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Volumn 12, Issue 4, 2002, Pages 1048-1074

An interior point constrained trust region method for a special class of nonlinear semidefinite programming problems

Author keywords

Interior point method; Nonconvex programming; Nonlinear semidefinite program; Optimal control; Primal method; Static output feedback; Trust region method

Indexed keywords


EID: 0036434767     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1052623400375865     Document Type: Article
Times cited : (69)

References (37)
  • 1
    • 0003169116 scopus 로고
    • Interior point methods in semidefinite programming with applications to combinatorial optimization
    • F. Alizadeh, Interior point methods in semidefinite programming with applications to combinatorial optimization, SIAM J. Optim., 5 (1995), pp. 13-51.
    • (1995) SIAM J. Optim. , vol.5 , pp. 13-51
    • Alizadeh, F.1
  • 2
    • 0032327612 scopus 로고    scopus 로고
    • Primal-dual interior-point methods for semidefinite programming: Convergence rates, stability and numerical results
    • F. Alizadeh, J.-P.A. Haeberly, and M.L. Overton, Primal-dual interior-point methods for semidefinite programming: Convergence rates, stability and numerical results, SIAM J. Optim., 8 (1998), pp. 746-768.
    • (1998) SIAM J. Optim. , vol.8 , pp. 746-768
    • Alizadeh, F.1    Haeberly, J.-P.A.2    Overton, M.L.3
  • 6
    • 0001130234 scopus 로고    scopus 로고
    • A trust region method based on interior point techniques for nonlinear programming
    • R.H. Byrd, J.C. Gilbert, and J. Nocedal, A trust region method based on interior point techniques for nonlinear programming, Math. Program., 89 (2000), pp. 149-185.
    • (2000) Math. Program. , vol.89 , pp. 149-185
    • Byrd, R.H.1    Gilbert, J.C.2    Nocedal, J.3
  • 7
    • 0030106747 scopus 로고    scopus 로고
    • ∞ design with pole placement constraints: An LMI approach
    • ∞ design with pole placement constraints: An LMI approach, IEEE Trans. Automat. Control, 41 (1996), pp. 358-367.
    • (1996) IEEE Trans. Automat. Control , vol.41 , pp. 358-367
    • Chilali, M.1    Gahinet, P.2
  • 8
    • 0000317378 scopus 로고    scopus 로고
    • A primal-dual trust-region algorithm for non-convex nonlinear programming
    • A.R. Conn, N.I.M. Gould, D. Orban, and Ph.L. Toint, A primal-dual trust-region algorithm for non-convex nonlinear programming, Math. Program., 87 (2000), pp. 215-249.
    • (2000) Math. Program. , vol.87 , pp. 215-249
    • Conn, A.R.1    Gould, N.I.M.2    Orban, D.3    Toint, Ph.L.4
  • 10
    • 0031542597 scopus 로고    scopus 로고
    • A global convergence theory for general trust-region-based algorithms for equality constrained optimization
    • J.E. Dennis, Jr., M. El-Alem, and M.C. Maciel, A global convergence theory for general trust-region-based algorithms for equality constrained optimization, SIAM J. Optim., 7 (1997), pp. 177-207.
    • (1997) SIAM J. Optim. , vol.7 , pp. 177-207
    • Dennis J.E., Jr.1    El-Alem, M.2    Maciel, M.C.3
  • 11
    • 0032165036 scopus 로고    scopus 로고
    • Trust-region interior-point SQP algorithms for a class of nonlinear programming problems
    • J.E. Dennis, M. Heinkenschloss, and L.N. Vicente, Trust-region interior-point SQP algorithms for a class of nonlinear programming problems, SIAM J. Control Optim., 36 (1998), pp. 1750-1794.
    • (1998) SIAM J. Control Optim. , vol.36 , pp. 1750-1794
    • Dennis, J.E.1    Heinkenschloss, M.2    Vicente, L.N.3
  • 12
    • 0026104343 scopus 로고
    • A global convergence theory for the Celis-Dennis-Tapia trust-region algorithm for constrained optimization
    • M. El-Alem, A global convergence theory for the Celis-Dennis-Tapia trust-region algorithm for constrained optimization, SIAM J. Numar. Anal., 28 (1991), pp. 266-290.
    • (1991) SIAM J. Numar. Anal. , vol.28 , pp. 266-290
    • El-Alem, M.1
  • 13
    • 0030541525 scopus 로고    scopus 로고
    • On the formulation and theory of Newton interior-point method for nonlinear programming
    • A.S. El-Bakry, R.A. Tapia, T. Tsuchiya, and Y. Zhang, On the formulation and theory of Newton interior-point method for nonlinear programming, J. Optim. Theory Appl., 89 (1996), pp. 507-541.
    • (1996) J. Optim. Theory Appl. , vol.89 , pp. 507-541
    • El-Bakry, A.S.1    Tapia, R.A.2    Tsuchiya, T.3    Zhang, Y.4
  • 14
    • 0032358968 scopus 로고    scopus 로고
    • Primal-dual interior methods for nonconvex nonlinear programming
    • A. Forsgren and Ph.E. Gill, Primal-dual interior methods for nonconvex nonlinear programming, SIAM J. Optim., 8 (1998), pp. 1132-1152.
    • (1998) SIAM J. Optim. , vol.8 , pp. 1132-1152
    • Forsgren, A.1    Gill, Ph.E.2
  • 15
    • 0002688960 scopus 로고    scopus 로고
    • A primal-dual interior point method for nonconvex nonlinear programming
