메뉴 건너뛰기




Volumn 35, Issue 2, 2016, Pages 475-499

A derivative-free trust-region algorithm for composite nonsmooth optimization

Author keywords

Derivative free optimization; Global convergence; Nonlinear programming; Nonsmooth optimization; Trust region methods; Worst case complexity

Indexed keywords

PROBLEM SOLVING;

EID: 84975865317     PISSN: 22383603     EISSN: 18070302     Source Type: Journal    
DOI: 10.1007/s40314-014-0201-4     Document Type: Article
Times cited : (32)

References (42)
  • 1
    • 33750265086 scopus 로고    scopus 로고
    • Mesh adaptive direct search algorithms for constrained optimization
    • Audet C, Dennis JE Jr (2006) Mesh adaptive direct search algorithms for constrained optimization. SIAM J Optim 17:188–217
    • (2006) SIAM J Optim , vol.17 , pp. 188-217
    • Audet, C.1    Dennis, J.E.2
  • 2
    • 43949152558 scopus 로고
    • A trust region algorithm for nonsmooth optimization
    • Bannert T (1994) A trust region algorithm for nonsmooth optimization. Math Program 67:247–264
    • (1994) Math Program , vol.67 , pp. 247-264
    • Bannert, T.1
  • 4
    • 84880062235 scopus 로고    scopus 로고
    • Inexact restoration method for derivative-free optimization with smooth constraints
    • Bueno LF, Friedlander A, Martínez JM, Sobral FNC (2013) Inexact restoration method for derivative-free optimization with smooth constraints. SIAM J Optim 23:1189–1213
    • (2013) SIAM J Optim , vol.23 , pp. 1189-1213
    • Bueno, L.F.1    Friedlander, A.2    Martínez, J.M.3    Sobral, F.N.C.4
  • 5
    • 81255179401 scopus 로고    scopus 로고
    • Adaptive cubic regularisation methods for unconstrained optimization. Part II: worst-case function—and derivative—evaluation complexity
    • Cartis C, Gould NIM, Toint PhL (2011a) Adaptive cubic regularisation methods for unconstrained optimization. Part II: worst-case function—and derivative—evaluation complexity. Math Program 130:295–319
    • (2011) Math Program , vol.130 , pp. 295-319
    • Cartis, C.1    Gould, N.I.M.2    Toint, P.L.3
  • 6
    • 84856057771 scopus 로고    scopus 로고
    • On the evaluation complexity of composite function minimization with applications to nonconvex nonlinear programming
    • Cartis C, Gould NIM, Toint PhL (2011b) On the evaluation complexity of composite function minimization with applications to nonconvex nonlinear programming. SIAM J Optim 21:1721–1739
    • (2011) SIAM J Optim , vol.21 , pp. 1721-1739
    • Cartis, C.1    Gould, N.I.M.2    Toint, P.L.3
  • 7
    • 84861621132 scopus 로고    scopus 로고
    • On the oracle complexity of first-order and derivative-free algorithms for smooth nonconvex minimization
    • Cartis C, Gould NIM, Toint PhL (2012) On the oracle complexity of first-order and derivative-free algorithms for smooth nonconvex minimization. SIAM J Optim 22:66–86
    • (2012) SIAM J Optim , vol.22 , pp. 66-86
    • Cartis, C.1    Gould, N.I.M.2    Toint, P.L.3
  • 8
    • 84886236255 scopus 로고    scopus 로고
    • On the evaluation complexity of cubic regularization methods for potentially rank-deficient nonlinear least-squares problems and its relevance to constrained nonlinear optimization
    • Cartis C, Gould NIM, Toint PhL (2013) On the evaluation complexity of cubic regularization methods for potentially rank-deficient nonlinear least-squares problems and its relevance to constrained nonlinear optimization. SIAM J Optim 23:1553–1574
    • (2013) SIAM J Optim , vol.23 , pp. 1553-1574
    • Cartis, C.1    Gould, N.I.M.2    Toint, P.L.3
  • 9
    • 84897112534 scopus 로고    scopus 로고
    • On the complexity of finding first-order critical points in constrained nonlinear optimization
    • Cartis C, Gould NIM, Toint PhL (2014) On the complexity of finding first-order critical points in constrained nonlinear optimization. Math Program 144:93–106
