메뉴 건너뛰기




Volumn 282, Issue , 2014, Pages 15-35

DC Programming and DCA for General DC Programs

Author keywords

Constraint qualification; DC constraints; DC programming; DCA; Nonsmooth penalty function; Subdifferential

Indexed keywords

CONSTRAINT QUALIFICATION; D-C PROGRAMMING; DC CONSTRAINTS; DCA; PENALTY FUNCTION; SUBDIFFERENTIALS;

EID: 84927666571     PISSN: 21945357     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-3-319-06569-4_2     Document Type: Article
Times cited : (88)

References (73)
  • 1
    • 85006611307 scopus 로고    scopus 로고
    • DC Programming and DCA, http://lita.sciences.univ-metz.fr/~lethi/DCA.html
  • 2
    • 0000939953 scopus 로고    scopus 로고
    • Convex analysis approach to dc programming: Theory, algorithms and applications
    • Pham Dinh, T., Le Thi, H.A.: Convex analysis approach to DC programming: Theory, Algorithms and Applications. Acta Mathematica Vietnamica 22(1), 289-355 (1997)
    • (1997) Acta Mathematica Vietnamica , vol.22 , Issue.1 , pp. 289-355
    • Pham Dinh, T.1    Le Thi, H.A.2
  • 3
    • 0032081028 scopus 로고    scopus 로고
    • A dc optimization algorithm for solving the trust region subproblem
    • Pham Dinh, T., Le Thi, H.A.: A DC Optimization algorithm for solving the trust region subproblem. SIAM J. Optim. 8(2), 476-505 (1998)
    • (1998) SIAM J. Optim , vol.8 , Issue.2 , pp. 476-505
    • Pham Dinh, T.1    Le Thi, H.A.2
  • 4
    • 0001445010 scopus 로고    scopus 로고
    • Solving a class of linearly constrained indefinite quadratic problems by dc algorithms
    • Le Thi, H.A., Pham Dinh, T.: Solving a class of linearly constrained indefinite quadratic problems by DC Algorithms. Journal of Global Optimization 11, 253-285 (1997)
    • (1997) Journal of Global Optimization , vol.11 , pp. 253-285
    • Le Thi, H.A.1    Pham Dinh, T.2
  • 7
    • 0013532015 scopus 로고    scopus 로고
    • An efficient algorithm for globally minimizing a quadratic function under convex quadratic constraints
    • Le Thi, H.A.: An efficient algorithm for globally minimizing a quadratic function under convex quadratic constraints. Mathematical Programming, Ser. A 87(3), 401-426 (2000)
    • (2000) Mathematical Programming, Ser. A , vol.87 , Issue.3 , pp. 401-426
    • Le Thi, H.A.1
  • 8
    • 1542380919 scopus 로고    scopus 로고
    • Large scale global molecular optimization from distance matrices by a dc optimization appoach
    • Le Thi, H.A., Pham Dinh, T.: Large scale global molecular optimization from distance matrices by a DC optimization appoach. SIAM J. Optim. 14(1), 77-116 (2003)
    • (2003) SIAM J. Optim , vol.14 , Issue.1 , pp. 77-116
    • Le Thi, H.A.1    Pham Dinh, T.2
  • 10
    • 15244346000 scopus 로고    scopus 로고
    • The dc (Difference of convex functions) programming and dca revisited with dc models of real-world nonconvex optimization problems
    • Le Thi, H.A., Pham Dinh, T.: The DC (Difference of Convex functions) Programming and DCA revisited with DC models of real-world nonconvex optimization problems. Annals of Operations Research 133, 23-48 (2005)
    • (2005) Annals of Operations Research , vol.133 , pp. 23-48
    • Le Thi, H.A.1    Pham Dinh, T.2
  • 11
    • 84927592376 scopus 로고    scopus 로고
    • A continuous approach for solving the concave cost supply problem by combining dca and b&b techniques
    • Le Thi, H.A., Nguyen, T.P., Pham Dinh, T.: A continuous approach for solving the concave cost supply problem by combining DCA and B&B techniques. European Journal of Operational Research 183, 1001-1012 (2007)
