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Volumn 16, Issue 1, 2006, Pages 146-169

An infeasible bundle method for nonsmooth convex constrained optimization without a penalty function or a filter

Author keywords

Bundle methods; Constrained optimization; Nonsmooth convex optimization

Indexed keywords

ALGORITHMS; ESTIMATION; OPTIMIZATION; PARAMETER ESTIMATION;

EID: 33144461315     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/040603875     Document Type: Article
Times cited : (74)

References (39)
  • 1
    • 0020702681 scopus 로고
    • Numerical methods for nondifferentiable convex optimization
    • A. AUSLENDER, Numerical methods for nondifferentiable convex optimization, Math. Programming Stud., 30 (1987), pp. 102-126.
    • (1987) Math. Programming Stud. , vol.30 , pp. 102-126
    • Auslender, A.1
  • 4
    • 0002921768 scopus 로고
    • Decay to uniform states in ecological interactions
    • P.N. BROWN, Decay to uniform states in ecological interactions, SIAM J. Appl. Math., 38 (1980), pp. 22-37.
    • (1980) SIAM J. Appl. Math. , vol.38 , pp. 22-37
    • Brown, P.N.1
  • 5
    • 0001106044 scopus 로고    scopus 로고
    • Proximal quasi-Newton methods for nondifferentiable convex optimization
    • X. CHEN AND M. FUKUSHIMA, Proximal quasi-Newton methods for nondifferentiable convex optimization, Math. Program., 85 (1999), pp. 313-334.
    • (1999) Math. Program. , vol.85 , pp. 313-334
    • Chen, X.1    Fukushima, M.2
  • 6
    • 0000882113 scopus 로고
    • Newton's method for convex programming and Tchebycheff approximations
    • E. CHENEY AND A. GOLDSTEIN, Newton's method for convex programming and Tchebycheff approximations, Numer. Math., 1 (1959), pp. 253-268.
    • (1959) Numer. Math. , vol.1 , pp. 253-268
    • Cheney, E.1    Goldstein, A.2
  • 7
    • 33646971357 scopus 로고
    • Convergence of some algorithms for convex minimization
    • R. CORREA AND C. LEMARÉCHAL, Convergence of some algorithms for convex minimization, Math. Program., 62 (1993), pp. 261-275.
    • (1993) Math. Program. , vol.62 , pp. 261-275
    • Correa, R.1    Lemaréchal, C.2
  • 8
    • 0742308730 scopus 로고    scopus 로고
    • A bundle filter method for nonsmooth nonlinear optimization
    • Department of Mathematics, The University of Dundee, Scotland
    • R. FLETCHER AND S. LEYFFER, A Bundle Filter Method for Nonsmooth Nonlinear Optimization, Numerical Analysis Report NA/195, Department of Mathematics, The University of Dundee, Scotland, 1999.
    • (1999) Numerical Analysis Report , vol.NA-195
    • Fletcher, R.1    Leyffer, S.2
  • 9
    • 0001556338 scopus 로고    scopus 로고
    • Nonlinear programming without a penalty function
    • R. FLETCHER AND S. LEYFFER, Nonlinear programming without a penalty function, Math. Program., 91 (2002), pp. 239-269.
    • (2002) Math. Program. , vol.91 , pp. 239-269
    • Fletcher, R.1    Leyffer, S.2
  • 10
    • 0030284068 scopus 로고    scopus 로고
    • Solving semidefinite quadratic optimization problems within nonsmooth optimization problems
    • A. FRANGIONI, Solving semidefinite quadratic optimization problems within nonsmooth optimization problems, Comput. Oper. Res., 23 (1996), pp. 1099-1118.
    • (1996) Comput. Oper. Res. , vol.23 , pp. 1099-1118
    • Frangioni, A.1
  • 11
    • 0037289034 scopus 로고    scopus 로고
    • Generalized bundle methods
    • A. FRANGIONI, Generalized bundle methods, SIAM J. Optim., 13 (2002), pp. 117-156.
    • (2002) SIAM J. Optim. , vol.13 , pp. 117-156
    • Frangioni, A.1
  • 12
    • 0000949338 scopus 로고
    • Decomposition and nondifferentiable optimization with the projective algorithm
    • J.L. GOFFIN, A. HAURIE, AND J. PH. VIAL, Decomposition and nondifferentiable optimization with the projective algorithm, Management Sci., 38 (1992), pp. 284-302.
    • (1992) Management Sci. , vol.38 , pp. 284-302
    • Goffin, J.L.1    Haurie, A.2    Vial, J.P.H.3
  • 13
