메뉴 건너뛰기




Volumn 133, Issue 1-4, 2005, Pages 23-46

The DC (difference of convex functions) programming and DCA revisited with DC models of real world nonconvex optimization problems

Author keywords

DC algorithms (DCA); DC duality; DC programming; Global optimality conditions; Local optimality conditions; Polyhedral DC programming; Regularization techniques

Indexed keywords


EID: 15244346000     PISSN: 02545330     EISSN: 15729338     Source Type: Journal    
DOI: 10.1007/s10479-004-5022-1     Document Type: Conference Paper
Times cited : (757)

References (64)
  • 3
    • 0013532015 scopus 로고    scopus 로고
    • An Efficient Algorithm for Globally Minimizing a Quadratic Function under Convex Quadratic Constraints
    • An, Le Thi Hoai. (2000). "An Efficient Algorithm for Globally Minimizing a Quadratic Function under Convex Quadratic Constraints." Math. Programming Ser. A 87(3), 401-426.
    • (2000) Math. Programming Ser. A , vol.87 , Issue.3 , pp. 401-426
    • An, L.T.H.1
  • 4
    • 0242485191 scopus 로고    scopus 로고
    • Solving Large Scale Molecular Distance Geometry Problem by a Smoothing Technique via the Gaussian Transform an DC Programming
    • An, Le Thi Hoai. (2003). "Solving Large Scale Molecular Distance Geometry Problem by a Smoothing Technique via the Gaussian Transform an DC Programming." J. Global Optim. 27, 375-397.
    • (2003) J. Global Optim. , vol.27 , pp. 375-397
    • An, L.T.H.1
  • 5
    • 0001445010 scopus 로고    scopus 로고
    • Solving a Class of Linearly Constrained Indefinite Quadratic Problems by DC Algorithms
    • An, Le Thi Hoai and Pham Dinh Tao. (1997). "Solving a Class of Linearly Constrained Indefinite Quadratic Problems by DC Algorithms." J. Global Optim. 11, 253-285.
    • (1997) J. Global Optim. , vol.11 , pp. 253-285
    • An, L.T.H.1    Tao, P.D.2
  • 6
    • 0001290246 scopus 로고    scopus 로고
    • Numerical Solution for Optimization over the Efficient Set by DC Optimization Algorithm
    • An, Le Thi Hoai, Pham Dinh Tao, and Le Dung Muu. (1996). "Numerical Solution for Optimization over the Efficient Set by DC Optimization Algorithm." Oper. Res. Lett. 19, 117-128.
    • (1996) Oper. Res. Lett. , vol.19 , pp. 117-128
    • An, L.T.H.1    Tao, P.D.2    Muu, L.D.3
  • 7
    • 0344166134 scopus 로고    scopus 로고
    • A Branch-and-Bound Method via DC Optimization Algorithm and Ellipsoidal Techniques for Box Constrained Nonconvex Quadratic Programming Problems
    • An, Le Thi Hoai and Pham Dinh Tao. (1998). "A Branch-and-Bound Method via DC Optimization Algorithm and Ellipsoidal Techniques for Box Constrained Nonconvex Quadratic Programming Problems." J. Global Optim. 13, 171-206.
    • (1998) J. Global Optim. , vol.13 , pp. 171-206
    • An, L.T.H.1    Tao, P.D.2
  • 8
    • 2342589523 scopus 로고    scopus 로고
    • A Combined DC Optimization - Ellipsoidal Branch-and-Bound Algorithm for Solving Nonconvex Quadratic Programming Problems
    • An, Le Thi Hoai, Pham Dinh Tao, and Le Dung Muu. (1998). "A Combined DC Optimization - Ellipsoidal Branch-and-Bound Algorithm for Solving Nonconvex Quadratic Programming Problems." J. Combin. Optim. 2(1), 9-28.