    • (2007) European Journal of Operational Research , vol.183 , pp. 1001-1012
    • Le Thi, H.A.1    Nguyen, T.P.2    Pham Dinh, T.3
  • 12
    • 38049053083 scopus 로고    scopus 로고
    • A continuous approach for the concave cost supply problem via dc programming and dca
    • Le Thi, H.A., Pham Dinh, T.: A continuous approach for the concave cost supply problem via DC Programming and DCA. Discrete Applied Mathematics 156, 325-338 (2008)
    • (2008) Discrete Applied Mathematics , vol.156 , pp. 325-338
    • Le Thi, H.A.1    Pham Dinh, T.2
  • 13
    • 78149282159 scopus 로고    scopus 로고
    • An efficient combination of dca and b&b using dc/sdp relaxation for globally solving binary quadratic programs
    • Pham Dinh, T., Nguyen, C.N., Le Thi, H.A.: An efficient combination of DCA and B&B using DC/SDP relaxation for globally solving binary quadratic programs. Journal of Global Optimization 48(4), 595-632 (2010)
    • (2010) Journal of Global Optimization , vol.48 , Issue.4 , pp. 595-632
    • Pham Dinh, T.1    Nguyen, C.N.2    Le Thi, H.A.3
  • 14
    • 77956525932 scopus 로고    scopus 로고
    • A dc programming approach for sparse eigenvalue problem
    • Thiao, M., Pham Dinh, T., Le Thi, H.A.: A DC programming approach for Sparse Eigenvalue Problem. In: ICML 2010, pp. 1063-1070 (2010)
    • (2010) ICML 2010 , pp. 1063-1070
    • Thiao, M.1    Pham Dinh, T.2    Le Thi, H.A.3
  • 15
    • 84927612691 scopus 로고    scopus 로고
    • Convergence Analysis of DC Algorithms for DC programming with subanalytic data, Research Report, National Institute for Applied Sciences, Rouen, France
    • Le Thi, H.A., Huynh, V.N., Pham Dinh, T.: Convergence Analysis of DC Algorithms for DC programming with subanalytic data, Research Report, National Institute for Applied Sciences, Rouen, France (2009)
    • (2009)
    • Le Thi, H.A.1    Huynh, V.N.2    Pham Dinh, T.3
  • 16
    • 84927608491 scopus 로고    scopus 로고
    • A DC programming approach for Sparse Eigenvalue Problem, Research Report, National Institute for Applied Sciences, Rouen, France
    • Thiao, M., Pham Dinh, T., Le Thi, H.A.: A DC programming approach for Sparse Eigenvalue Problem, Research Report, National Institute for Applied Sciences, Rouen, France (2011)
    • (2011)
    • Thiao, M.1    Pham Dinh, T.2    Le Thi, H.A.3
  • 17
    • 84927623216 scopus 로고    scopus 로고
    • Approximation and Penalization of the tb-norm in DC Programming, Research Report, National Institute for Applied Sciences, Rouen, France
    • Le Thi, H.A., Pham Dinh, T.: Approximation and Penalization of the tb-norm in DC Programming, Research Report, National Institute for Applied Sciences, Rouen, France (2010)
    • (2010)
    • Le Thi, H.A.1    Pham Dinh, T.2
  • 18
    • 84947201370 scopus 로고    scopus 로고
    • 0-norm, Research Report, National Institute for Applied Sciences, Rouen, France
    • Le Thi, H.A., Pham Dinh, T.: DC Programming and DCA for solving nonconvex programs involving ¿0-norm, Research Report, National Institute for Applied Sciences, Rouen, France (2010)
    • (2010)
    • Le Thi, H.A.1    Pham Dinh, T.2
  • 19
    • 85139379902 scopus 로고    scopus 로고
    • Long-Short Portfolio Optimization Under Cardinality Constraints by Difference of Convex Functions Algorithm. Journal of Optimization Theory & Applications, 27 pages
    • Le Thi, H.A., Moeini, M.: Long-Short Portfolio Optimization Under Cardinality Constraints by Difference of Convex Functions Algorithm. Journal of Optimization Theory & Applications, 27 pages (October 2012), doi:10.1007/s10957-012-0197-0.