    • 0035546512 scopus 로고    scopus 로고
    • A proximal bundle method based on approximate subgradients
    • M. HINTERMÜLLER, A proximal bundle method based on approximate subgradients, Comput. Optim. Appl., 20 (2001), pp. 245-266.
    • (2001) Comput. Optim. Appl. , vol.20 , pp. 245-266
    • Hintermüller, M.1
  • 14
    • 0003316862 scopus 로고
    • Convex analysis and minimization algorithms
    • 2 Vols., Springer-Verlag, Berlin
    • J.-B. HIRIART-URRUTY AND C. LEMARÉCHAL, Convex Analysis and Minimization Algorithms, 2 Vols., Grund. der Math. Wiss. 305-306, Springer-Verlag, Berlin, 1993.
    • (1993) Grund. der Math. Wiss. , vol.305-306
    • Hiriart-Urruty, J.-B.1    Lemaréchal, C.2
  • 15
    • 0003296427 scopus 로고
    • Test examples for nonlinear programming codes
    • Springer-Verlag, Berlin
    • W. HOCK AND K. SCHITTKOWSKI, Test Examples for Nonlinear Programming Codes, Lecture Notes in Econ. Math. Syst. 187, Springer-Verlag, Berlin, 1981.
    • (1981) Lecture Notes in Econ. Math. Syst. , vol.187
    • Hock, W.1    Schittkowski, K.2
  • 16
    • 0001547779 scopus 로고
    • The cutting-plane method for solving convex programs
    • J.E. KELLEY, Jr., The cutting-plane method for solving convex programs, J. Soc. Indust. Appl. Math., 8 (1960), pp. 703-712.
    • (1960) J. Soc. Indust. Appl. Math. , vol.8 , pp. 703-712
    • Kelley Jr., J.E.1
  • 17
    • 0003296464 scopus 로고
    • Methods of descent for nondifferentiable optimization
    • Springer-Verlag, Berlin
    • K.C. KIWIEL, Methods of Descent for Nondifferentiable Optimization, Lecture Notes in Math. 1133, Springer-Verlag, Berlin, 1985.
    • (1985) Lecture Notes in Math. , vol.1133
    • Kiwiel, K.C.1
  • 18
    • 0000135467 scopus 로고
    • An exact penalty function algorithm for nonsmooth convex constrained minimization problems
    • K.C. KIWIEL, An exact penalty function algorithm for nonsmooth convex constrained minimization problems, IMA J. Numer. Anal., 5 (1985), pp. 111-119.
    • (1985) IMA J. Numer. Anal. , vol.5 , pp. 111-119
    • Kiwiel, K.C.1
  • 19
    • 0001260166 scopus 로고
    • A method for solving certain quadratic programming problems arising in non smooth optimization
    • K.C. KIWIEL, A method for solving certain quadratic programming problems arising in non smooth optimization, IMA J. Numer. Anal., 6 (1986), pp. 137-152.
    • (1986) IMA J. Numer. Anal. , vol.6 , pp. 137-152
    • Kiwiel, K.C.1
  • 20
    • 0000695140 scopus 로고
    • A constraint linearization method for nondifferentiable convex minimization
    • K.C. KIWIEL, A constraint linearization method for nondifferentiable convex minimization, Numer. Math., 51 (1987), pp. 395-414.
    • (1987) Numer. Math. , vol.51 , pp. 395-414
    • Kiwiel, K.C.1
  • 21
    • 0023578135 scopus 로고
    • A subgradient selection method for minimizing convex functions subject to linear constraints
    • K.C. KIWIEL, A subgradient selection method for minimizing convex functions subject to linear constraints, Computing, 39 (1987), pp. 293-305.
    • (1987) Computing , vol.39 , pp. 293-305
    • Kiwiel, K.C.1
  • 22
    • 0025208765 scopus 로고
    • Proximity control in bundle methods for convex nondifferentiable minimization
    • K.C. KIWIEL, Proximity control in bundle methods for convex nondifferentiable minimization, Math. Program., 46 (1990), pp. 105-122.
    • (1990) Math. Program. , vol.46 , pp. 105-122
    • Kiwiel, K.C.1
  • 23
    • 34249923238 scopus 로고
    • Exact penalty functions in proximal bundle methods for constrained convex non-differentiable minimization
    • K.C. KIWIEL, Exact penalty functions in proximal bundle methods for constrained convex non-differentiable minimization, Math. Program., 52 (1991), pp. 285-302.
    • (1991) Math. Program. , vol.52 , pp. 285-302
    • Kiwiel, K.C.1
  • 24
    • 0011282601 scopus 로고
    • A set of nonsmooth optimization test problems
    • C. Lemaréchal and R. Mifflin, eds., Pergamon Press, Oxford