    • (1998) J. Combin. Optim. , vol.2 , Issue.1 , pp. 9-28
    • An, L.T.H.1    Tao, P.D.2    Muu, L.D.3
  • 9
    • 15244346730 scopus 로고    scopus 로고
    • Exact Penalty in DC Programming
    • An, Le Thi Hoai, Pham Dinh Tao, and Le Dung Muu. (1999). "Exact Penalty in DC Programming." Vietnam J. Math. 27(2), 169-178.
    • (1999) Vietnam J. Math. , vol.27 , Issue.2 , pp. 169-178
    • An, L.T.H.1    Tao, P.D.2    Muu, L.D.3
  • 11
    • 84872987720 scopus 로고    scopus 로고
    • DC Programming Approach for Large-Scale Molecular Optimization via the General Distance Geometry Problem
    • Nonconvex Optimization and Its Applications, Kluwer Academic
    • An, Le Thi Hoai and Pham Dinh Tao. (2000a). "DC Programming Approach for Large-Scale Molecular Optimization via the General Distance Geometry Problem." In Optimization in Computational Chemistry and Molecular Biology: Local and Global Approaches. Nonconvex Optimization and Its Applications, Vol. 40. Kluwer Academic, pp. 301-339.
    • (2000) Optimization in Computational Chemistry and Molecular Biology: Local and Global Approaches , vol.40 , pp. 301-339
    • An, L.T.H.1    Tao, P.D.2
  • 12
    • 84873001135 scopus 로고    scopus 로고
    • Large Scale Molecular Conformation via the Exact Distance Geometry Problem
    • Lecture Notes in Economics and Mathematical Systems, Heidelberg: Springer
    • An, Le Thi Hoai and Pham Dinh Tao. (2000b). "Large Scale Molecular Conformation via the Exact Distance Geometry Problem." In Optimization. Lecture Notes in Economics and Mathematical Systems, Vol. 481. Heidelberg: Springer, pp. 260-277.
    • (2000) Optimization , vol.481 , pp. 260-277
    • An, L.T.H.1    Tao, P.D.2
  • 13
    • 3543094538 scopus 로고    scopus 로고
    • A Continuous Approach for Large-Scale Linearly Constrained Quadratic Zero-One Programming
    • An, Le Thi Hoai and Pham Dinh Tao. (2001a). "A Continuous Approach for Large-Scale Linearly Constrained Quadratic Zero-One Programming." Optim. 50(1,2), 93-120.
    • (2001) Optim. , vol.50 , Issue.1-2 , pp. 93-120
    • An, L.T.H.1    Tao, P.D.2
  • 14
    • 84873016624 scopus 로고    scopus 로고
    • DC Optimization Approaches via Markov Models for Restoration of Signals (1-D) and (2-D)
    • Nonconvex Optimization and Its Applications, Kluwer Academic
    • An, Le Thi Hoai and Pham Dinh Tao. (2001b). "DC Optimization Approaches via Markov Models for Restoration of Signals (1-D) and (2-D)." In Advances in Convex Analysis and Global Optimization. Nonconvex Optimization and Its Applications, Vol. 54. Kluwer Academic, pp. 300-317.
    • (2001) Advances in Convex Analysis and Global Optimization , vol.54 , pp. 300-317
    • An, L.T.H.1    Tao, P.D.2
  • 15
    • 70450225635 scopus 로고    scopus 로고
    • DC Programming Approach and Solution Algorithm to the Multidimensional Scaling Problem
    • Nonconvex Optimization and Its Applications, Kluwer Academic
    • An, Le Thi Hoai and Pham Dinh Tao. (2001c). "DC Programming Approach and Solution Algorithm to the Multidimensional Scaling Problem." In From Local to Global Optimization. Nonconvex Optimization and Its Applications, Vol. 53. Kluwer Academic, pp. 231-276.