    • (2012)
    • Le Thi, H.A.1    Moeini, M.2
  • 20
    • 84859231961 scopus 로고    scopus 로고
    • Exact penalty and error bounds in dc programming. Journal of global optimization, in memory of reiner horst
    • Le Thi, H.A., Pham Dinh, T., Huynh, V.N.: Exact penalty and Error Bounds in DC programming. Journal of Global Optimization, in Memory of Reiner Horst, Founder of the Journal 52(3), 509-535 (2012)
    • (2012) Founder of the Journal , vol.52 , Issue.3 , pp. 509-535
    • Le Thi, H.A.1    Pham Dinh, T.2    Huynh, V.N.3
  • 21
    • 84927584490 scopus 로고    scopus 로고
    • Exact Penalty in Mixed Integer DC Programming, Research Report, Lorraine University, France
    • Le Thi, H.A., Pham Dinh, T.: Exact Penalty in Mixed Integer DC Programming, Research Report, Lorraine University, France (2011)
    • (2011)
    • Le Thi, H.A.1    Pham Dinh, T.2
  • 25
    • 84856523908 scopus 로고    scopus 로고
    • Globally solving a nonlinear uav task assignment problem by stochastic and derministic optimization approaches
    • Le Thi, H.A., Nguyen, D.M., Pham Dinh, T.: Globally solving a Nonlinear UAV Task Assignment Problem by stochastic and derministic optimization approaches. Optimization Letters 6(2), 315-329 (2012)
    • (2012) Optimization Letters , vol.6 , Issue.2 , pp. 315-329
    • Le Thi, H.A.1    Nguyen, D.M.2    Pham Dinh, T.3
  • 27
    • 84864652507 scopus 로고    scopus 로고
    • Solving continuous min max problem for single period portfolio selection with discrete constraints by dca
    • Le Thi, H.A., Tran Duc, Q.: Solving Continuous Min Max Problem for Single Period Portfolio Selection with Discrete Constraints by DCA. Optimization 61(8) (2012)
    • (2012) Optimization , vol.61 , Issue.8
    • Le Thi, H.A.1    Tran Duc, Q.2
  • 28
    • 84867269069 scopus 로고    scopus 로고
    • Solving the minimum m-dominating set problem by a continuous optimization approach based on dc programming and dca
    • Schleich, J., Le Thi, H.A., Bouvry, P.: Solving the Minimum m-Dominating Set problem by a Continuous Optimization Approach based on DC Programming and DCA. Journal of Combinatorial Optimization 24(4), 397-412 (2012)
    • (2012) Journal of Combinatorial Optimization , vol.24 , Issue.4 , pp. 397-412
    • Schleich, J.1    Le Thi, H.A.2    Bouvry, P.3
  • 29
    • 84859508506 scopus 로고    scopus 로고
    • Optimizing radial basis functions by d.C. programming and its use in direct search for global derivative-free optimization
    • Le Thi, H.A., Vaz, A.I.F., Vicente, L.N.: Optimizing radial basis functions by D.C. programming and its use in direct search for global derivative-free optimization. TOP 20(1), 190-214 (2012)
    • (2012) TOP , vol.20 , Issue.1 , pp. 190-214
    • Le Thi, H.A.1    Vaz, A.2    Vicente, L.N.3
  • 30
    • 84880831781 scopus 로고    scopus 로고
    • Spherical separation by DC programming and DCA. To appear in Journal of Global Optimization, 17 pages (Online first Feabruary
    • Le Thi, H.A., Le Hoai, M., Pham Dinh, T., Huynh, V.N.: Spherical separation by DC programming and DCA. To appear in Journal of Global Optimization, 17 pages (Online first Feabruary 2012), doi:10.1007/s10898-012-9859-6.
