메뉴 건너뛰기




Volumn 18, Issue 4, 2007, Pages 1326-1350

Exact regularization of convex programs

Author keywords

Conic program; Convex program; Degeneracy; Exact penalization; Interior point algorithms; Lagrange multiplier; Linear program; Regularization; Sparse solutions

Indexed keywords

CONIC PROGRAM; CONVEX PROGRAM; DEGENERACY; EXACT PENALIZATION; INTERIOR-POINT ALGORITHMS; LINEAR PROGRAM; REGULARIZATION; SPARSE SOLUTIONS;

EID: 56749091502     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/060675320     Document Type: Article
Times cited : (97)

References (48)
  • 1
    • 0033296703 scopus 로고    scopus 로고
    • Regularized symmetric indefinite systems in interior point methods for linear and quadratic optimization
    • A. ALTMAN AND J. GONDZIO, Regularized symmetric indefinite systems in interior point methods for linear and quadratic optimization, Optim. Methods Softw., 11 (1999), pp. 275-302.
    • (1999) Optim. Methods Softw , vol.11 , pp. 275-302
    • ALTMAN, A.1    GONDZIO, J.2
  • 2
    • 84898952043 scopus 로고    scopus 로고
    • Computing regularization paths for learning multiple kernels
    • L. Saul, Y. Weiss, and L. Bottou, eds, Morgan Kaufmann, San Mateo, CA
    • F. R. BACH, R. THIBAUX, AND M. I. JORDAN, Computing regularization paths for learning multiple kernels, in Advances in Neural Information Processing Systems (NIPS) 17, L. Saul, Y. Weiss, and L. Bottou, eds., Morgan Kaufmann, San Mateo, CA, 2005.
    • (2005) Advances in Neural Information Processing Systems (NIPS) , vol.17
    • BACH, F.R.1    THIBAUX, R.2    JORDAN, M.I.3
  • 3
    • 0347242385 scopus 로고    scopus 로고
    • Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications
    • SIAM, Philadelphia
    • A. BEN-TAL AND A. NEMIROVSKI, Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications, MPS/SIAM Ser. Optim. 2, SIAM, Philadelphia, 2001.
    • (2001) MPS/SIAM Ser. Optim , vol.2
    • BEN-TAL, A.1    NEMIROVSKI, A.2
  • 4
    • 0016536931 scopus 로고
    • Necessary and sufficient conditions for a penalty method to be exact
    • D. P. BERTSEKAS, Necessary and sufficient conditions for a penalty method to be exact, Math. Programming, 9 (1975), pp. 87-99.
    • (1975) Math. Programming , vol.9 , pp. 87-99
    • BERTSEKAS, D.P.1
  • 6
    • 0041544835 scopus 로고    scopus 로고
    • A note on error bounds for convex and nonconvex programs
    • D. P. BERTSEKAS, A note on error bounds for convex and nonconvex programs, Comput. Optim. Appl., 12 (1999), pp. 41-51.
    • (1999) Comput. Optim. Appl , vol.12 , pp. 41-51
    • BERTSEKAS, D.P.1
  • 9
    • 0026190240 scopus 로고
    • An exact penalization viewpoint of constrained optimization
    • J. V. BURKE, An exact penalization viewpoint of constrained optimization, SIAM J. Control Optim., 29 (1991), pp. 968-998.
    • (1991) SIAM J. Control Optim , vol.29 , pp. 968-998
    • BURKE, J.V.1
  • 11
    • 0027656872 scopus 로고
    • Weak sharp minima in mathematical programming
    • J. V. BURKE AND M. C. FERRIS, Weak sharp minima in mathematical programming, SIAM J. Control Optim., 31 (1993), pp. 1340-1359.
    • (1993) SIAM J. Control Optim , vol.31 , pp. 1340-1359
    • BURKE, J.V.1    FERRIS, M.C.2
  • 12
    • 33745604236 scopus 로고    scopus 로고
