The DTC (difference of tangentially convex functions) programming: optimality conditions

We focus on optimality conditions for an important class of nonconvex and nonsmooth optimization problems, where the objective and constraint functions are presented as a difference of two tangentially convex functions. The main contribution of this paper is to clarify several kinds of stationary so...

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Vydané v:TOP Ročník 30; číslo 2; s. 270 - 295
Hlavní autori: Mashkoorzadeh, F., Movahedian, N., Nobakhtian, S.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2022
Springer Nature B.V
Predmet:
Business and Management
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Finance
Industrial and Production Engineering
Insurance
Management
Operations Research/Decision Theory
Optimization
Original Paper
Statistics for Business
Optimality conditions
Nonconvex optimization
90C30
49J52
Nonsmooth optimization
90C26
Tangential subdifferential
Difference of tangentially convex functions
ISSN:1134-5764, 1863-8279
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Abstract We focus on optimality conditions for an important class of nonconvex and nonsmooth optimization problems, where the objective and constraint functions are presented as a difference of two tangentially convex functions. The main contribution of this paper is to clarify several kinds of stationary solutions and their relations, and establish local optimality conditions with a nonconvex feasible set. Finally, several examples are given to illustrate the effectiveness of the obtained results.
AbstractList We focus on optimality conditions for an important class of nonconvex and nonsmooth optimization problems, where the objective and constraint functions are presented as a difference of two tangentially convex functions. The main contribution of this paper is to clarify several kinds of stationary solutions and their relations, and establish local optimality conditions with a nonconvex feasible set. Finally, several examples are given to illustrate the effectiveness of the obtained results.
Author Nobakhtian, S.
Movahedian, N.
Mashkoorzadeh, F.
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Cites_doi 10.1007/s10107-018-1235-y
10.1287/moor.2016.0795
10.1007/978-3-662-02598-7
10.1137/0324061
10.1023/A:1008233531797
10.1007/s11590-014-0822-y
10.1007/0-387-28395-1
10.1023/A:1021765131316
10.1007/s10898-014-0171-5
10.1007/s10898-019-00809-7
10.1080/10556788.2017.1371717
10.1006/jfan.1994.1086
10.1137/1.9781611974997
10.1007/s11590-009-0153-6
10.1080/02331938608843204
10.1007/s11590-011-0410-3
10.1137/16M1084754
10.1007/978-1-4471-4820-3
10.1007/s101070050050
10.1016/j.patcog.2015.11.011
10.1002/0471787779
10.1137/0315061
10.1007/s10589-012-9486-7
10.1007/s10479-004-5022-1
10.1287/opre.46.4.548
10.1007/s10107-017-1208-6
10.1080/01630563.2019.1640249
10.1137/16M1115733
10.1007/s10479-006-0145-1
10.1006/jmaa.1999.6496
10.1007/978-3-642-45610-7_3
10.1111/j.1540-6261.1952.tb01525.x
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Issue 2
Keywords Optimality conditions
Nonconvex optimization
90C30
49J52
Nonsmooth optimization
90C26
Tangential subdifferential
Difference of tangentially convex functions
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References Dutta, Lalitha (CR14) 2013; 7
Penot (CR35) 1998; 12
Joki, Bagirov, Karmitsa, Mäkelä, Taheri (CR21) 2018; 28