    • (2001) From Local to Global Optimization , vol.53 , pp. 231-276
    • An, L.T.H.1    Tao, P.D.2
  • 16
    • 31244434168 scopus 로고    scopus 로고
    • DC Programming Approach for Multicommodity Network Optimization Problems with Step Increasing Cost Functions
    • dedicated to Professor R. Horst on the occasion of his 60th birthday
    • An, Le Thi Hoai and Pham Dinh Tao. (2002a). "DC Programming Approach for Multicommodity Network Optimization Problems with Step Increasing Cost Functions." J. Global Optim. 22(1-4), 204-233. Special Issue, dedicated to Professor R. Horst on the occasion of his 60th birthday.
    • (2002) J. Global Optim. , vol.22 , Issue.1-4 SPEC. ISSUE , pp. 204-233
    • An, L.T.H.1    Tao, P.D.2
  • 17
    • 84927630367 scopus 로고    scopus 로고
    • DC Programming. Theory, Algorithms, Applications: The State of the Art
    • Valbonne-Sophia Antipolis, France, October 2-4, 2002. Research Report, 28 pages. Laboratory of Modeling, Optimization & Operations Research, Insa-Rouen, France (2002)
    • An, Le Thi Hoai and Pham Dinh Tao. (2002b). "DC Programming. Theory, Algorithms, Applications: The State of the Art." In First International Workshop on Global Constrained Optimization and Constraint Satisfaction. Valbonne-Sophia Antipolis, France, October 2-4, 2002. Research Report, 28 pages. Laboratory of Modeling, Optimization & Operations Research, Insa-Rouen, France (2002).
    • (2002) First International Workshop on Global Constrained Optimization and Constraint Satisfaction
    • An, L.T.H.1    Tao, P.D.2
  • 18
    • 1542380919 scopus 로고    scopus 로고
    • Large Scale Global Molecular Optimization from Exact Distance Matrices by a DC Optimization Approach
    • An, Le Thi Hoai and Pham Dinh Tao. (2003a). "Large Scale Global Molecular Optimization from Exact Distance Matrices by a DC Optimization Approach." SIAM J. Optim. 14(1), 77-114.
    • (2003) SIAM J. Optim. , vol.14 , Issue.1 , pp. 77-114
    • An, L.T.H.1    Tao, P.D.2
  • 19
    • 84855214839 scopus 로고    scopus 로고
    • A New Algorithm for Solving Large Scale Molecular Distance Geometry Problems, Applied Optimization
    • Kluwer Academic
    • An, Le Thi Hoai and Pham Dinh Tao. (2003b). "A New Algorithm for Solving Large Scale Molecular Distance Geometry Problems, Applied Optimization." In Hight Performance Algorithms and Software for Nonlinear Optimization. Kluwer Academic, pp. 276-296.
    • (2003) Hight Performance Algorithms and Software for Nonlinear Optimization , pp. 276-296
    • An, L.T.H.1    Tao, P.D.2
  • 20
    • 0037120697 scopus 로고    scopus 로고
    • Combination between Local and Global Methods for Solving an Optimization Problem over the Efficient Set
    • An, Le Thi Hoai, Pham Dinh Tao, and Nguyen Van Thoai. (2002). "Combination between Local and Global Methods for Solving an Optimization Problem over the Efficient Set." European J. Oper. Res. 142, 257-270.
    • (2002) European J. Oper. Res. , vol.142 , pp. 257-270
    • An, L.T.H.1    Tao, P.D.2    Van Thoai, N.3
  • 21
    • 0037865630 scopus 로고    scopus 로고
    • Simplicially Constrained DC Optimization over the Efficient Set and Weakly Efficient Sets
    • An, Le Thi Hoai, Pham Dinh Tao, and Le Dung Muu. (2003a). "Simplicially Constrained DC Optimization over the Efficient Set and Weakly Efficient Sets." J. Optim. Theory Appl. 117(3), 503-531.