    • Stable signal recovery from incomplete and inaccurate measurements
    • E. J. CANDES, J. ROMBERG, AND T. TAO, Stable signal recovery from incomplete and inaccurate measurements, Comm. Pure Appl. Math., 59 (2006), pp. 1207-1223.
    • (2006) Comm. Pure Appl. Math , vol.59 , pp. 1207-1223
    • CANDES, E.J.1    ROMBERG, J.2    TAO, T.3
  • 13
    • 31744440684 scopus 로고    scopus 로고
    • Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information
    • E. J. CANDÉS, J. ROMBERG, AND T. TAO, Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information, IEEE Trans. Inform. Theory, 52 (2006), pp. 489-509.
    • (2006) IEEE Trans. Inform. Theory , vol.52 , pp. 489-509
    • CANDÉS, E.J.1    ROMBERG, J.2    TAO, T.3
  • 14
    • 0035273106 scopus 로고    scopus 로고
    • Atomic decomposition by basis pursuit
    • S. S. CHEN, D. L. DONOHO, AND M. A. SAUNDERS, Atomic decomposition by basis pursuit, SIAM Rev., 43 (2001), pp. 129-159.
    • (2001) SIAM Rev , vol.43 , pp. 129-159
    • CHEN, S.S.1    DONOHO, D.L.2    SAUNDERS, M.A.3
  • 17
    • 33144483155 scopus 로고    scopus 로고
    • Stable recovery of sparse overcomplete representations in the presence of noise
    • D. L. DONOHO, M. ELAD, AND V. TEMLYAKOV, Stable recovery of sparse overcomplete representations in the presence of noise, IEEE Trans. Inform. Theory, 52 (2006), pp. 6-18.
    • (2006) IEEE Trans. Inform. Theory , vol.52 , pp. 6-18
    • DONOHO, D.L.1    ELAD, M.2    TEMLYAKOV, V.3
  • 18
    • 22144488449 scopus 로고    scopus 로고
    • Sparse nonnegative solution of underdetermined linear equations by linear programming
    • D. L. DONOHO AND J. TANNER, Sparse nonnegative solution of underdetermined linear equations by linear programming, Proc. Natl. Acad. Sci. USA, 102 (2005), pp. 9446-9451.
    • (2005) Proc. Natl. Acad. Sci. USA , vol.102 , pp. 9446-9451
    • DONOHO, D.L.1    TANNER, J.2
  • 20
    • 0043030977 scopus 로고
    • Finite perturbation of convex programs
    • M. C. FERRIS AND O. L. MANGASARIAN, Finite perturbation of convex programs, Appl. Math. Optim., 23 (1991), pp. 263-273.
    • (1991) Appl. Math. Optim , vol.23 , pp. 263-273
    • FERRIS, M.C.1    MANGASARIAN, O.L.2
  • 21
    • 0003079262 scopus 로고
    • 1 penalty method for nonlinear constraints
    • P. T. Boggs, R. H. Byrd, and R. B. Schnabel, eds, SIAM, Philadelphia
    • 1 penalty method for nonlinear constraints, in Numerical Optimization, 1984, P. T. Boggs, R. H. Byrd, and R. B. Schnabel, eds., SIAM, Philadelphia, 1985, pp. 26-40.
    • (1985) Numerical Optimization, 1984 , pp. 26-40
    • FLETCHER, R.1
  • 23
    • 33645485197 scopus 로고    scopus 로고
    • Generation of Degenerate Linear Programming Problems
    • Tech. report, Department of Mathematics, Federal University of Santa Catarina, Santa Catarina, Brazil
    • C. C. GONZAGA, Generation of Degenerate Linear Programming Problems, Tech. report, Department of Mathematics, Federal University of Santa Catarina, Santa Catarina, Brazil, 2003.
    • (2003)
    • GONZAGA, C.C.1
  • 24
    • 34250270048 scopus 로고
    • Exact penalty functions in nonlinear programming
    • S.-P. HAN AND O. L. MANGASARIAN, Exact penalty functions in nonlinear programming, Math. Programming, 17 (1979), pp. 251-269.