Studniarski (CR41) 1986; 24
CR39
Bagirov, Ugon (CR3) 2018; 33
CR16
CR38
Astorino, Fuduli, Gaudioso (CR2) 2012; 53
CR15
CR36
CR12
Martínez-Legaz, Volle (CR30) 1999; 237
Le Thi, Pham Dinh (CR25) 2018; 169
Lobo, Fazel, Boyd (CR26) 2007; 152
Pshenichnyi (CR37) 1971
Mifflin (CR32) 1977; 15
Beck (CR6) 2017
Jara-Moroni, Pang, Wächter (CR20) 2018; 169
Pang, Razaviyayn, Alvarado (CR34) 2017; 42
Horst, Thoai (CR18) 1999; 103
Martínez-Legaz (CR29) 2015; 9
Cesarone, Scozzari, Tardella (CR8) 2020; 76
Bazaraa, Sherali, Shetty (CR5) 2006
Delfour (CR13) 1994; 123
Clarke (CR11) 2013
Ordin, Bagirov (CR33) 2015; 61
Bagirov, Taheri, Ugon (CR4) 2016; 53
Clarke (CR10) 1998
CR28
CR27
Ahn, Pang, Xin (CR1) 2017; 27
Lemaréchal (CR23) 1986; 17
Horst, Tuy (CR19) 1990
Lasserre (CR22) 2010; 4
Chen, Hansen, Jaumard, Tuy (CR9) 1998; 46
Holmberg, Tuy (CR17) 1999; 85
Borwein, Lewis (CR7) 2010
Le Thi, Pham Dinh (CR24) 2005; 133
Mashkoorzadeh, Movahedian, Nobakhtian (CR31) 2019; 40
Singer (CR40) 2006
BN Pshenichnyi (615_CR37) 1971
PC Chen (615_CR9) 1998; 46
MS Lobo (615_CR26) 2007; 152
615_CR15
JP Penot (615_CR35) 1998; 12
615_CR16
HA Le Thi (615_CR24) 2005; 133
615_CR38
JE Martínez-Legaz (615_CR29) 2015; 9
615_CR39
K Holmberg (615_CR17) 1999; 85
M Ahn (615_CR1) 2017; 27
MS Bazaraa (615_CR5) 2006
615_CR12
615_CR36
I Singer (615_CR40) 2006
JS Pang (615_CR34) 2017; 42
JB Lasserre (615_CR22) 2010; 4
F Mashkoorzadeh (615_CR31) 2019; 40
A Beck (615_CR6) 2017
R Horst (615_CR18) 1999; 103
F Jara-Moroni (615_CR20) 2018; 169
M Studniarski (615_CR41) 1986; 24
AM Bagirov (615_CR4) 2016; 53
F Cesarone (615_CR8) 2020; 76
FH Clarke (615_CR10) 1998
J Dutta (615_CR14) 2013; 7
615_CR27
615_CR28
JM Borwein (615_CR7) 2010
M Lemaréchal (615_CR23) 1986; 17
B Ordin (615_CR33) 2015; 61
A Astorino (615_CR2) 2012; 53
HA Le Thi (615_CR25) 2018; 169
R Mifflin (615_CR32) 1977; 15
MC Delfour (615_CR13) 1994; 123
FH Clarke (615_CR11) 2013
K Joki (615_CR21) 2018; 28
AM Bagirov (615_CR3) 2018; 33
R Horst (615_CR19) 1990
JE Martínez-Legaz (615_CR30) 1999; 237
References_xml – volume: 169
  start-page: 5
  year: 2018
  end-page: 68
  ident: CR25
  article-title: DC programming and DCA: thirty years of developments
  publication-title: Math Program
  doi: 10.1007/s10107-018-1235-y
– volume: 42
  start-page: 95
  year: 2017
  end-page: 118
  ident: CR34
  article-title: Computing B-stationary points of nonsmooth DC programs
  publication-title: Math Oper Res
  doi: 10.1287/moor.2016.0795
– year: 1990
  ident: CR19
  publication-title: Global optimization
  doi: 10.1007/978-3-662-02598-7
– volume: 24
  start-page: 1044
  year: 1986
  end-page: 1049
  ident: CR41
  article-title: Necessary and sufficient conditions for isolated local minima of nonsmooth functions
  publication-title: SIAM J Control Optim
  doi: 10.1137/0324061
– volume: 12
  start-page: 373
  year: 1998
  end-page: 382
  ident: CR35
  article-title: On the minimization of difference functions
  publication-title: J Global Optim
  doi: 10.1023/A:1008233531797
– volume: 9
  start-page: 1017
  year: 2015
  end-page: 1023
  ident: CR29
  article-title: Optimality conditions for pseudoconvex minimization over convex sets defined by tangentially convex constraints
  publication-title: Optim Lett
  doi: 10.1007/s11590-014-0822-y
– ident: CR39
– ident: CR16
– ident: CR12
– year: 1971
  ident: CR37
  publication-title: Necessary conditions for an extremum
– year: 2006
  ident: CR40
