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Volumn 7, Issue 3, 1997, Pages 579-594

Optimality conditions for the minimization of a quadratic with two quadratic constraints

Author keywords

Constrained optimization; Global minimizer; Quadratic constraint; Subproblem; Trust region method

Indexed keywords


EID: 0031285896     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1052623494261520     Document Type: Article
Times cited : (89)

References (17)
  • 1
    • 0002336672 scopus 로고
    • A trust region strategy for nonlinear equality constrained optimization
    • P. T. Boggs, R. H. Byrd, and R. B. Schnabel, eds., SIAM, Philadelphia, PA
    • M. R. CELIS, J. E. DENNIS, JR., AND R. A. TAPIA, A trust region strategy for nonlinear equality constrained optimization, in Numerical Optimization, P. T. Boggs, R. H. Byrd, and R. B. Schnabel, eds., SIAM, Philadelphia, PA, 1985, pp. 71-82.
    • (1985) Numerical Optimization , pp. 71-82
    • Celis, M.R.1    Dennis J.E., Jr.2    Tapia, R.A.3
  • 4
    • 0000955796 scopus 로고
    • Computing optimal locally constrained steps
    • D. M. GAY, Computing optimal locally constrained steps, SIAM J. Sci. Statist. Comput., 2 (1981), pp. 186-197.
    • (1981) SIAM J. Sci. Statist. Comput. , vol.2 , pp. 186-197
    • Gay, D.M.1
  • 6
    • 84966240889 scopus 로고
    • A theorem on quadratic forms and its application in the calculus of variations
    • M. R. HESTENES AND E. J. MCSHANE, A theorem on quadratic forms and its application in the calculus of variations, Trans. Amer. Math. Soc., 40 (1940), pp. 501-512.
    • (1940) Trans. Amer. Math. Soc. , vol.40 , pp. 501-512
    • Hestenes, M.R.1    McShane, E.J.2
  • 7
    • 0000442245 scopus 로고
    • Local minimizers of quadratic functions on Euclidean balls and spheres
    • J. M. MARTÍNEZ, Local minimizers of quadratic functions on Euclidean balls and spheres, SIAM J. Optim., 4 (1994), pp. 159-176.
    • (1994) SIAM J. Optim. , vol.4 , pp. 159-176
    • Martínez, J.M.1
  • 9
    • 0027901827 scopus 로고
    • Generalization of the trust region problem
    • J. J. MORÉ, Generalization of the trust region problem, Optim. Methods Software, 2 (1993), pp. 189-209.
    • (1993) Optim. Methods Software , vol.2 , pp. 189-209
    • Moré, J.J.1
  • 11
    • 0025540157 scopus 로고
    • A trust region algorithm for equality constrained optimization
    • M. J. D. POWELL AND Y. YUAN, A trust region algorithm for equality constrained optimization, Math. Programming, 49 (1991), pp. 189-211.
    • (1991) Math. Programming , vol.49 , pp. 189-211
    • Powell, M.J.D.1    Yuan, Y.2
  • 12
    • 0001382978 scopus 로고
    • Newton's method with a model trust region modification
    • D. C. SORENSEN, Newton's method with a model trust region modification, SIAM J. Numer. Anal., 19 (1982), pp. 409-426.
    • (1982) SIAM J. Numer. Anal. , vol.19 , pp. 409-426
    • Sorensen, D.C.1
  • 14
    • 0001175776 scopus 로고
    • A recurring theorem about pairs of quadratic forms and extensions: A survey
    • F. UHLIG, A recurring theorem about pairs of quadratic forms and extensions: A survey, Linear Algebra Appl., 25 (1979), pp. 219-237.
    • (1979) Linear Algebra Appl. , vol.25 , pp. 219-237
    • Uhlig, F.1
  • 15
    • 0002765829 scopus 로고
    • On a subproblem of trust region algorithms for constrained optimization
    • Y. YUAN, On a subproblem of trust region algorithms for constrained optimization, Math. Programming, 47 (1990), pp. 53-63.
    • (1990) Math. Programming , vol.47 , pp. 53-63
    • Yuan, Y.1
  • 16
    • 0001321667 scopus 로고
    • A dual algorithm for minimizing a quadratic function with two quadratic constraints
    • Y. YUAN, A dual algorithm for minimizing a quadratic function with two quadratic constraints, J. Comput. Math., 9 (1991), pp. 348-359.
    • (1991) J. Comput. Math. , vol.9 , pp. 348-359
    • Yuan, Y.1
  • 17
    • 0027113508 scopus 로고
    • Computing a Celis-Dennis-Tapia trust-region step for equality constrained optimization
    • Y. ZHANG, Computing a Celis-Dennis-Tapia trust-region step for equality constrained optimization, Math. Programming, 55 (1992), pp. 109-124.
    • (1992) Math. Programming , vol.55 , pp. 109-124
    • Zhang, Y.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.