    • (2014) Math Program , vol.144 , pp. 93-106
    • Cartis, C.1    Gould, N.I.M.2    Toint, P.L.3
  • 10
    • 84942156915 scopus 로고    scopus 로고
    • Introduction to derivative-free optimization. SIAM, Philadelphia
    • Conn AR, Scheinberg K, Vicente LN (2009a) Introduction to derivative-free optimization. SIAM, Philadelphia
    • (2009) Vicente LN
    • Conn, A.R.1    Scheinberg, K.2
  • 11
    • 70450200040 scopus 로고    scopus 로고
    • Global convergence of general derivative-free trust-region algorithms to first and second order critical points
    • Conn AR, Scheinberg K, Vicente LN (2009b) Global convergence of general derivative-free trust-region algorithms to first and second order critical points. SIAM J Optim 20:387–415
    • (2009) SIAM J Optim , vol.20 , pp. 387-415
    • Conn, A.R.1    Scheinberg, K.2    Vicente, L.N.3
  • 12
    • 84880051566 scopus 로고    scopus 로고
    • Global convergence of trust-region algorithms for convex constrained minimization without derivatives
    • Conejo PD, Karas EW, Pedroso LG, Ribeiro AA, Sachine M (2013) Global convergence of trust-region algorithms for convex constrained minimization without derivatives. Appl Math Comput 20:324–330
    • (2013) Appl Math Comput , vol.20 , pp. 324-330
    • Conejo, P.D.1    Karas, E.W.2    Pedroso, L.G.3    Ribeiro, A.A.4    Sachine, M.5
  • 13
    • 84975841504 scopus 로고    scopus 로고
    • A trust-region derivative-free algorithm for constrained optimization. Technical Report. Department of Mathematics
    • Conejo PD, Karas EW, Pedroso LG (2014) A trust-region derivative-free algorithm for constrained optimization. Technical Report. Department of Mathematics, Federal University of Paraná
    • (2014) Federal University of Paraná
    • Conejo, P.D.1    Karas, E.W.2    Pedroso, L.G.3
  • 14
    • 0000143851 scopus 로고
    • A smooth method for the finite minimax problem
    • Di Pillo G, Grippo L, Lucidi S (1993) A smooth method for the finite minimax problem. Math Program 60:187–214
    • (1993) Math Program , vol.60 , pp. 187-214
    • Di Pillo, G.1    Grippo, L.2    Lucidi, S.3
  • 15
    • 79953678396 scopus 로고    scopus 로고
    • Derivative-free methods for nonlinear programming with general lower-level constraints
    • Diniz-Ehrhardt MA, Martínez JM, Pedroso LG (2011) Derivative-free methods for nonlinear programming with general lower-level constraints. Comput Appl Math 30:19–52
    • (2011) Comput Appl Math , vol.30 , pp. 19-52
    • Diniz-Ehrhardt, M.A.1    Martínez, J.M.2    Pedroso, L.G.3
  • 16
    • 0001963239 scopus 로고
    • A model algorithm for composite nondifferentiable optimization problems
    • Fletcher R (1982a) A model algorithm for composite nondifferentiable optimization problems. Math Program 17:67–76
    • (1982) Math Program , vol.17 , pp. 67-76
    • Fletcher, R.1
  • 17
    • 0040133819 scopus 로고
    • Second order correction for nondifferentiable optimization
    • Watson GA, (ed), Springer, Berlin
    • Fletcher R (1982b) Second order correction for nondifferentiable optimization. In: Watson GA (ed) Numerical analysis. Springer, Berlin, pp 85–114
    • (1982) Numerical analysis , pp. 85-114
    • Fletcher, R.1
  • 18
    • 84880321255 scopus 로고    scopus 로고
    • Smoothing and worst-case complexity for direct-search methods in nonsmooth optimization
    • Garmanjani R, Vicente LN (2013) Smoothing and worst-case complexity for direct-search methods in nonsmooth optimization. IMA J Numer Anal 33:1008–1028
    • (2013) IMA J Numer Anal , vol.33 , pp. 1008-1028
    • Garmanjani, R.1    Vicente, L.N.2
  • 19
    • 84937967811 scopus 로고    scopus 로고
    • On the convergence and worst-case complexity of trust-region and regularization methods for unconstrained optimization