    • (2012)
    • Le Thi, H.A.1    Le Hoai, M.2    Pham Dinh, T.3    Huynh, V.N.4
  • 31
    • 84865834616 scopus 로고    scopus 로고
    • A new decomposition algorithm for globally solving mathematical programs with affine equilibrium constraints
    • Muu, L.D., Tran Dinh, Q., Le Thi, H.A., Pham Dinh, T.: A new decomposition algorithm for globally solving mathematical programs with affine equilibrium constraints. Acta Mathematica Vietnamica 37(2), 201-218 (2012)
    • (2012) Acta Mathematica Vietnamica , vol.37 , Issue.2 , pp. 201-218
    • Muu, L.D.1    Tran Dinh, Q.2    Le Thi, H.A.3    Pham Dinh, T.4
  • 32
    • 84880234389 scopus 로고    scopus 로고
    • Efficient dc programming approaches for asymmetric eigenvalue complementarity problem
    • Niu, Y.S., Pham Dinh, T., Le Thi, H.A., Judice, J.: Efficient DC Programming Approaches for Asymmetric Eigenvalue Complementarity Problem. Optimization Methods and Software 28(4), 812-829 (2013)
    • (2013) Optimization Methods and Software , vol.28 , Issue.4 , pp. 812-829
    • Niu, Y.S.1    Pham Dinh, T.2    Le Thi, H.A.3    Judice, J.4
  • 34
    • 84890144494 scopus 로고    scopus 로고
    • A dc programming approach for a class of bilevel programming problems and its application in portfolio selection. naco numerical algebra
    • Le Thi, H.A., Pham Dinh, T., Tran Duc, Q.: A DC programming approach for a class of bilevel programming problems and its application in portfolio selection. NACO Numerical Algebra, Control and Optimization 2(1), 167-185 (2012)
    • (2012) Control and Optimization , vol.2 , Issue.1 , pp. 167-185
    • Le Thi, H.A.1    Pham Dinh, T.2    Tran Duc, Q.3
  • 35
    • 84880232279 scopus 로고    scopus 로고
    • Learning sparse classifiers with difference of convex functions algorithms
    • Cheng, S.O., Le Thi, H.A.: Learning sparse classifiers with Difference of Convex functions Algorithms. Optimization Methods and Software 28(4), 830-854 (2013).
    • (2013) Optimization Methods and Software , vol.28 , Issue.4 , pp. 830-854
    • Cheng, S.O.1    Le Thi, H.A.2
  • 36
    • 84887222892 scopus 로고    scopus 로고
    • An armijo-type method for pseudomonotone equilibrium problems and its applications
    • Anh, P.N., Le Thi, H.A.: An Armijo-type method for pseudomonotone equilibrium problems and its applications. Journal of Global Optimization 57, 803-820 (2013).
    • (2013) Journal of Global Optimization , vol.57 , pp. 803-820
    • Anh, P.N.1    Le Thi, H.A.2
  • 37
    • 85139379902 scopus 로고    scopus 로고
    • Long-Short Portfolio Optimization Under Cardinality Constraints by Difference of Convex Functions Algorithm. Journal of Optimization Theory & Applications, 26 pages
    • Le Thi, H.A., Moeini, M.: Long-Short Portfolio Optimization Under Cardinality Constraints by Difference of Convex Functions Algorithm. Journal of Optimization Theory & Applications, 26 pages (October 2012), doi:10.1007/s10957-012-0197-0.
    • (2012)
    • Le Thi, H.A.1    Moeini, M.2
  • 38
    • 84898912932 scopus 로고    scopus 로고
    • Solving the Multidimensional Assignment Problem by a Cross-Entropy method. Journal of Combinatorial Optimization, 16 pages (Online first
    • Nguyen, D.M., Le Thi, H.A., Pham Dinh, T.: Solving the Multidimensional Assignment Problem by a Cross-Entropy method. Journal of Combinatorial Optimization, 16 pages (Online first October 2012), doi:10.1007/s10878-012-9554-z.
