메뉴 건너뛰기




Volumn 4, Issue 3, 2008, Pages 571-604

A proximity control algorithm to minimize nonsmooth and nonconvex functions

Author keywords

Bundle methods; Global convergence; H synthesis; Nonconvex programming; Nonsmooth programming; Proximity control

Indexed keywords


EID: 80054936825     PISSN: 13489151     EISSN: 13498169     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (63)

References (33)
  • 1
    • 33847397990 scopus 로고    scopus 로고
    • Nonsmooth optimization for multidisk H1 synthesis
    • P. Apkarian and D. Noll, Nonsmooth optimization for multidisk H1 synthesis, European J. Control 12 (2006) 229-244.
    • (2006) European J. Control , vol.12 , pp. 229-244
    • Apkarian, P.1    Noll, D.2
  • 2
    • 31344446586 scopus 로고    scopus 로고
    • Controller design via nonsmooth multi-directional search
    • P. Apkarian and D. Noll, Controller design via nonsmooth multi-directional search, SIAM J. Control and Optim. 44 (2006) 1923-1949.
    • (2006) SIAM J. Control and Optim. , vol.44 , pp. 1923-1949
    • Apkarian, P.1    Noll, D.2
  • 3
    • 33749987037 scopus 로고    scopus 로고
    • IQC analysis and synthesis via nonsmooth optimization
    • P. Apkarian and D. Noll, IQC analysis and synthesis via nonsmooth optimization, Systems and Control Letters 55 (2006) 971-981.
    • (2006) Systems and Control Letters , vol.55 , pp. 971-981
    • Apkarian, P.1    Noll, D.2
  • 5
    • 34548067100 scopus 로고    scopus 로고
    • Second-order nonsmooth optimization of the H1 norm
    • V. Bompart, D. Noll and P. Apkarian, Second-order nonsmooth optimization of the H1 norm, Numerische Mathematik 107 (2007) 433-454.
    • (2007) Numerische Mathematik , vol.107 , pp. 433-454
    • Bompart, V.1    Noll, D.2    Apkarian, P.3
  • 7
    • 0025461046 scopus 로고
    • A regularity result for the singular values of a transfer matrix and a quadratically convergent algorithm for computing its L1-norm
    • S. Boyd and V. Balakrishnan, A regularity result for the singular values of a transfer matrix and a quadratically convergent algorithm for computing its L1-norm, Systems and Control Letters 15 (1990) 1-7.
    • (1990) Systems and Control Letters , vol.15 , pp. 1-7
    • Boyd, S.1    Balakrishnan, V.2
  • 8
    • 0003859933 scopus 로고
    • Canadian Math. Society Series, John Wiley & Sons, New York
    • F. Clarke, Optimization and Nonsmooth Analysis, Canadian Math. Society Series, John Wiley & Sons, New York, 1983.
    • (1983) Optimization and Nonsmooth Analysis
    • Clarke, F.1
  • 10
    • 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) 261-275.
    • (1993) Math. Program. , vol.62 , pp. 261-275
    • Correa, R.1    Lemaréchal, C.2
  • 12
    • 1542285805 scopus 로고    scopus 로고
    • A DC piecewise affine model and a bundling technique in nonconvex nonsmooth optimization
    • A. Fuduli, M. Gaudioso and G. Giallombardo, A DC piecewise affine model and a bundling technique in nonconvex nonsmooth optimization, Optimization Method and Software 19 (2004) 89-102.
    • (2004) Optimization Method and Software , vol.19 , pp. 89-102
    • Fuduli, A.1    Gaudioso, M.2    Giallombardo, G.3
  • 13
    • 4043148628 scopus 로고    scopus 로고
    • Minimizing nonconvex nonsmooth functions via cutting planes and proximity control
    • A. Fuduli, M. Gaudioso and G. Giallombardo, Minimizing nonconvex nonsmooth functions via cutting planes and proximity control, SIAM J. Optim. 14 (2004) 743-756.
    • (2004) SIAM J. Optim. , vol.14 , pp. 743-756
    • Fuduli, A.1    Gaudioso, M.2    Giallombardo, G.3
  • 14
    • 48449090961 scopus 로고    scopus 로고
    • Computing proximal points of nonconvex functions
    • Series B. Published electronically may
    • W.L. Hare and C. Sagastizábal, Computing proximal points of nonconvex functions, Math. Program. Series B. Published electronically may 2007.
    • (2007) Math. Program.
    • Hare, W.L.1    Sagastizábal, C.2
  • 16
    • 0025208765 scopus 로고
    • Proximity control in bundle methods for convex nondifferentiable optimization
    • K.C. Kiwiel, Proximity control in bundle methods for convex nondifferentiable optimization, Math. Program. 46 (1990) 105-122.