    • (2003) J. Optim. Theory Appl. , vol.117 , Issue.3 , pp. 503-531
    • An, L.T.H.1    Tao, P.D.2    Muu, L.D.3
  • 23
    • 0038729435 scopus 로고    scopus 로고
    • Towards Tikhonov Regularization of Non-linear Ill-Posed Problems: A DC Programming Approach
    • An, Le Thi Hoai, Pham Dinh Tao, and Dinh Nho Hao. (2002). "Towards Tikhonov Regularization of Non-linear Ill-Posed Problems: A DC Programming Approach." C.R. Acad. Sci. Paris Ser. I 335, 1073-1078.
    • (2002) C.R. Acad. Sci. Paris Ser. I , vol.335 , pp. 1073-1078
    • An, L.T.H.1    Tao, P.D.2    Hao, D.N.3
  • 24
    • 84867939324 scopus 로고    scopus 로고
    • Solving Inverse Problems for an Elliptic Equations by D.C. (Difference of Convex Functions) Programming
    • An, Le Thi Hoai, Pham Dinh Tao, and Dinh Nho Hao. (2003). "Solving Inverse Problems for an Elliptic Equations by D.C. (Difference of Convex Functions) Programming." J. Global Optim. 25(4), 407-423.
    • (2003) J. Global Optim. , vol.25 , Issue.4 , pp. 407-423
    • An, L.T.H.1    Tao, P.D.2    Hao, D.N.3
  • 25
    • 84872987059 scopus 로고    scopus 로고
    • On the Ill-Posedness of the Trust Region Subproblem
    • to appear
    • An, Le Thi Hoai, Pham Dinh Tao, and Dinh Nho Hao. (2004a). "On the Ill-Posedness of the Trust Region Subproblem." J. Inverse Ill-Posed Problems, to appear.
    • (2004) J. Inverse Ill-Posed Problems
    • An, L.T.H.1    Tao, P.D.2    Hao, D.N.3
  • 28
    • 0041001171 scopus 로고
    • Conditions nécessaires et suffisantes d'optimalité globule en optimisation de différences de deux fonctions convexes
    • Hiriat Urruty, J.B. (1989). "Conditions nécessaires et suffisantes d'optimalité globule en optimisation de différences de deux fonctions convexes." C.R. Acad. Sci. Paris Ser. I 309, 459-462.
    • (1989) C.R. Acad. Sci. Paris Ser. I , vol.309 , pp. 459-462
    • Hiriat Urruty, J.B.1
  • 31
    • 0033246194 scopus 로고    scopus 로고
    • DC Programming: Overview
    • Horst, R. and Nguyen Van Thoai. (1999). "DC Programming: Overview." J. Optim. Theory Appl. 2103(1), 1-43.
    • (1999) J. Optim. Theory Appl. , vol.2103 , Issue.1 , pp. 1-43
    • Horst, R.1    Van Thoai, N.2
  • 35
    • 0039630337 scopus 로고
    • Partial Regularization of the Sum of Two Maximal Monotone Operators
    • 2AN) 27, 375-395.
    • (1993) 2AN) , vol.27 , pp. 375-395
    • Mahey, P.1    Tao, P.D.2
  • 36
    • 0000860796 scopus 로고
    • Proximal Decomposition of the Graph of Maximal Monotone Operator
    • Mahey, P. and Pham Dinh Tao. (1995). "Proximal Decomposition of the Graph of Maximal Monotone Operator." SIAM J. Optim. 5, 454-468.
    • (1995) SIAM J. Optim. , vol.5 , pp. 454-468
    • Mahey, P.1    Tao, P.D.2
  • 37
    • 0031285908 scopus 로고    scopus 로고
    • Global Continuation for Distance Geometry Problems
    • More, J.J. and Z. Wu. (1997). "Global Continuation for Distance Geometry Problems." SIAM J. Optim. 8, 814-836.
