature - SN SciGraph project
    63 rdf:type schema:Organization
    64 N6558a5210d6b46bb950d954ba161f25b schema:name dimensions_id
    65 schema:value 7184049
    66 rdf:type schema:PropertyValue
    67 N9ce1c7049ae64813b4e13bece18ffb03 schema:member sg:person.016072273611.19
    68 schema:roleName PI
    69 rdf:type schema:Role
    70 Nac27a74e6c0c4ebaae0be8bd0c45e5d9 schema:name nsfc_id
    71 schema:value 11301515
    72 rdf:type schema:PropertyValue
    73 Nd6a57a01b35044d6aa49052a84c6d89c schema:currency CNY
    74 schema:value 220000
    75 rdf:type schema:MonetaryAmount
    76 anzsrc-for:2201 schema:inDefinedTermSet anzsrc-for:
    77 rdf:type schema:DefinedTerm
    78 sg:person.016072273611.19 schema:affiliation https://www.grid.ac/institutes/grid.458463.8
    79 schema:familyName Ding
    80 schema:givenName Chao
    81 rdf:type schema:Person
    82 https://www.grid.ac/institutes/grid.419696.5 schema:Organization
    83 https://www.grid.ac/institutes/grid.458463.8 schema:name Academy of Mathematics and Systems Science, Chinese Academy of Sciences
    84 rdf:type schema:Organization
     




    Preview window. Press ESC to close (or click here)


    ...