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Volumn 64, Issue 1, 2006, Pages 55-77

On the S-procedure and some variants

Author keywords

Control theory; Robust optimization; S Lemma; S Procedure

Indexed keywords

CONTROL THEORY; MATHEMATICAL TECHNIQUES; OPTIMIZATION; ROBUSTNESS (CONTROL SYSTEMS);

EID: 33747194381     PISSN: 14322994     EISSN: 14325217     Source Type: Journal    
DOI: 10.1007/s00186-006-0070-8     Document Type: Article
Times cited : (100)

References (37)
  • 1
    • 84968518180 scopus 로고
    • A theorem on a mapping from a sphere to the circle and the simultaneous diagonalisation of two hermitian matrices
    • Au-Yeung YH (1969) A theorem on a mapping from a sphere to the circle and the simultaneous diagonalisation of two hermitian matrices. Proc Am Math Soc 20:545-548
    • (1969) Proc Am Math Soc , vol.20 , pp. 545-548
    • Au-Yeung, Y.H.1
  • 2
    • 0002825729 scopus 로고
    • A remark on the convexity and positive definiteness concerning hermitian matrices
    • Au-Yeung YH, Poon YT (1979) A remark on the convexity and positive definiteness concerning hermitian matrices. Southeast Asian Bull Math 3:85-92
    • (1979) Southeast Asian Bull Math , vol.3 , pp. 85-92
    • Au-Yeung, Y.H.1    Poon, Y.T.2
  • 3
    • 51249170448 scopus 로고
    • Problems of distance geometry and convex properties of quadratic maps
    • Barvinok AI (1995) Problems of distance geometry and convex properties of quadratic maps. Discrete Comput Geom 13:189-202
    • (1995) Discrete Comput Geom , vol.13 , pp. 189-202
    • Barvinok, A.I.1
  • 4
    • 14944360644 scopus 로고    scopus 로고
    • Conic and robust optimization
    • Israel Institute of Technology, Technion
    • Ben-Tal A (2002) Conic and robust optimization. Technical report, Israel Institute of Technology, Technion
    • (2002) Technical Report
    • Ben-Tal, A.1
  • 8
    • 0037797197 scopus 로고    scopus 로고
    • Robust solutions of uncertain quadratic and conic-quadratic problems
    • Ben-Tal A, Nemirovski A, Roos C (2002) Robust solutions of uncertain quadratic and conic-quadratic problems. SIAM J Optim 13:535-560
    • (2002) SIAM J Optim , vol.13 , pp. 535-560
    • Ben-Tal, A.1    Nemirovski, A.2    Roos, C.3
  • 10
    • 0010120775 scopus 로고
    • On the fields of values of a matrix
    • Brickman L (1961) On the fields of values of a matrix. Proc Am Math Soc 12:61-66
    • (1961) Proc Am Math Soc , vol.12 , pp. 61-66
    • Brickman, L.1
  • 11
    • 84966261323 scopus 로고
    • Linear systems of real quadratic forms
    • Calabi E (1964) Linear systems of real quadratic forms. Proc Am Math 15:844-846
    • (1964) Proc Am Math , vol.15 , pp. 844-846
    • Calabi, E.1
  • 13
    • 0037958862 scopus 로고
    • On the mapping of quadratic forms
    • Dines LL (1941) On the mapping of quadratic forms. Bull Am Math Soc 47:494-498
    • (1941) Bull Am Math Soc , vol.47 , pp. 494-498
    • Dines, L.L.1
  • 14
    • 84966260909 scopus 로고
    • On the mapping of n quadratic forms
    • Dines LL (1942) On the mapping of n quadratic forms. Bull Am Math Soc 48:467-471
    • (1942) Bull Am Math Soc , vol.48 , pp. 467-471
    • Dines, L.L.1
  • 15
    • 10344240568 scopus 로고
    • On linear combinations of quadratic forms
    • Dines LL (1943) On linear combinations of quadratic forms. Bull Am Math Soc 49:388-393
    • (1943) Bull Am Math Soc , vol.49 , pp. 388-393