    • C. LEMARÉCHAL AND R. MIFFLIN, A set of nonsmooth optimization test problems in Nonsmooth Optimization, C. Lemaréchal and R. Mifflin, eds., Pergamon Press, Oxford, 1978, pp. 151-165.
    • (1978) Nonsmooth Optimization , pp. 151-165
    • Lemaréchal, C.1    Mifflin, R.2
  • 26
    • 0000275440 scopus 로고    scopus 로고
    • Variable metric bundle methods: From conceptual to implementable forms
    • C. LEMARÉCHAL AND C. SAGASTIZÁBAL, Variable metric bundle methods: From conceptual to implementable forms, Math. Program., 76 (1997), pp. 393-410.
    • (1997) Math. Program. , vol.76 , pp. 393-410
    • Lemaréchal, C.1    Sagastizábal, C.2
  • 27
    • 0033245906 scopus 로고    scopus 로고
    • Globally convergent variable metric method for convex nonsmooth unconstrained optimization
    • L. LUKŠAN AND J. VLČEK, Globally convergent variable metric method for convex nonsmooth unconstrained optimization, J. Optim. Theory Appl., 102 (1999), pp. 593-613.
    • (1999) J. Optim. Theory Appl. , vol.102 , pp. 593-613
    • Lukšan, L.1    Vlček, J.2
  • 29
    • 0000009213 scopus 로고
    • An algorithm for constrained optimization with semismooth functions
    • R. MIFFLIN, An algorithm for constrained optimization with semismooth functions, Math. Oper. Res., 2 (1977), pp. 191-207.
    • (1977) Math. Oper. Res. , vol.2 , pp. 191-207
    • Mifflin, R.1
  • 30
    • 0003108675 scopus 로고
    • A modification and extension of Lemarechal's algorithm for nonsmooth minimization
    • R. MIFFLIN, A modification and extension of Lemarechal's algorithm for nonsmooth minimization, Math. Programming Stud., 17 (1982), pp. 77-90.
    • (1982) Math. Programming Stud. , vol.17 , pp. 77-90
    • Mifflin, R.1
  • 31
    • 0020752069 scopus 로고
    • A superlinearly convergent algorithm for one-dimensional constrained minimization problems with convex functions
    • R. MIFFLIN, A superlinearly convergent algorithm for one-dimensional constrained minimization problems with convex functions, Math. Oper. Res., 8 (1983), pp. 185-195.
    • (1983) Math. Oper. Res. , vol.8 , pp. 185-195
    • Mifflin, R.1
  • 32
    • 0001844687 scopus 로고    scopus 로고
    • A quasi-second-order proximal bundle algorithm
    • R. MIFFLIN, A quasi-second-order proximal bundle algorithm, Math. Program., 73 (1996), pp. 51-72.
    • (1996) Math. Program. , vol.73 , pp. 51-72
    • Mifflin, R.1
  • 33
    • 0002364867 scopus 로고
    • Rate of convergence of a class of methods of feasible directions
    • O. PIRONNEAU AND E. POLAK, Rate of convergence of a class of methods of feasible directions, SIAM J. Numer. Anal., 10 (1973), pp. 161-174.
    • (1973) SIAM J. Numer. Anal. , vol.10 , pp. 161-174
    • Pironneau, O.1    Polak, E.2
  • 35
    • 0036554469 scopus 로고    scopus 로고
    • Dynamical adjustment of the prox-parameter in bundle methods
    • P. REY AND C. SAGASTIZÁBAL, Dynamical adjustment of the prox-parameter in bundle methods, Optimization, 51 (2002), pp. 423-447.
    • (2002) Optimization , vol.51 , pp. 423-447
    • Rey, P.1    Sagastizábal, C.2
  • 36
    • 0000091855 scopus 로고
    • A version of the bundle idea for minimizing a nonsmooth function: Conceptual idea, convergence analysis, numerical results
    • H. SCHRAMM AND J. ZOWE, A version of the bundle idea for minimizing a nonsmooth function: Conceptual idea, convergence analysis, numerical results, SIAM J. Optim., 2 (1992), pp. 121-152.
    • (1992) SIAM J. Optim. , vol.2 , pp. 121-152
    • Schramm, H.1    Zowe, J.2
  • 38
    • 0345374653 scopus 로고    scopus 로고
    • On approximations with finite precision in bundle methods for nonsmooth optimization
    • M.V. SOLODOV, On approximations with finite precision in bundle methods for nonsmooth optimization, J. Optim. Theory Appl., 119 (2003), pp. 151-165.
    • (2003) J. Optim. Theory Appl. , vol.119 , pp. 151-165
    • Solodov, M.V.1


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