    • (1979) Math. Programming , vol.17 , pp. 251-269
    • HAN, S.-P.1    MANGASARIAN, O.L.2
  • 25
    • 0037287439 scopus 로고    scopus 로고
    • On the minimum norm solution of linear programs
    • C. KANZOW, H. QI, AND L. QI, On the minimum norm solution of linear programs, J. Optim. Theory Appl., 116 (2003), pp. 333-345.
    • (2003) J. Optim. Theory Appl , vol.116 , pp. 333-345
    • KANZOW, C.1    QI, H.2    QI, L.3
  • 26
    • 0011629799 scopus 로고
    • A finite algorithm for the least two-norm solution of a linear program
    • S. LUCIDI, A finite algorithm for the least two-norm solution of a linear program, Optimization, 18 (1987), pp. 809-823.
    • (1987) Optimization , vol.18 , pp. 809-823
    • LUCIDI, S.1
  • 27
    • 0023434930 scopus 로고
    • A new result in the theory and computation of the least-norm solution of a linear program
    • S. LUCIDI, A new result in the theory and computation of the least-norm solution of a linear program, J. Optim. Theory Appl., 55 (1987), pp. 103-117.
    • (1987) J. Optim. Theory Appl , vol.55 , pp. 103-117
    • LUCIDI, S.1
  • 28
    • 0028524430 scopus 로고
    • Error bounds for analytic systems and their applications
    • Z.-Q. LUO AND J.-S. PANG, Error bounds for analytic systems and their applications, Math. Programming, 67 (1994), pp. 1-28.
    • (1994) Math. Programming , vol.67 , pp. 1-28
    • LUO, Z.-Q.1    PANG, J.-S.2
  • 29
    • 56749121917 scopus 로고    scopus 로고
    • Z.-Q. LUO AND J.-S. PANG, eds., Error bounds in mathematical programming, Math. Program., 88 (2000), pp. 221-410.
    • Z.-Q. LUO AND J.-S. PANG, eds., Error bounds in mathematical programming, Math. Program., 88 (2000), pp. 221-410.
  • 30
    • 0020873291 scopus 로고
    • Normal solutions of linear programs
    • O. L. MANGASARIAN, Normal solutions of linear programs, Math. Programming Stud., 22 (1984), pp. 206-216.
    • (1984) Math. Programming Stud , vol.22 , pp. 206-216
    • MANGASARIAN, O.L.1
  • 31
    • 0021873712 scopus 로고
    • Sufficiency of exact penalty minimization
    • O. L. MANGASARIAN, Sufficiency of exact penalty minimization, SIAM J. Control Optim., 23 (1985), pp. 30-37.
    • (1985) SIAM J. Control Optim , vol.23 , pp. 30-37
    • MANGASARIAN, O.L.1
  • 32
    • 0023960693 scopus 로고
    • A simple characterization of solution sets of convex programs
    • O. L. MANGASARIAN, A simple characterization of solution sets of convex programs, Oper. Res. Lett., 7 (1988), pp. 21-26.
    • (1988) Oper. Res. Lett , vol.7 , pp. 21-26
    • MANGASARIAN, O.L.1
  • 33
    • 4043182563 scopus 로고    scopus 로고
    • A Newton method for linear programming
    • O. L. MANGASARIAN, A Newton method for linear programming, J. Optim. Theory Appl., 121 (2004), pp. 1-18.
    • (2004) J. Optim. Theory Appl , vol.121 , pp. 1-18
    • MANGASARIAN, O.L.1
  • 34
    • 0018543889 scopus 로고
    • Nonlinear perturbation of linear programs
    • O. L. MANGASARIAN AND R. R. MEYER, Nonlinear perturbation of linear programs, SIAM J. Control Optim., 17 (1979), pp. 745-752.
    • (1979) SIAM J. Control Optim , vol.17 , pp. 745-752
    • MANGASARIAN, O.L.1    MEYER, R.R.2
  • 36
  • 38
    • 0005366663 scopus 로고    scopus 로고
    • A Mathematical View of Interior-Point Methods in Convex Optimization
    • SIAM, Philadelphia