  publication-title: Duality for nonconvex approximation and optimization
  doi: 10.1007/0-387-28395-1
– volume: 103
  start-page: 1
  year: 1999
  end-page: 43
  ident: CR18
  article-title: DC programming: overview
  publication-title: J Optim Theory Appl
  doi: 10.1023/A:1021765131316
– volume: 61
  start-page: 341
  year: 2015
  end-page: 361
  ident: CR33
  article-title: A heuristic algorithm for solving the minimum sum-of-squares clustering problems
  publication-title: J Global Optim
  doi: 10.1007/s10898-014-0171-5
– volume: 76
  start-page: 245
  year: 2020
  end-page: 265
  ident: CR8
  article-title: An optimization-diversification approach to portfolio selection
  publication-title: J Global Optim
  doi: 10.1007/s10898-019-00809-7
– volume: 33
  start-page: 194
  year: 2018
  end-page: 219
  ident: CR3
  article-title: Nonsmooth DC programming approach to clusterwise linear regression: optimality conditions and algorithms
  publication-title: Optim Method Softw
  doi: 10.1080/10556788.2017.1371717
– year: 2010
  ident: CR7
  publication-title: Convex analysis and nonlinear optimization: theory and examples
– volume: 123
  start-page: 129
  year: 1994
  end-page: 201
  ident: CR13
  article-title: Shape analysis via oriented distance functions
  publication-title: J Funct Anal
  doi: 10.1006/jfan.1994.1086
– year: 2017
  ident: CR6
  publication-title: First-order methods in optimization
  doi: 10.1137/1.9781611974997
– ident: CR27
– volume: 4
  start-page: 1
  year: 2010
  end-page: 5
  ident: CR22
  article-title: On representations of the the feasible set in convex optimization
  publication-title: Optim Lett
  doi: 10.1007/s11590-009-0153-6
– year: 1998
  ident: CR10
  publication-title: Nonsmooth analysis and control theory
– volume: 17
  start-page: 827
  year: 1986
  end-page: 858
  ident: CR23
  article-title: An introduction to the theory of nonsmooth optimization
  publication-title: Optimization
  doi: 10.1080/02331938608843204
– volume: 7
  start-page: 221
  year: 2013
  end-page: 229
  ident: CR14
  article-title: Optimality conditions in convex optimization revisited
  publication-title: Optim Lett
  doi: 10.1007/s11590-011-0410-3
– volume: 27
  start-page: 1637
  issue: 3
  year: 2017
  end-page: 1665
  ident: CR1
  article-title: Difference-of-convex learning: directional stationarity, optimality, and sparsity
  publication-title: SIAM J Optim
  doi: 10.1137/16M1084754
– year: 2013
  ident: CR11
  publication-title: Functional analysis, calculus of variations and optimal control
  doi: 10.1007/978-1-4471-4820-3
– volume: 85
  start-page: 157
  year: 1999
  end-page: 179
  ident: CR17
  article-title: A production-transportation problem with stochastic demand and concave production costs
  publication-title: Math Program
  doi: 10.1007/s101070050050
– volume: 53
  start-page: 12
  year: 2016
  end-page: 24
  ident: CR4
  article-title: Nonsmooth DC programming approach to the minimum sum-of-squares clustering problems
  publication-title: Pattern Recongnit
  doi: 10.1016/j.patcog.2015.11.011
– year: 2006
  ident: CR5
  publication-title: Nonlinear programming: theory and algorithms
  doi: 10.1002/0471787779
– ident: CR15
– ident: CR38
– volume: 15
  start-page: 959
  year: 1977
  end-page: 972
  ident: CR32
  article-title: Semismooth and semiconvex functions in constrained optimization
  publication-title: SIAM J Control Optim
  doi: 10.1137/0315061