    • Grapiglia GN, Yuan J, Yuan Y (2014) On the convergence and worst-case complexity of trust-region and regularization methods for unconstrained optimization. Math Prog. doi:10.1007/s10107-014-0794-9
    • (2014) Math Prog.
    • Grapiglia, G.N.1    Yuan, J.2    Yuan, Y.3
  • 20
    • 84968466715 scopus 로고
    • A quasi-Newton method with no derivatives
    • Greenstadt J (1972) A quasi-Newton method with no derivatives. Math Comput 26:145–166
    • (1972) Math Comput , vol.26 , pp. 145-166
    • Greenstadt, J.1
  • 21
    • 84938447945 scopus 로고
    • Direct search solution of numerical and statistical problems
    • Hooke R, Jeeves TA (1961) Direct search solution of numerical and statistical problems. J Assoc Comput Mach 8:212–229
    • (1961) J Assoc Comput Mach , vol.8 , pp. 212-229
    • Hooke, R.1    Jeeves, T.A.2
  • 22
    • 0001547779 scopus 로고
    • The cutting plane method for solving convex programs
    • Kelly JE (1960) The cutting plane method for solving convex programs. J SIAM 8:703–712
    • (1960) J SIAM , vol.8 , pp. 703-712
    • Kelly, J.E.1
  • 23
    • 79952528772 scopus 로고    scopus 로고
    • Algorithm 909: NOMAD: Nonlinear optimization with the MADS algorithm
    • Le Digabel S (2011) Algorithm 909: NOMAD: Nonlinear optimization with the MADS algorithm. ACM Trans Math Softw 37:41:1–44:15
    • (2011) ACM Trans Math Softw 37 , vol.1-44 , Issue.15 , pp. 41
    • Le Digabel, S.1
  • 24
    • 0001796318 scopus 로고
    • Bundle methods in nonsmooth optimization
    • Lemaréchal C, Mifflin R, (eds), Pergamon, Oxford
    • Lemaréchal C (1978) Bundle methods in nonsmooth optimization. In: Lemaréchal C, Mifflin R (eds) Nonsmooth optimization. Pergamon, Oxford, pp 79–102
    • (1978) Nonsmooth optimization , pp. 79-102
    • Lemaréchal, C.1
  • 25
    • 84975803400 scopus 로고    scopus 로고
    • Test problems for nonsmooth unconstrained and linearly constrained optimization. Technical Report 198
    • Luksǎn L, Vlček J (2000) Test problems for nonsmooth unconstrained and linearly constrained optimization. Technical Report 198, Academy of Sciences of the Czech Republic
    • (2000) Academy of Sciences of the Czech Republic
    • Luksǎn, L.1    Vlček, J.2
  • 26
    • 0016647171 scopus 로고
    • Minimax solution of non-linear equations without calculating derivatives
    • Madsen K (1975) Minimax solution of non-linear equations without calculating derivatives. Math Program Study 3:110–126
    • (1975) Math Program Study , vol.3 , pp. 110-126
    • Madsen, K.1
  • 27
    • 84879692890 scopus 로고    scopus 로고
    • Derivative-free constrained optimization in thin domains
    • Martínez JM, Sobral FNC (2013) Derivative-free constrained optimization in thin domains. J Glob Optim 56:1217–1232
    • (2013) J Glob Optim , vol.56 , pp. 1217-1232
    • Martínez, J.M.1    Sobral, F.N.C.2
  • 28
    • 0016538991 scopus 로고
    • A superlinearly convergent algorithm for minimization without evaluating derivatives
    • Mifflin R (1975) A superlinearly convergent algorithm for minimization without evaluating derivatives. Math Program 9:100–117
    • (1975) Math Program , vol.9 , pp. 100-117
    • Mifflin, R.1
  • 29
    • 68949099095 scopus 로고    scopus 로고
    • Benchmarking derivative-free optimization algorithms
    • Moré JJ, Wild SM (2009) Benchmarking derivative-free optimization algorithms. SIAM J Optim 20:172–191
    • (2009) SIAM J Optim , vol.20 , pp. 172-191
    • Moré, J.J.1    Wild, S.M.2
  • 30
    • 0000238336 scopus 로고
    • A simplex method for function minimization
    • Nelder JA, Mead R (1965) A simplex method for function minimization. Comput J 7:308–313
    • (1965) Comput J , vol.7 , pp. 308-313
    • Nelder, J.A.1    Mead, R.2
  • 31
    • 84860610528 scopus 로고    scopus 로고
    • Random gradient-free minimization of convex functions. Technical Report 2011/1