    • Y. Yuan, ed., Kluwer Academic Publishers, Norwell, MA
    • D.M. Gay, M.L. Overton, and M.H. Wright, A primal-dual interior point method for nonconvex nonlinear programming, in Advances in Nonlinear Programming, Y. Yuan, ed., Kluwer Academic Publishers, Norwell, MA, 1998, pp. 31-56.
    • (1998) Advances in Nonlinear Programming , pp. 31-56
    • Gay, D.M.1    Overton, M.L.2    Wright, M.H.3
  • 17
    • 0003279816 scopus 로고
    • Multivariable feedback: A quasi-classical approach
    • Springer-Verlag, Berlin, Heidelberg, New York
    • Y.S. Hung and A.G.J. MacFarlane, Multivariable Feedback: A Quasi-Classical Approach, Lecture Notes in Control and Inform. Sci. 40, Springer-Verlag, Berlin, Heidelberg, New York, 1982.
    • (1982) Lecture Notes in Control and Inform. Sci. , vol.40
    • Hung, Y.S.1    MacFarlane, A.G.J.2
  • 21
    • 0001427240 scopus 로고
    • A prospective look at SQP methods for semilinear parabolic control problems
    • Optimal Control of Partial Differential Equations, K.-H. Hoffmann and W. Krabs, eds., Springer
    • F.-S. Kupfer and E.W. Sachs, A prospective look at SQP methods for semilinear parabolic control problems, in Optimal Control of Partial Differential Equations, K.-H. Hoffmann and W. Krabs, eds., Lecture Notes in Control and Inform. Sci. 149, Springer, 1991, pp. 143-157.
    • (1991) Lecture Notes in Control and Inform. Sci. , vol.149 , pp. 143-157
    • Kupfer, F.-S.1    Sachs, E.W.2
  • 26
    • 0035661982 scopus 로고    scopus 로고
    • ∞ output feedback controllers
    • ∞ output feedback controllers, SIAM J. Control Optim., 39 (2001), pp. 1711-1735.
    • (2001) SIAM J. Control Optim. , vol.39 , pp. 1711-1735
    • Leibfritz, F.1
  • 29
    • 0011572607 scopus 로고    scopus 로고
    • Ph.D. thesis, Department of Mathematics, Faculty of Science, Alexandria University, Alexandria, Egypt
    • El-S.M.E. Mostafa, Efficient Trust-Region Methods in Numerical Optimization, Ph.D. thesis, Department of Mathematics, Faculty of Science, Alexandria University, Alexandria, Egypt, 2000.
    • (2000) Efficient Trust-Region Methods in Numerical Optimization
    • Mostafa, E.-S.M.E.1
  • 30
    • 0003254248 scopus 로고
    • Interior-point polynomial algorithms in convex programming
    • Siam, Philadelphia
    • Y. Nesterov and A. Nemirovskii, Interior-Point Polynomial Algorithms in Convex Programming, SIAM Stud. Appl. Math. 13, SIAM, Philadelphia, 1994.
    • (1994) Siam Stud. Appl. Math. , vol.13
    • Nesterov, Y.1    Nemirovskii, A.2
  • 31
    • 0031285915 scopus 로고    scopus 로고
    • Computational design of optimal output feedback controllers
    • T. Rautert and E.W. Sachs, Computational design of optimal output feedback controllers, SIAM J. Optim., 7 (1997), pp. 837-852.
    • (1997) SIAM J. Optim. , vol.7 , pp. 837-852
    • Rautert, T.1    Sachs, E.W.2
  • 32
    • 0029425729 scopus 로고
    • Max-min eigcnvalue problems, primal-dual interior point algorithms, and trust region subproblems
    • F. Rendel, R.J. Vanderbei, and H. Wolkowicz, Max-min eigcnvalue problems, primal-dual interior point algorithms, and trust region subproblems, Optim. Methods Softw., 5 (1995), pp. 1-16.
    • (1995) Optim. Methods Softw. , vol.5 , pp. 1-16
    • Rendel, F.1    Vanderbei, R.J.2    Wolkowicz, H.3
  • 33
    • 0000305846 scopus 로고
    • The conjugate gradient method and trust regions in large scale optimization
    • T. Steihaug, The conjugate gradient method and trust regions in large scale optimization, SIAM J. Numer. Anal., 20 (1983), pp. 626-637.
    • (1983) SIAM J. Numer. Anal. , vol.20 , pp. 626-637
    • Steihaug, T.1
  • 34
    • 0023404426 scopus 로고
    • Newton's method for solving parametric linear quadratic control problems
    • H.T. Toivonen and P.M. Mäkilä, Newton's method for solving parametric linear quadratic control problems, Internat. J. Control, 46 (1987), pp. 897-911.
    • (1987) Internat. J. Control , vol.46 , pp. 897-911
    • Toivonen, H.T.1    Mäkilä, P.M.2
  • 35
    • 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
  • 36
    • 0000287204 scopus 로고    scopus 로고
    • An interior point algorithm for nonconvex nonlinear programming
    • R.J. Vanderbei and D.F. Shanno, An interior point algorithm for nonconvex nonlinear programming, Comput. Optim. Appl., 13 (1999), pp. 231-252.
    • (1999) Comput. Optim. Appl. , vol.13 , pp. 231-252
    • Vanderbei, R.J.1    Shanno, D.F.2
  • 37
    • 84963294959 scopus 로고
    • A trust-region typed dogleg method for nonlinear optimization
    • J. Zhang and D. Zhu, A trust-region typed dogleg method for nonlinear optimization, Optimization, 21 (1990), pp. 543-557.
    • (1990) Optimization , vol.21 , pp. 543-557
    • Zhang, J.1    Zhu, D.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.