– volume: 53
  start-page: 301
  year: 2012
  end-page: 322
  ident: CR2
  article-title: Margin maximization in spherical separation
  publication-title: Comput Optim Appl
  doi: 10.1007/s10589-012-9486-7
– volume: 133
  start-page: 23
  year: 2005
  end-page: 46
  ident: CR24
  article-title: The DC (difference of convex functions) programming and DCA revisited with DC models of real world nonconvex optimization problems
  publication-title: Ann Oper Res
  doi: 10.1007/s10479-004-5022-1
– ident: CR36
– volume: 46
  start-page: 548
  year: 1998
  end-page: 562
  ident: CR9
  article-title: Solution of the multisource Weber and conditional Weber problems by d.c. programming
  publication-title: Oper Res
  doi: 10.1287/opre.46.4.548
– volume: 169
  start-page: 221
  year: 2018
  end-page: 254
  ident: CR20
  article-title: A study of the difference-of-convex approach for solving linear programs with complementarity constraints
  publication-title: Math Program
  doi: 10.1007/s10107-017-1208-6
– volume: 40
  start-page: 1918
  year: 2019
  end-page: 1938
  ident: CR31
  article-title: Optimality conditions for nonconvex constrained optimization problems
  publication-title: Numer Funct Anal Optim
  doi: 10.1080/01630563.2019.1640249
– ident: CR28
– volume: 28
  start-page: 1892
  year: 2018
  end-page: 1919
  ident: CR21
  article-title: Double bundle method for finding Clarke stationary points in nonsmooth DC programming
  publication-title: SIAM J Optim
  doi: 10.1137/16M1115733
– volume: 152
  start-page: 341
  year: 2007
  end-page: 365
  ident: CR26
  article-title: Portfolio optimization with linear and fixed transaction costs
  publication-title: Ann Oper Res
  doi: 10.1007/s10479-006-0145-1
– volume: 237
  start-page: 657
  year: 1999
  end-page: 671
  ident: CR30
  article-title: Duality in DC programming: the case of several DC constraints
  publication-title: J Math Anal Appl
  doi: 10.1006/jmaa.1999.6496
– volume-title: Convex analysis and nonlinear optimization: theory and examples
  year: 2010
  ident: 615_CR7
– volume: 17
  start-page: 827
  year: 1986
  ident: 615_CR23
  publication-title: Optimization
  doi: 10.1080/02331938608843204
– volume-title: Global optimization
  year: 1990
  ident: 615_CR19
  doi: 10.1007/978-3-662-02598-7
– ident: 615_CR16
  doi: 10.1007/978-3-642-45610-7_3
– volume: 61
  start-page: 341
  year: 2015
  ident: 615_CR33
  publication-title: J Global Optim
  doi: 10.1007/s10898-014-0171-5
– ident: 615_CR27
  doi: 10.1111/j.1540-6261.1952.tb01525.x
– volume: 9
  start-page: 1017
  year: 2015
  ident: 615_CR29
  publication-title: Optim Lett
  doi: 10.1007/s11590-014-0822-y
– volume-title: Functional analysis, calculus of variations and optimal control
  year: 2013
  ident: 615_CR11
  doi: 10.1007/978-1-4471-4820-3
– volume: 12
  start-page: 373
  year: 1998
  ident: 615_CR35
  publication-title: J Global Optim
  doi: 10.1023/A:1008233531797
– volume-title: First-order methods in optimization
  year: 2017
  ident: 615_CR6
  doi: 10.1137/1.9781611974997
– volume: 40
  start-page: 1918
  year: 2019
  ident: 615_CR31
  publication-title: Numer Funct Anal Optim
  doi: 10.1080/01630563.2019.1640249
– volume: 28
  start-page: 1892
  year: 2018
  ident: 615_CR21
  publication-title: SIAM J Optim
  doi: 10.1137/16M1115733
– volume-title: Duality for nonconvex approximation and optimization
  year: 2006
  ident: 615_CR40
  doi: 10.1007/0-387-28395-1