    • J. RENEGAR, A Mathematical View of Interior-Point Methods in Convex Optimization, MPS/SIAM Ser. Optim. 3, SIAM, Philadelphia, 2001.
    • (2001) MPS/SIAM Ser. Optim , vol.3
    • RENEGAR, J.1
  • 39
    • 0020901152 scopus 로고
    • Local structure of feasible sets in nonlinear programming
    • S. M. ROBINSON, Local structure of feasible sets in nonlinear programming. II. Nondegeneracy, Math. Programming Stud., 22 (1984), pp. 217-230.
    • (1984) II. Nondegeneracy, Math. Programming Stud , vol.22 , pp. 217-230
    • ROBINSON, S.M.1
  • 40
    • 0004267646 scopus 로고
    • Princeton University Press, Princeton, NJ
    • R. T. ROCKAFELLAR, Convex Analysis, Princeton University Press, Princeton, NJ, 1970.
    • (1970) Convex Analysis
    • ROCKAFELLAR, R.T.1
  • 41
    • 2142722218 scopus 로고    scopus 로고
    • On the statistical analysis of smoothing by maximizing dirty Markov random field posterior distributions
    • S. SARDY AND P. TSENG, On the statistical analysis of smoothing by maximizing dirty Markov random field posterior distributions, J. Amer. Statist. Assoc., 99 (2004), pp. 191-204.
    • (2004) J. Amer. Statist. Assoc , vol.99 , pp. 191-204
    • SARDY, S.1    TSENG, P.2
  • 42
    • 0039169750 scopus 로고    scopus 로고
    • Cholesky-based methods for sparse least squares: The benefits of regularization
    • L. Adams and J. L. Nazareth, eds, SIAM, Philadelphia
    • M. A. SAUNDERS, Cholesky-based methods for sparse least squares: The benefits of regularization, in Linear and Nonlinear Conjugate Gradient-Related Methods, L. Adams and J. L. Nazareth, eds., SIAM, Philadelphia, 1996, pp. 92-100.
    • (1996) Linear and Nonlinear Conjugate Gradient-Related Methods , pp. 92-100
    • SAUNDERS, M.A.1
  • 43
    • 56749140643 scopus 로고    scopus 로고
    • J. F. STURM, Using Sedumi 1.02, a Matlab Toolbox for Optimization over Symmetric Cones (updated for Version 1.05), Tech. report, Department of Econometrics, Tilburg University, Tilburg, The Netherlands, 2001.
    • J. F. STURM, Using Sedumi 1.02, a Matlab Toolbox for Optimization over Symmetric Cones (updated for Version 1.05), Tech. report, Department of Econometrics, Tilburg University, Tilburg, The Netherlands, 2001.
  • 44
    • 0001287271 scopus 로고    scopus 로고
    • Regression shrinkage and selection via the Lasso
    • R. TIBSHIRANI, Regression shrinkage and selection via the Lasso, J. Roy. Statist. Soc. Ser. B, 58 (1996), pp. 267-288.
    • (1996) J. Roy. Statist. Soc. Ser. B , vol.58 , pp. 267-288
    • TIBSHIRANI, R.1
  • 46
    • 0242711330 scopus 로고    scopus 로고
    • On error bounds for lower semicontinuous functions
    • Z. WU AND J. J. YE, On error bounds for lower semicontinuous functions, Math. Program., 92 (2002), pp. 301-314.
    • (2002) Math. Program , vol.92 , pp. 301-314
    • WU, Z.1    YE, J.J.2
  • 48
    • 0036436108 scopus 로고    scopus 로고
    • Locating the least 2-norm solution of linear programs via a path-following method
    • Y.-B. ZHAO AND D. LI, Locating the least 2-norm solution of linear programs via a path-following method, SIAM J. Optim., 12 (2002), pp. 893-912.
    • (2002) SIAM J. Optim , vol.12 , pp. 893-912
    • ZHAO, Y.-B.1    LI, D.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.