    • (2012)
    • Nguyen, D.M.1    Le Thi, H.A.2    Pham Dinh, T.3
  • 39
    • 84885947360 scopus 로고    scopus 로고
    • A deterministic optimization approach for planning a multisensor multizone search for a target
    • Le Thi, H.A., Pham Dinh, T., Nguyen, D.M.: A deterministic optimization approach for planning a multisensor multizone search for a target. Computer & Operations Research 41, 231-239 (2014)
    • (2014) Computer &Amp; Operations Research , vol.41 , pp. 231-239
    • Le Thi, H.A.1    Pham Dinh, T.2    Nguyen, D.M.3
  • 40
    • 85116181899 scopus 로고    scopus 로고
    • The Subgradient Extragradient Method Ex tended to Equilibrium Problems, Optimization (online first
    • Anh, P.N., Le Thi, H.A.: The Subgradient Extragradient Method Ex tended to Equilibrium Problems, Optimization (online first December 2012), doi:10.1080/02331934.2012.745528
    • (2012)
    • Anh, P.N.1    Le Thi, H.A.2
  • 42
    • 84927655636 scopus 로고    scopus 로고
    • New and efficient algorithms for transfer prices and inventory holding policies in two-enterprise supply chains. Journal of Global Optimization (in press)
    • Le Thi, H.A., Tran Duc, Q.: New and efficient algorithms for transfer prices and inventory holding policies in two-enterprise supply chains. Journal of Global Optimization (in press)
    • Le Thi, H.A.1    Tran Duc, Q.2
  • 43
    • 84927641325 scopus 로고    scopus 로고
    • New and efficient DCA based algorithms for Minimum Sum-of-Squares Clustering. Pattern Recognition (in press)
    • Le Thi, H.A., Le Hoai, M., Pham Dinh, T.: New and efficient DCA based algorithms for Minimum Sum-of-Squares Clustering. Pattern Recognition (in press)
    • Le Thi, H.A.1    Le Hoai, M.2    Pham Dinh, T.3
  • 44
    • 84927602827 scopus 로고    scopus 로고
    • DC Programming and DCA for Binary Quadratic Programming in Diversity Data Mining. To appear in Optimization
    • Le Thi, H.A., Pham Dinh, T., Nguyen, C.N., Le Hoai, M.: DC Programming and DCA for Binary Quadratic Programming in Diversity Data Mining. To appear in Optimization
    • Le Thi, H.A.1    Pham Dinh, T.2    Nguyen, C.N.3    Le Hoai, M.4
  • 45
    • 84927629320 scopus 로고    scopus 로고
    • A Difference of Convex functions Algorithm for Optimal Scheduling and real-time assignment of preventive maintenance jobs on parallel processors. To appear in JIMO Journal of Industrial and Management Optimization
    • Le Thi, H.A., Tran Duc, Q., Adjallah, K.H.: A Difference of Convex functions Algorithm for Optimal Scheduling and real-time assignment of preventive maintenance jobs on parallel processors. To appear in JIMO Journal of Industrial and Management Optimization
    • Le Thi, H.A.1    Tran Duc, Q.2    Adjallah, K.H.3
  • 46
    • 84927594675 scopus 로고    scopus 로고
    • Optimizing a multi-stage production/inventory system by DC programming based approaches. Computational Optimization an Applications (in press)
    • An, L.T.H., Quynh, T.D.: Optimizing a multi-stage production/inventory system by DC programming based approaches. Computational Optimization an Applications (in press)
    • An, L.1    Quynh, T.D.2
  • 47
    • 84927593801 scopus 로고    scopus 로고
    • DCA based algorithms for Multiple Sequence Alignment (MSA). Central European Journal of Operations Research (in press)
    • An, L.T.H., Tao, P.D., Belghiti, T.: DCA based algorithms for Multiple Sequence Alignment (MSA). Central European Journal of Operations Research (in press).