    • Dines, L.L.1
  • 16
    • 0031536271 scopus 로고    scopus 로고
    • Robust solutions to least-squares problems with uncertain data
    • El-Ghaoui L, Lebret H (1997) Robust solutions to least-squares problems with uncertain data. SIAM J Matrix Anal Appl 18(4):1035-1064
    • (1997) SIAM J Matrix Anal Appl , vol.18 , Issue.4 , pp. 1035-1064
    • El-Ghaoui, L.1    Lebret, H.2
  • 17
    • 0032252302 scopus 로고    scopus 로고
    • Robust solutions to uncertain semidefinite programs
    • El-Ghaoui L, Oustry F, Lebret H (1998) Robust solutions to uncertain semidefinite programs. SIAM J Optim 9:33-52
    • (1998) SIAM J Optim , vol.9 , pp. 33-52
    • El-Ghaoui, L.1    Oustry, F.2    Lebret, H.3
  • 18
    • 0001641947 scopus 로고
    • Über das vorkommen definiter und semidefiniter formen in scharen quadratischer formen
    • Finsler P ( 1936/37) Über das vorkommen definiter und semidefiniter formen in scharen quadratischer formen. Comment Math Helv 9:188-192
    • (1936) Comment Math Helv , vol.9 , pp. 188-192
    • Finsler, P.1
  • 19
    • 10344221770 scopus 로고
    • Duality theorems for certain nonconvex extremum problems
    • Fradkov AL (1973) Duality theorems for certain nonconvex extremum problems. Siberian Math J 14:247-264
    • (1973) Siberian Math J , vol.14 , pp. 247-264
    • Fradkov, A.L.1
  • 20
    • 0000130163 scopus 로고
    • Der wertvorrat einer bilinearform
    • Hausdorff F (1919) Der wertvorrat einer bilinearform. Math Z 3:314-316
    • (1919) Math Z , vol.3 , pp. 314-316
    • Hausdorff, F.1
  • 21
    • 84966240889 scopus 로고
    • A theorem on quadratic forms and its application in the calculus of variations
    • Hestenes MR, McShane EJ (1940) A theorem on quadratic forms and its application in the calculus of variations. Trans Am Math Soc 40:501-512
    • (1940) Trans Am Math Soc , vol.40 , pp. 501-512
    • Hestenes, M.R.1    McShane, E.J.2
  • 22
    • 0141938582 scopus 로고    scopus 로고
    • Permanently going back and forth between the quadratic world and the convexity world in optimization
    • Hiriart-Urruty JB, Torki M (2002) Permanently going back and forth between the quadratic world and the convexity world in optimization. Appl Math Optim 45:169-184
    • (2002) Appl Math Optim , vol.45 , pp. 169-184
    • Hiriart-Urruty, J.B.1    Torki, M.2
  • 24
    • 33747164923 scopus 로고
    • A note on the maximum principle for elliptic differential equations
    • John F (1938) A note on the maximum principle for elliptic differential equations. Bull Am Math Soc 44:268-271
    • (1938) Bull Am Math Soc , vol.44 , pp. 268-271
    • John, F.1
  • 25
    • 0040253203 scopus 로고
    • Über eine klasse j-selbstadjungierter operatoren
    • Kühne R (1964) Über eine klasse j-selbstadjungierter operatoren. Math Ann 154:56-69
    • (1964) Math Ann , vol.154 , pp. 56-69
    • Kühne, R.1
  • 26
    • 33747151206 scopus 로고    scopus 로고
    • Multivariate nonnegative quadratic mappings
    • Chinese University of Hong-Kong
    • Luo Z-Q, Sturm J, Zhang S-Z (2003) Multivariate nonnegative quadratic mappings. Technical report, Chinese University of Hong-Kong
    • (2003) Technical Report
    • Luo, Z.-Q.1    Sturm, J.2    Zhang, S.-Z.3
  • 27
    • 0000075780 scopus 로고
    • On the theory of stability of control systems
    • Lur'e AI, Postnikov VN (1944) On the theory of stability of control systems (in Russian). Appl Math Mech 8(3)
