메뉴 건너뛰기




Volumn 15, Issue 1, 2005, Pages 303-318

A global algorithm for nonlinear semidefinite programming

Author keywords

Global convergence; Nonlinear semidefinite programming; Sequentially programming

Indexed keywords

ALGORITHMS; EIGENVALUES AND EIGENFUNCTIONS; FUNCTIONS; GLOBAL OPTIMIZATION; LAGRANGE MULTIPLIERS; LINEAR EQUATIONS; MATHEMATICAL MODELS; MATRIX ALGEBRA; PROBLEM SOLVING; SET THEORY; VECTORS;

EID: 14944366899     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1052623402417298     Document Type: Article
Times cited : (87)

References (26)
  • 1
    • 14944355272 scopus 로고    scopus 로고
    • A prototype primal-dual LMI-interior algorithm for nonconvex robust control problems
    • MIP, UMR 5640
    • P. APKARIAN, D. NOLL, AND D. TUAN, A Prototype Primal-Dual LMI-Interior Algorithm for Nonconvex Robust Control Problems, Technical report, 01-08, MIP, UMR 5640, http://mip.ups-tlse.fr/publi/publi.html (2001).
    • (2001) Technical Report , vol.1 , Issue.8
    • Apkarian, P.1    Noll, D.2    Tuan, D.3
  • 2
    • 0033434223 scopus 로고    scopus 로고
    • Second-order optimally conditions based on parabolic second-order tangent sets
    • J. F. BONNANS, R. COMINETTI, AND A. SHAPIRO, Second-order optimally conditions based on parabolic second-order tangent sets, SIAM J. Optim., 9 (1999), pp. 466-492.
    • (1999) SIAM J. Optim. , vol.9 , pp. 466-492
    • Bonnans, J.F.1    Cominetti, R.2    Shapiro, A.3
  • 6
    • 0001303990 scopus 로고
    • Metric regularity, tangent sets and second-order optimality conditions
    • R. COMINETTI, Metric regularity, tangent sets and second-order optimality conditions, Appl. Math. Optim., 21 (1990), pp. 265-287.
    • (1990) Appl. Math. Optim. , vol.21 , pp. 265-287
    • Cominetti, R.1
  • 7
    • 0021787163 scopus 로고
    • Directional derivatives of minimax functions
    • R. CORREA AND A. SEEGER, Directional derivatives of minimax functions, Nonlinear Anal., 9 (1985), pp. 13-22.
    • (1985) Nonlinear Anal. , vol.9 , pp. 13-22
    • Correa, R.1    Seeger, A.2
  • 8
    • 0035836297 scopus 로고    scopus 로고
    • An augmented Lagrangian method for a class of LMI-constrained problems in robust control theory
    • B. FARES, P. APKARIAN, AND D. NOLL, An augmented Lagrangian method for a class of LMI-Constrained problems in robust control theory, Int. J. Control, 74 (2001), pp. 348-360.
    • (2001) Int. J. Control , vol.74 , pp. 348-360
    • Fares, B.1    Apkarian, P.2    Noll, D.3
  • 9
    • 0036930053 scopus 로고    scopus 로고
    • Robust control via sequential semidefinite programming
    • B. FARES, D. NOLL, AND P. APKARIAN, Robust control via sequential semidefinite programming, SIAM J. Control Optim., 40 (2002), pp. 1791-1820.
    • (2002) SIAM J. Control Optim. , vol.40 , pp. 1791-1820
    • Fares, B.1    Noll, D.2    Apkarian, P.3
  • 11
    • 34250293137 scopus 로고
    • A globally convergent method for nonlinear programming
    • S. P. HAN, A globally convergent method for nonlinear programming, J. Optim. Theory Appl., 22 (1977), pp. 297-309.
    • (1977) J. Optim. Theory Appl. , vol.22 , pp. 297-309
    • Han, S.P.1
  • 13
    • 0004151494 scopus 로고
    • Cambridge University Press, Cambridge, UK