    • An, L.1    Tao, P.D.2    Belghiti, T.3
  • 48
    • 84927629270 scopus 로고    scopus 로고
    • Recent advances in DC programming and DCA. To appear in Transactions on Computational Collective Intelligence, 37 pages
    • Tao, P.D., An, L.T.H.: Recent advances in DC programming and DCA. To appear in Transactions on Computational Collective Intelligence, 37 pages (2013)
    • (2013)
    • Tao, P.D.1    An, L.2
  • 49
    • 84927667327 scopus 로고    scopus 로고
    • DC programming in Communication Systems: challenging models and methods. To appear in Vietnam Journal of Computer Science, 21 pages. Springer (invited issue)
    • An, L.T.H., Tao, P.D.: DC programming in Communication Systems: challenging models and methods. To appear in Vietnam Journal of Computer Science, 21 pages. Springer (invited issue)
    • An, L.1    Tao, P.D.2
  • 50
    • 85192404349 scopus 로고    scopus 로고
    • Dc programming approaches for distance geometry problems
    • Mucherino, A., Lavor, C., Liberti, L., Maculan, N. (eds.), Springer
    • An, L.T.H., Tao, P.D.: DC programming approaches for Distance Geometry problems. In: Mucherino, A., Lavor, C., Liberti, L., Maculan, N. (eds.) Distance Geometry: Theory, Methods and Applications, vol. XVI, 57, 420 pages. Springer (2013)
    • (2013) Distance Geometry: Theory, Methods and Applications , vol.16 , Issue.57 , pp. 420
    • An, L.1    Tao, P.D.2
  • 52
    • 0032022704 scopus 로고    scopus 로고
    • Nonlinear wavelet image processing: Variational problems, compression, and noise removal through wavelet shrinkage
    • Chambolle, A., DeVore, R.A., Lee, N.Y., Lucier, B.J.: Nonlinear wavelet image processing: Variational problems, compression, and noise removal through wavelet shrinkage. IEEE Trans. Image Process. 7, 319-335 (1998)
    • (1998) IEEE Trans. Image Process , vol.7 , pp. 319-335
    • Chambolle, A.1    DeVore, R.A.2    Lee, N.Y.3    Lucier, B.J.4
  • 53
    • 85006564237 scopus 로고
    • Maximum likelihood from incomplete data via the em algorithm
    • Dempster, A.P., Laird, N.M., Rubin, D.B.: Maximum likelihood from incomplete data via the EM algorithm. J. Roy. Stat. Soc. B 39, 1-38 (1977)
    • (1977) J. Roy. Stat. Soc. B , vol.39 , pp. 1-38
    • Dempster, A.P.1    Laird, N.M.2    Rubin, D.B.3
  • 55
    • 44649149897 scopus 로고
    • Sequential quadratic programming
    • Bogg, P.T., Tolle, J.W.: Sequential Quadratic Programming. Acta Numerica, 1-51 (1995)
    • (1995) Acta Numerica , pp. 1-51
    • Bogg, P.T.1    Tolle, J.W.2
  • 57
    • 84927666850 scopus 로고    scopus 로고
    • Convex Analysis and Global Optimization. Kluwer Academic
    • Tuy, H.: Convex Analysis and Global Optimization. Kluwer Academic (2000).