    • (1944) Appl Math Mech , vol.8 , Issue.3
    • Lur'e, A.I.1    Postnikov, V.N.2
  • 28
    • 0001253761 scopus 로고
    • Power distribution inequalities in optimization and robustness of uncertain systems
    • Megretsky A, Treil S (1993) Power distribution inequalities in optimization and robustness of uncertain systems. Math Syst Estimation Control 3:301-319
    • (1993) Math Syst Estimation Control , vol.3 , pp. 301-319
    • Megretsky, A.1    Treil, S.2
  • 29
    • 0003878614 scopus 로고    scopus 로고
    • Five lectures on modern convex optimization
    • Israel Institute of Technology, Technion
    • Nemirovski A (2002) Five lectures on modern convex optimization. Technical report, Israel Institute of Technology, Technion
    • (2002) Technical Report
    • Nemirovski, A.1
  • 30
    • 0031285896 scopus 로고    scopus 로고
    • Optimality conditions for the minimization of a quadratic with two quadratic constraints
    • Peng JM, Yuan Y-X (1997) Optimality conditions for the minimization of a quadratic with two quadratic constraints. SIAM J Optim 7:579-594
    • (1997) SIAM J Optim , vol.7 , pp. 579-594
    • Peng, J.M.1    Yuan, Y.-X.2
  • 31
    • 0032259651 scopus 로고    scopus 로고
    • Convexity of quadratic transformations and its use in control and optimization
    • Polyak BT (1998) Convexity of quadratic transformations and its use in control and optimization. J Optim Theory Appl 99:553-583
    • (1998) J Optim Theory Appl , vol.99 , pp. 553-583
    • Polyak, B.T.1
  • 32
    • 21744437382 scopus 로고    scopus 로고
    • Generalized numerical ranges, joint positive definiteness and multiple eigenvalues
    • Poon YT (1997) Generalized numerical ranges, joint positive definiteness and multiple eigenvalues. Proc Am Math Soc 125:1625-1634
    • (1997) Proc Am Math Soc , vol.125 , pp. 1625-1634
    • Poon, Y.T.1
  • 33
    • 33747158961 scopus 로고
    • Positive-definite matrices
    • Shisha O (ed) Academic. New York
    • Taussky O (1967) Positive-definite matrices. In: Shisha O (ed) Inequalities. Academic. New York, pp 309-319
    • (1967) Inequalities , pp. 309-319
    • Taussky, O.1
  • 34
    • 34250972218 scopus 로고
    • Das algebraische analogen zu einem satze von fejér
    • Toeplitz O (1918) Das algebraische analogen zu einem satze von fejér. Math Z 2:187-197
    • (1918) Math Z , vol.2 , pp. 187-197
    • Toeplitz, O.1
  • 35
    • 0001175776 scopus 로고
    • A recurring theorem about pairs of quadratic forms and extension: A survey
    • Uhlig F (1979) A recurring theorem about pairs of quadratic forms and extension: a survey. Linear Algebra Appl 25:219-237
    • (1979) Linear Algebra Appl , vol.25 , pp. 219-237
    • Uhlig, F.1
  • 36
    • 0002182462 scopus 로고
    • The s-procedure in nonlinear control theory
    • in Russian, 1971, 62-77
    • Yakubovich VA (1971) The s-procedure in nonlinear control theory. Vestnik Leningr Univ 4: 73-93 in Russian, 1971, No.1, 62-77
    • (1971) Vestnik Leningr Univ , vol.4 , Issue.1 , pp. 73-93
    • Yakubovich, V.A.1
  • 37
    • 0002765829 scopus 로고
    • On a subproblem of trust region algorithms for constrained optimization
    • Yuan Y (1990) On a subproblem of trust region algorithms for constrained optimization. Math Program 47:53-63
    • (1990) Math Program , vol.47 , pp. 53-63
    • Yuan, Y.1


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