    • (1997) SIAM J. Optim. , vol.8 , pp. 814-836
    • More, J.J.1    Wu, Z.2
  • 39
    • 0000276924 scopus 로고
    • Proximité et dualité dans un espace Hilbertien
    • Moreau, J.J. (1965). "Proximité et dualité dans un espace Hilbertien." Bull. Soc. Math. France 93, 273-299.
    • (1965) Bull. Soc. Math. France , vol.93 , pp. 273-299
    • Moreau, J.J.1
  • 43
    • 0016985417 scopus 로고
    • Monotone Operators and the Proximal Point Algorithm
    • Rockafellar, R.T. (1976). "Monotone Operators and the Proximal Point Algorithm." SIAM J. Control Optim. 14, 877-898.
    • (1976) SIAM J. Control Optim. , vol.14 , pp. 877-898
    • Rockafellar, R.T.1
  • 47
    • 0001861849 scopus 로고
    • Convergence of Subgradient Method for Computing the Bound Norm of Matrices
    • Tao, Pham Dinh. (1984). "Convergence of Subgradient Method for Computing the Bound Norm of Matrices." Linear Algebra Appl. 62, 163-182.
    • (1984) Linear Algebra Appl. , vol.62 , pp. 163-182
    • Tao, P.D.1
  • 48
    • 0042001731 scopus 로고
    • Algorithmes de calcul d'une forme quadratique sur la boule unité de la norme maximum
    • Tao, Pham Dinh. (1985). "Algorithmes de calcul d'une forme quadratique sur la boule unité de la norme maximum." Numer. Math. 45, 377-440.
    • (1985) Numer. Math. , vol.45 , pp. 377-440
    • Tao, P.D.1
  • 50
    • 0001501337 scopus 로고
    • Duality in D.C. (Difference of Convex Functions) Optimization. Subgradient Methods
    • International Series of Numerical Mathematics, Birkhäuser
    • Tao, Pham Dinh. (1988). "Duality in D.C. (Difference of Convex Functions) Optimization. Subgradient Methods." In Trends in Mathematical Optimization, International Series of Numerical Mathematics, Vol. 84. Birkhäuser, pp. 277-293.
    • (1988) Trends in Mathematical Optimization , vol.84 , pp. 277-293
    • Tao, P.D.1
  • 51
    • 0013501148 scopus 로고
    • Stabilité de la dualité lagrangienne en optimisation DC (différence de deux fonctions convexes)
    • Tao, Pham Dinh and Le Thi Hoai An. (1994). "Stabilité de la dualité lagrangienne en optimisation DC (différence de deux fonctions convexes)." C.R. Acad. Sci. Paris Sér. I 318, 379-384.
    • (1994) C.R. Acad. Sci. Paris Sér. I , vol.318 , pp. 379-384
    • Tao, P.D.1    An, L.T.H.2
  • 52
    • 0000582448 scopus 로고
    • Lagrangian Stability and Global Optimality in Nonconvex Quadratic Minimization over Euclidean Balls and Spheres
    • Tao, Pham Dinh and Le Thi Hoai An. (1995). "Lagrangian Stability and Global Optimality in Nonconvex Quadratic Minimization over Euclidean Balls and Spheres." J. Convex Anal. 2, 263-276.
    • (1995) J. Convex Anal. , vol.2 , pp. 263-276
    • Tao, P.D.1    An, L.T.H.2
  • 53
    • 0032081028 scopus 로고    scopus 로고
    • DC Optimization Algorithms for Solving the Trust Region Subproblem
    • Tao, Pham Dinh and Le Thi Hoai An. (1998). "DC Optimization Algorithms for Solving the Trust Region Subproblem." SIAM J. Optim. 8, 476-505.
    • (1998) SIAM J. Optim. , vol.8 , pp. 476-505
    • Tao, P.D.1    An, L.T.H.2
  • 54
    • 0000939953 scopus 로고    scopus 로고
    • Convex Analysis Approach to DC Programming: Theory, Algorithms and Applications
    • Tao, Pham Dinh and Le Thi Hoai An. (1997). "Convex Analysis Approach to DC Programming: Theory, Algorithms and Applications." Acta Math. Vietnamica 22(1), 287-355.