    • (1990) Math. Program. , vol.46 , pp. 105-122
    • Kiwiel, K.C.1
  • 18
    • 0020912156 scopus 로고
    • An aggregate subgradient method for nonsmooth convex minimization
    • K.C. Kiwiel, An aggregate subgradient method for nonsmooth convex minimization, Math. Program. 27 (1983) 320-341.
    • (1983) Math. Program. , vol.27 , pp. 320-341
    • Kiwiel, K.C.1
  • 21
    • 77957820648 scopus 로고
    • Chapter VII in: Handbooks in Operations Research and Management Sciences
    • C. Lemaréchal, Nondifferentiable Optimization. Chapter VII in: Handbooks in Operations Research and Management Sciences, vol. 1, 1989.
    • (1989) Nondifferentiable Optimization , vol.1
    • Lemaréchal, C.1
  • 23
    • 0002450587 scopus 로고    scopus 로고
    • A bundle-Newton method for nonsmooth unconstrained minimization
    • L. Lukšan and J. Vlček, A bundle-Newton method for nonsmooth unconstrained minimization, Math. Program. 83 (1998) 373-391.
    • (1998) Math. Program. , vol.83 , pp. 373-391
    • Lukšan, L.1    Vlček, J.2
  • 24
    • 27244452234 scopus 로고    scopus 로고
    • Spectral bundle method for nonconvex maximum eigenvalue functions: First-order methods
    • Series B
    • D. Noll and P. Apkarian, Spectral bundle method for nonconvex maximum eigenvalue functions: first-order methods, Math. Program. Series B, 104 (2005) 701-727.
    • (2005) Math. Program. , vol.104 , pp. 701-727
    • Noll, D.1    Apkarian, P.2
  • 25
    • 27244457351 scopus 로고    scopus 로고
    • Spectral bundle method for nonconvex maximum eigenvalue functions: Second-order methods
    • Series B
    • D. Noll and P. Apkarian, Spectral bundle method for nonconvex maximum eigenvalue functions: second-order methods, Math. Program. Series B, 104 (2005) 729-747.
    • (2005) Math. Program. , vol.104 , pp. 729-747
    • Noll, D.1    Apkarian, P.2
  • 26
    • 0023314734 scopus 로고
    • On the mathematical foundations of nondifferentiable optimization in engineering design
    • E. Polak, On the mathematical foundations of nondifferentiable optimization in engineering design, SIAM Review 29 (1987) 21-89.
    • (1987) SIAM Review , vol.29 , pp. 21-89
    • Polak, E.1
  • 28
    • 0003207873 scopus 로고
    • Eine Kombination von Bundle-und Trust-Region-Verfahren zur Lösung nicht-differenzierbarer Optimierungsprobleme
    • Heft 30, Bayreuth
    • H. Schramm, Eine Kombination von Bundle-und Trust-Region-Verfahren zur Lösung nicht-differenzierbarer Optimierungsprobleme. Bayreuther Mathematische Schriften, Heft 30, Bayreuth 1989.
    • (1989) Bayreuther Mathematische Schriften
    • Schramm, H.1
  • 29
    • 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) 121-152.
    • (1992) SIAM J. Optim. , vol.2 , pp. 121-152
    • Schramm, H.1    Zowe, J.2
  • 31
    • 0001219945 scopus 로고
    • Indefinite trust region programs and nonsymmetric eigenvalue perturbations
    • R.J. Stern and H. Wolkowicz, Indefinite trust region programs and nonsymmetric eigenvalue perturbations, SIAM J. Optim. 5 (1995) 286-313.
    • (1995) SIAM J. Optim. , vol.5 , pp. 286-313
    • Stern, R.J.1    Wolkowicz, H.2
  • 32
    • 0016621235 scopus 로고
    • A method of conjugate subgradients for minimizing nondifferentiable functions
    • in, M.L. Balinski, P. Wolfe (eds.), Math. Programming Studies, North-Holland
    • P. Wolfe, A method of conjugate subgradients for minimizing nondifferentiable functions, in Nondifferentiable Optimization, M.L. Balinski, P. Wolfe (eds.), Math. Programming Studies, vol. 3. North-Holland, 1975, pp. 145-173.
    • (1975) Nondifferentiable Optimization , vol.3 , pp. 117-145
    • Wolfe, P.1
  • 33
    • 0041970000 scopus 로고
    • The BT-Algorithm for minimizing a nonsmooth functional subject to linear constraints
    • in, F. H. Clarke, V. F. Demyanov, F. Gianessi (eds.), Plenum Press
    • J. Zowe, The BT-Algorithm for minimizing a nonsmooth functional subject to linear constraints, in Nonsmooth Optimization and Related Topics, F. H. Clarke, V. F. Demyanov, F. Gianessi (eds.), Plenum Press, 1989.
    • (1989) Nonsmooth Optimization and Related Topics
    • Zowe, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.