    • (2000)
    • Tuy, H.1
  • 58
    • 0001556338 scopus 로고    scopus 로고
    • Nonlinear programming without a penalty function
    • Fletcher, R., Leyfer, S.: Nonlinear programming without a penalty function. Math. Program. 91, 239-270 (2002)
    • (2002) Math. Program , vol.91 , pp. 239-270
    • Fletcher, R.1    Leyfer, S.2
  • 59
    • 1542380919 scopus 로고    scopus 로고
    • Large scale molecular optimization from distance matrices by a d.C. optimization approach
    • An, L.T.H., Tao, P.D.: Large Scale Molecular Optimization From Distance Matrices by a D.C. Optimization Approach. SIAM Journal on Optimization 14(1), 77-116(2003)
    • (2003) SIAM Journal on Optimization , vol.14 , Issue.1 , pp. 77-116
    • An, L.1    Tao, P.D.2
  • 60
    • 15244346000 scopus 로고    scopus 로고
    • The dc (Difference of convex functions) programming and dca revisited with dc models of real world nonconvex optimization problems
    • An, L.T.H., Tao, P.D.: The DC (Difference of Convex functions) Programming and DCA revisited with DC models of real world nonconvex optimization problems. Annals of Operations Research 133, 23-46 (2005)
    • (2005) Annals of Operations Research , vol.133 , pp. 23-46
    • An, L.1    Tao, P.D.2
  • 62
    • 0035600660 scopus 로고    scopus 로고
    • A computationally efficient feasible sequential quadratic programming algorithm
    • Lawrence, C.T., Tits, A.: A computationally efficient feasible sequential quadratic programming algorithm. SIAM J. Optim. 11, 1092-1118 (2001)
    • (2001) SIAM J. Optim , vol.11 , pp. 1092-1118
    • Lawrence, C.T.1    Tits, A.2
  • 63
    • 49949133603 scopus 로고
    • The fritz john necessay optimality conditions in the presence of equality constraints
    • Mangasarian, O.L., Fromovitz, S.: The Fritz John necessay optimality conditions in the presence of equality constraints. J. Math. Anal. Appl. 17, 34-47 (1967).
    • (1967) J. Math. Anal. Appl , vol.17 , pp. 34-47
    • Mangasarian, O.L.1    Fromovitz, S.2
  • 66
    • 0038878813 scopus 로고    scopus 로고
    • Exact penalty functions for mathematical programs with linear complementary constraints
    • Pang, J.-S.: Exact penalty functions for mathematical programs with linear complementary constraints. Optimization 42, 1-8 (1997)
    • (1997) Optimization , vol.42 , pp. 1-8
    • Pang, J.-S.1
  • 67
    • 84927624346 scopus 로고    scopus 로고
    • Optimization. Springer. New York
    • Polak, E.: Optimization. Springer. New York (1997)
    • (1997)
    • Polak, E.1
  • 68
    • 84927588673 scopus 로고
    • Convex Analysis. Princeton University Press
    • Rockafellar, R.T.: Convex Analysis. Princeton University Press (1970)
    • (1970)
    • Rockafellar, R.T.1
  • 69
    • 84936632376 scopus 로고
    • Penalty methods and augmanted lagrangians nonlinear programming
    • In: Conti, R., Ruberti, A. (eds.), Springer, Heidelberg
    • Rockafellar, R.T.: Penalty methods and augmanted Lagrangians nonlinear programming. In: Conti, R., Ruberti, A. (eds.) 5th Conference on Optimization Techniques Part I. LNCS, vol. 3, pp. 418-425. Springer, Heidelberg (1973)
    • (1973) Conference on Optimization Techniques Part I. LNCS , vol.3 , pp. 418-425
    • Rockafellar, R.T.1
  • 71
    • 4043068448 scopus 로고    scopus 로고
    • On the sequential quadratically constrained quadratic programming methods. Mathematics of oper
    • Solodov, M.V.: On the sequential quadratically constrained quadratic programming methods. Mathematics of Oper. Research 29, 64-79 (2004)
    • (2004) Research , vol.29 , pp. 64-79
    • Solodov, M.V.1
  • 72
    • 33144473914 scopus 로고    scopus 로고
    • A sufficient condition for exact penalty constrained optimization. Siam
    • Zaslavski, A.J.: A sufficient condition for exact penalty constrained optimization. SIAM J. Optim. 16, 250-262 (2005)
    • (2005) J. Optim , vol.16 , pp. 250-262
    • Zaslavski, A.J.1
  • 73
    • 0037686659 scopus 로고    scopus 로고
    • The concave-convex procedure
    • Yuille, A.L., Rangarajan, A.: The concave-convex procedure. Neural Computation 15(4), 915-936 (2003)
    • (2003) Neural Computation , vol.15 , Issue.4 , pp. 915-936
    • Yuille, A.L.1    Rangarajan, A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.