    • (1997) Acta Math. Vietnamica , vol.22 , Issue.1 , pp. 287-355
    • Tao, P.D.1    An, L.T.H.2
  • 55
    • 85047103342 scopus 로고
    • DC Sets, D.C. Functions and Nonlinear Equations
    • Thach, Phan Thien. (1993a). "DC Sets, D.C. Functions and Nonlinear Equations." Math. Programming 58, 415-428.
    • (1993) Math. Programming , vol.58 , pp. 415-428
    • Thach, P.T.1
  • 56
    • 21344494857 scopus 로고
    • Global Optimality Criteria and Duality with Zero Gap in Nonconvex Optimization Problems
    • Thach, Phan Thien. (1993b). "Global Optimality Criteria and Duality with Zero Gap in Nonconvex Optimization Problems." SIAM J. Math. Anal. 24, 1537-1556.
    • (1993) SIAM J. Math. Anal. , vol.24 , pp. 1537-1556
    • Thach, P.T.1
  • 57
    • 0011280208 scopus 로고
    • A Nonconvex Duality with Zero Gap and Applications
    • Thach, Phan Thien. (1994). "A Nonconvex Duality with Zero Gap and Applications." SIAM J. Optim. 4, 44-64.
    • (1994) SIAM J. Optim. , vol.4 , pp. 44-64
    • Thach, P.T.1
  • 58
    • 15244339898 scopus 로고    scopus 로고
    • On the Degree and Separability of Nonconvexity and Applications to Optimization Problems
    • Thach, Phan Thien. (1996). "On the Degree and Separability of Nonconvexity and Applications to Optimization Problems." Math. Programming 77, 23-47.
    • (1996) Math. Programming , vol.77 , pp. 23-47
    • Thach, P.T.1
  • 59
    • 0008984095 scopus 로고
    • Duality in Nonconvex Optimization
    • Toland, J.F. (1978). "Duality in Nonconvex Optimization." J. Math. Anal. Appl. 66, 399-415.
    • (1978) J. Math. Anal. Appl. , vol.66 , pp. 399-415
    • Toland, J.F.1
  • 60
    • 0013553271 scopus 로고
    • On Subdifferential Calculus and Duality in Nonconvex Optimization
    • Toland, J.F. (1979). "On Subdifferential Calculus and Duality in Nonconvex Optimization." Bull. Soc. Math. France, Mémoire 60, 177-183.
    • (1979) Bull. Soc. Math. France, Mémoire , vol.60 , pp. 177-183
    • Toland, J.F.1
  • 61
    • 0001553298 scopus 로고
    • Concave Programming under Linear Constraints
    • Tuy, Hoang. (1964). "Concave Programming under Linear Constraints." Translated Soviet Mathematics 5, 1437-1440.
    • (1964) Translated Soviet Mathematics , vol.5 , pp. 1437-1440
    • Tuy, H.1
  • 63
    • 0034353741 scopus 로고    scopus 로고
    • Monotonic Optimization: Problems and Solution Approaches
    • Tuy, Hoang. (2000). "Monotonic Optimization: Problems and Solution Approaches." SIAM J. Optim. 2, 464-494.
    • (2000) SIAM J. Optim. , vol.2 , pp. 464-494
    • Tuy, H.1
  • 64
    • 0030303861 scopus 로고    scopus 로고
    • The Effective Energy Transformation Scheme as a Special Continuation Approach to Global Optimization with Application to Molecular Conformation
    • Wu, Z. (1996). "The Effective Energy Transformation Scheme as a Special Continuation Approach to Global Optimization with Application to Molecular Conformation." SIAM J. Optim. 6, 748-768.
    • (1996) SIAM J. Optim. , vol.6 , pp. 748-768
    • Wu, Z.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.