    • Nesterov Y (2011) Random gradient-free minimization of convex functions. Technical Report 2011/1, CORE
    • (2011) CORE
    • Nesterov, Y.1
  • 32
    • 5644246442 scopus 로고
    • General algorithm for discrete nonlinear approximation calculations
    • Chui CK, Schumaker LL, Ward LD, (eds), Academic Press, New York
    • Powell MJD (1983) General algorithm for discrete nonlinear approximation calculations. In: Chui CK, Schumaker LL, Ward LD (eds) Approximation theory IV. Academic Press, New York, pp 187–218
    • (1983) Approximation theory IV , pp. 187-218
    • Powell, M.J.D.1
  • 33
    • 0021482384 scopus 로고
    • On the global convergence of trust region algorithms for unconstrained minimization
    • Powell MJD (1984) On the global convergence of trust region algorithms for unconstrained minimization. Math Program 29:297–303
    • (1984) Math Program , vol.29 , pp. 297-303
    • Powell, M.J.D.1
  • 34
    • 33846538819 scopus 로고    scopus 로고
    • The NEWUOA software for unconstrained optimization without derivatives
    • Pillo G, Roma M, (eds), Springer, New York
    • Powell MJD (2006) The NEWUOA software for unconstrained optimization without derivatives. In: Di Pillo G, Roma M (eds) Large nonlinear optimization. Springer, New York, pp 255–297
    • (2006) Large nonlinear optimization , pp. 255-297
    • Powell, M.J.D.1
  • 35
    • 0028480086 scopus 로고
    • A trust region algorithm for minimization of locally Lipschitzian functions
    • Qi L, Sun J (1994) A trust region algorithm for minimization of locally Lipschitzian functions. Math Program 66:25–43
    • (1994) Math Program , vol.66 , pp. 25-43
    • Qi, L.1    Sun, J.2
  • 36
    • 79251516126 scopus 로고    scopus 로고
    • Self-correcting geometry in model-based algorithms for derivative-free unconstrained optimization
    • Scheinberg K, Toint PhL (2010) Self-correcting geometry in model-based algorithms for derivative-free unconstrained optimization. SIAM J Optim 20:3512–3532
    • (2010) SIAM J Optim , vol.20 , pp. 3512-3532
    • Scheinberg, K.1    Toint, P.L.2
  • 37
    • 0003326338 scopus 로고
    • Subgradient methods: a survey of the Soviet research
    • Lemaréchal C, Mifflin R, (eds), Pergamon, Oxford
    • Shor NZ (1978) Subgradient methods: a survey of the Soviet research. In: Lemaréchal C, Mifflin R (eds) Nonsmooth optimization. Pergamon, Oxford
    • (1978) Nonsmooth optimization
    • Shor, N.Z.1
  • 38
    • 0002912764 scopus 로고
    • A modification of Davidon’s minimization method to accept difference approximations of derivatives
    • Stewart GW (1967) A modification of Davidon’s minimization method to accept difference approximations of derivatives. J Assoc Comput Mach 14:72–83
    • (1967) J Assoc Comput Mach , vol.14 , pp. 72-83
    • Stewart, G.W.1
  • 40
    • 0001406729 scopus 로고
    • Function minimization by interpolation in a data table
    • Winfield D (1973) Function minimization by interpolation in a data table. J Inst Math Appl 12:339–347
    • (1973) J Inst Math Appl , vol.12 , pp. 339-347
    • Winfield, D.1
  • 41
    • 0022010767 scopus 로고
    • Conditions for convergence of trust region algorithms for nonsmooth optimization
    • Yuan Y (1985a) Conditions for convergence of trust region algorithms for nonsmooth optimization. Math Program 31:220–228
    • (1985) Math Program , vol.31 , pp. 220-228
    • Yuan, Y.1
  • 42
    • 0022028162 scopus 로고
    • On the superlinear convergence of a trust region algorithm for nonsmooth optimization
    • Yuan Y (1985b) On the superlinear convergence of a trust region algorithm for nonsmooth optimization. Math Program 31:269–285
    • (1985) Math Program , vol.31 , pp. 269-285
    • Yuan, Y.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.