    • R. HORN AND C. JOHNSON, Matrix Analysis, Cambridge University Press, Cambridge, UK, 1985.
    • (1985) Matrix Analysis
    • Horn, R.1    Johnson, C.2
  • 14
    • 0017001951 scopus 로고
    • On the existence and nonexistence of Lagrange multipliers in Banach spaces
    • S. KURCYUSZ, On the existence and nonexistence of Lagrange multipliers in Banach spaces, J. Optim. Theory Appl., 20 (1976), pp. 81-110.
    • (1976) J. Optim. Theory Appl. , vol.20 , pp. 81-110
    • Kurcyusz, S.1
  • 15
  • 17
    • 0016962866 scopus 로고
    • First-order conditions for general nonlinear optimization
    • S. M. ROBINSON, First-order conditions for general nonlinear optimization, SIAM J. Appl. Math., 30 (1976), pp. 597-607.
    • (1976) SIAM J. Appl. Math. , vol.30 , pp. 597-607
    • Robinson, S.M.1
  • 18
    • 0016993914 scopus 로고
    • Stability theorems for systems of inequalities, part II: Differentiable nonlinear systems
    • S. M. ROBINSON, Stability theorems for systems of inequalities, Part II: Differentiable nonlinear systems, SIAM J. Numer. Anal., 13 (1976), pp. 497-513.
    • (1976) SIAM J. Numer. Anal. , vol.13 , pp. 497-513
    • Robinson, S.M.1
  • 19
    • 0020165423 scopus 로고
    • Generalized equations and their solutions, part II: Applications to nonlinear programming
    • S. M. ROBINSON, Generalized equations and their solutions, Part II: Applications to nonlinear programming, Math Programming Stud., 19 (1982), pp. 200-221.
    • (1982) Math Programming Stud. , vol.19 , pp. 200-221
    • Robinson, S.M.1
  • 21
    • 0031139858 scopus 로고    scopus 로고
    • First and second-order analysis of nonlinear semidefinite programs
    • A. SHAPIRO, First and second-order Analysis of nonlinear semidefinite programs, Math. Programming, 77 (1997), pp. 301-320.
    • (1997) Math. Programming , vol.77 , pp. 301-320
    • Shapiro, A.1
  • 22
    • 84976150915 scopus 로고
    • An inequality for the trace of the product of two symmetric matrices
    • C. M. THEOBALD, An inequality for the trace of the product of two symmetric matrices, Math. Proc. Cambridge Philos. Soc., 77 (1975), pp. 77-265.
    • (1975) Math. Proc. Cambridge Philos. Soc. , vol.77 , pp. 77-265
    • Theobald, C.M.1
  • 23
    • 0030106462 scopus 로고    scopus 로고
    • Semidefinite programming
    • L. VANDENBERGHE AND S. BOYD, Semidefinite programming, SIAM Rev., 38 (1996), pp. 49-95.
    • (1996) SIAM Rev. , vol.38 , pp. 49-95
    • Vandenberghe, L.1    Boyd, S.2
  • 24
    • 0000011340 scopus 로고
    • Some matrix inequalities and metrization of matrix-space
    • J. VON NEUMANN, Some matrix inequalities and metrization of matrix-space, Tomsk University Review, 1 (1937), pp. 286-300. In Collected Works, Vol. IV, Pergamon, Oxford, 1962, pp. 205-218.
    • (1937) Tomsk University Review , vol.1 , pp. 286-300
    • Von Neumann, J.1
  • 25
    • 0011328006 scopus 로고
    • Pergamon, Oxford
    • J. VON NEUMANN, Some matrix inequalities and metrization of matrix-space, Tomsk University Review, 1 (1937), pp. 286-300. In Collected Works, Vol. IV, Pergamon, Oxford, 1962, pp. 205-218.
    • (1962) Collected Works , vol.4 , pp. 205-218


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.