– volume: 7
  start-page: 221
  year: 2013
  ident: 615_CR14
  publication-title: Optim Lett
  doi: 10.1007/s11590-011-0410-3
– volume: 123
  start-page: 129
  year: 1994
  ident: 615_CR13
  publication-title: J Funct Anal
  doi: 10.1006/jfan.1994.1086
– volume-title: Nonlinear programming: theory and algorithms
  year: 2006
  ident: 615_CR5
  doi: 10.1002/0471787779
– volume-title: Necessary conditions for an extremum
  year: 1971
  ident: 615_CR37
– volume: 33
  start-page: 194
  year: 2018
  ident: 615_CR3
  publication-title: Optim Method Softw
  doi: 10.1080/10556788.2017.1371717
– volume: 237
  start-page: 657
  year: 1999
  ident: 615_CR30
  publication-title: J Math Anal Appl
  doi: 10.1006/jmaa.1999.6496
– volume: 24
  start-page: 1044
  year: 1986
  ident: 615_CR41
  publication-title: SIAM J Control Optim
  doi: 10.1137/0324061
– volume: 152
  start-page: 341
  year: 2007
  ident: 615_CR26
  publication-title: Ann Oper Res
  doi: 10.1007/s10479-006-0145-1
– volume: 42
  start-page: 95
  year: 2017
  ident: 615_CR34
  publication-title: Math Oper Res
  doi: 10.1287/moor.2016.0795
– ident: 615_CR38
– ident: 615_CR15
– ident: 615_CR36
– volume: 53
  start-page: 12
  year: 2016
  ident: 615_CR4
  publication-title: Pattern Recongnit
  doi: 10.1016/j.patcog.2015.11.011
– volume-title: Nonsmooth analysis and control theory
  year: 1998
  ident: 615_CR10
– volume: 103
  start-page: 1
  year: 1999
  ident: 615_CR18
  publication-title: J Optim Theory Appl
  doi: 10.1023/A:1021765131316
– volume: 85
  start-page: 157
  year: 1999
  ident: 615_CR17
  publication-title: Math Program
  doi: 10.1007/s101070050050
– volume: 4
  start-page: 1
  year: 2010
  ident: 615_CR22
  publication-title: Optim Lett
  doi: 10.1007/s11590-009-0153-6
– ident: 615_CR28
– volume: 169
  start-page: 5
  year: 2018
  ident: 615_CR25
  publication-title: Math Program
  doi: 10.1007/s10107-018-1235-y
– ident: 615_CR12
– volume: 133
  start-page: 23
  year: 2005
  ident: 615_CR24
  publication-title: Ann Oper Res
  doi: 10.1007/s10479-004-5022-1
– volume: 76
  start-page: 245
  year: 2020
  ident: 615_CR8
  publication-title: J Global Optim
  doi: 10.1007/s10898-019-00809-7
– volume: 27
  start-page: 1637
  issue: 3
  year: 2017
  ident: 615_CR1
  publication-title: SIAM J Optim
  doi: 10.1137/16M1084754
– volume: 15
  start-page: 959
  year: 1977
  ident: 615_CR32
  publication-title: SIAM J Control Optim
  doi: 10.1137/0315061
– ident: 615_CR39
– volume: 169
  start-page: 221
  year: 2018
  ident: 615_CR20
  publication-title: Math Program
  doi: 10.1007/s10107-017-1208-6
– volume: 46
  start-page: 548
  year: 1998
  ident: 615_CR9
  publication-title: Oper Res
  doi: 10.1287/opre.46.4.548
– volume: 53
  start-page: 301
  year: 2012
  ident: 615_CR2
  publication-title: Comput Optim Appl
  doi: 10.1007/s10589-012-9486-7
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Snippet We focus on optimality conditions for an important class of nonconvex and nonsmooth optimization problems, where the objective and constraint functions are...
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Insurance
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Operations Research/Decision Theory
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Title The DTC (difference of tangentially convex functions) programming: optimality conditions
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